SweetStudy (HomeworkMarket.com)
  • chat0

Basic Fractions Notes for Hp.pdf

Is there anything else you׳d like to ask?
Our top-rated tutors can help you.

Click here to post a question
Related Documents
1 / 213100%
Basic Fractions Notes
Math Instructor
July 23, 2024
1 Introduction
Fractions represent parts of a whole or a ratio between two numbers. Under-
standing fractions is essential for many areas of mathematics and real-world
applications.
2 Definition
A fraction is written as a
b, where:
•ais the numerator, which indicates how many parts are considered.
•bis the denominator, which indicates the total number of equal parts.
For example, in the fraction 3
4, 3 is the numerator and 4 is the denominator.
3 Types of Fractions
•Proper Fractions: The numerator is less than the denominator (e.g.,
2
5).
•Improper Fractions: The numerator is greater than or equal to the
denominator (e.g., 7
4).
•Mixed Numbers: A combination of a whole number and a proper
fraction (e.g., 13
4).
1
4 Operations with Fractions
4.1 Addition and Subtraction
To add or subtract fractions:
1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the com-
mon denominator.
3. Add or subtract the numerators.
4. Write the result over the common denominator and simplify
if possible.
4.1.1 Example: Addition
1
4+2
5=5
20 +8
20 =13
20
4.1.2 Example: Subtraction
3
4−1
6=9
12 −2
12 =7
12
4.2 Multiplication
To multiply fractions:
1. Multiply the numerators together.
2. Multiply the denominators together.
3. Write the result as a fraction and simplify if possible.
4.2.1 Example
2
3×4
5=8
15
2
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
6.1.1 Example
7
4= 13
4
6.2 From Mixed Numbers to Improper Fractions
1. Multiply the whole number part by the denominator.
2. Add the result to the numerator.
3. Write this sum over the original denominator.
6.2.1 Example
12
3=5
3
7 Conclusion
Mastering fractions is a key part of mathematical literacy. Practice with
different operations and conversions will build a solid foundation for more
advanced math concepts.
4
4 Operations with Fractions
4.1 Addition and Subtraction
To add or subtract fractions:
1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the com-
mon denominator.
3. Add or subtract the numerators.
4. Write the result over the common denominator and simplify
if possible.
4.1.1 Example: Addition
1
4+2
5=5
20 +8
20 =13
20
4.1.2 Example: Subtraction
3
4−1
6=9
12 −2
12 =7
12
4.2 Multiplication
To multiply fractions:
1. Multiply the numerators together.
2. Multiply the denominators together.
3. Write the result as a fraction and simplify if possible.
4.2.1 Example
2
3×4
5=8
15
2
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
6.1.1 Example
7
4= 13
4
6.2 From Mixed Numbers to Improper Fractions
1. Multiply the whole number part by the denominator.
2. Add the result to the numerator.
3. Write this sum over the original denominator.
6.2.1 Example
12
3=5
3
7 Conclusion
Mastering fractions is a key part of mathematical literacy. Practice with
different operations and conversions will build a solid foundation for more
advanced math concepts.
4
4 Operations with Fractions
4.1 Addition and Subtraction
To add or subtract fractions:
1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the com-
mon denominator.
3. Add or subtract the numerators.
4. Write the result over the common denominator and simplify
if possible.
4.1.1 Example: Addition
1
4+2
5=5
20 +8
20 =13
20
4.1.2 Example: Subtraction
3
4−1
6=9
12 −2
12 =7
12
4.2 Multiplication
To multiply fractions:
1. Multiply the numerators together.
2. Multiply the denominators together.
3. Write the result as a fraction and simplify if possible.
4.2.1 Example
2
3×4
5=8
15
2
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
6.1.1 Example
7
4= 13
4
6.2 From Mixed Numbers to Improper Fractions
1. Multiply the whole number part by the denominator.
2. Add the result to the numerator.
3. Write this sum over the original denominator.
6.2.1 Example
12
3=5
3
7 Conclusion
Mastering fractions is a key part of mathematical literacy. Practice with
different operations and conversions will build a solid foundation for more
advanced math concepts.
4
4 Operations with Fractions
4.1 Addition and Subtraction
To add or subtract fractions:
1. Find a common denominator.
2. Convert each fraction to an equivalent fraction with the com-
mon denominator.
3. Add or subtract the numerators.
4. Write the result over the common denominator and simplify
if possible.
4.1.1 Example: Addition
1
4+2
5=5
20 +8
20 =13
20
4.1.2 Example: Subtraction
3
4−1
6=9
12 −2
12 =7
12
4.2 Multiplication
To multiply fractions:
1. Multiply the numerators together.
2. Multiply the denominators together.
3. Write the result as a fraction and simplify if possible.
4.2.1 Example
2
3×4
5=8
15
2
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
4.3 Division
To divide fractions:
1. Invert the second fraction (find its reciprocal).
2. Multiply the first fraction by this reciprocal.
3. Write the result as a fraction and simplify if possible.
4.3.1 Example
3
4÷2
5=3
4×5
2=15
8
5 Simplifying Fractions
To simplify a fraction:
1. Find the greatest common divisor (GCD) of the numerator
and denominator.
2. Divide both the numerator and the denominator by the GCD.
5.0.1 Example
8
12 =2
3
6 Converting Between Mixed Numbers and
Improper Fractions
6.1 From Improper Fractions to Mixed Numbers
1. Divide the numerator by the denominator.
2. The quotient is the whole number part.
3. The remainder becomes the new numerator over the original
denominator.
3
6.1.1 Example
7
4= 13
4
6.2 From Mixed Numbers to Improper Fractions
1. Multiply the whole number part by the denominator.
2. Add the result to the numerator.
3. Write this sum over the original denominator.
6.2.1 Example
12
3=5
3
7 Conclusion
Mastering fractions is a key part of mathematical literacy. Practice with
different operations and conversions will build a solid foundation for more
advanced math concepts.
4
Students also viewed