Unit3 test

Unit 3: Making Sense of Rational Expressions 173

Practice

Factor each of these and then simplify. Look for hints within the problem. Refer to the previous page as necessary. Show essential steps.

1.

2.

Sometimes, it is necessary to factor both the numerator and denominator. Examine the example below, then simplify each of the following expressions.

Example:

Note: The x’s do not cancel.

3.

4.

a2 – 3a + 2 =a – 2

b2 – 2b – 3 = b – 3

x2 – 4 = x2 + x – 6

(x + 2)(x – 2) (x + 3)(x – 2)

= (x + 2) (x + 3)

1

1 =

x + 2 x + 3

2r2 + r – 6 = r2 + r – 2

x2 + x – 2 = x2 – 1

Unit 3: Making Sense of Rational Expressions174

Practice

Simplify each expression. Show essential steps.

1.

2.

3.

4.

5b – 10 = b – 2

6a – 9 = 10a – 15

9x + 3 = 9

6b + 9 = 12

Unit 3: Making Sense of Rational Expressions 175

5.

6.

7.

8.

3a2b + 6ab – 9b2 = 3b

x2 – 16 = x + 4

2a – b = b2 – 4a2

6x2 + 2 = 9x2 + 3

Unit 3: Making Sense of Rational Expressions176

Practice

Factor each of these expressions and then simplify. Show essential steps.

1.

2.

3.

4.

y2 + 5y – 14 =

y + 2

a2 – 5a + 4 = a – 4

6m2 – m – 1 = 2m2 + 9m – 5

2x2 + x – 6 =4x

2 – 9

Unit 3: Making Sense of Rational Expressions 177

Practice

Use the list below to write the correct term for each definition on the line provided.

denominator expression fraction

rational expression real numbers variable

________________________ 1. a collection of numbers, symbols, and/or operation signs that stands for a number

________________________ 2. the top number of a fraction, indicating the number of equal parts being considered

________________________ 3. the bottom number of a fraction, indicating the number of equal parts a whole was divided into

________________________ 4. the set of all rational and irrational numbers

________________________ 5. any part of a whole

________________________ 6. a fraction whose numerator and/or denominator are polynomials

________________________ 7. any symbol, usually a letter, which could represent a number

________________________ 8. a monomial or sum of monomials; any rational expression with no variable in the denominator

________________________ 9. the result of dividing two numbers

numerator polynomial quotient

Unit 3: Making Sense of Rational Expressions178

Practice

Use the list below to complete the following statements.

canceling cross multiplication equivalent factor

integers product simplify an expression terms

1. If you multiply both the numerator and the denominator by the same

number, the new fraction will be because

it is the same number expressed in a different form.

2. are the numbers in the set

{… , -4, -3, -2, -1, 0, 1, 2, 3, 4, …}.

3. If you divide a numerator and a denominator by a common factor to

write a fraction in lowest terms or before multiplying fractions, you

are .

4. To , you need to perform as many of the

indicated operations as possible.

5. Numbers, variables, products, or quotients in an expression are

called .

Unit 3: Making Sense of Rational Expressions 179

6. A is a number or expression that divides

evenly into another number.

7. When you multiply numbers together, the result is called the

.

8. To find a missing numerator or denominator in equivalent fractions

or ratios, you can use a method called

and make the cross products equal.

Unit 3: Making Sense of Rational Expressions206

Practice

Solve and check each equation. Use the examples on pages 200-205 for reference. Show essential steps.

Hint: Find a step that looks similar to the problem you need help with and follow from that point.

Remember: To check your work, replace the variable in the original problem with the answer you found.

1. 3x – 7 = 17

2. 4x + 20 = x – 4

3. x6 = 1.5

4. 2x5 = 3.2

Unit 3: Making Sense of Rational Expressions 207

5. 5(x – 4) = 20

6. 5(4x – 7) = 0

7. 8x – 2x = 42

8. 5x – 3 = 2x + 18

9. -2x + 4 = -4x – 10

Unit 3: Making Sense of Rational Expressions208

Practice

Solve and check each equation. Use the examples on pages 200-205 for reference. Show essential steps.

1. 2(3x – 4) + 6 = 10

2. 3(x – 7) – x = -9

3. 23 x = 1

Hint: 23 x = 2x 3 . Rewrite 1 as

1 1 and cross multiply.

4. -12 x – 3 4 = 4

Unit 3: Making Sense of Rational Expressions 209

5. -3x = -338

6. -2x = 8

7. -3x – 32 = 11 2

Unit 3: Making Sense of Rational Expressions210

Practice

Solve and check each equation.

1. -87 = 9 – 8x

2. 4k + 3 = 3k + 1

3. 5a + 9 = 64

4. b3 + 5 = -2

Unit 3: Making Sense of Rational Expressions 211

5. 4x = -(9 – x)

6. x 5 = -10

7. 3x – 1 = -x + 19

Unit 3: Making Sense of Rational Expressions212

Practice

Solve and check each equation. Reduce fractions to simplest form.

1. 5x – 3 = 2x + 18

2. 6x – (4x – 12) = 3x + 5

3. x6 = -24

5

4. 4(x – 2) = -3(x + 5)

Unit 3: Making Sense of Rational Expressions 213

5. 5( 13 x – 2) = 4

6. x 4 + 32 =

5 8

7. 9 2

x = 5 1

8. -12 + 8x 5 =

-7 8