Algebraic Summary
GCSE Mathematics – Basics of number
SLIDE NUMBER 1
May 2019
© VIDLEARN® 2019
Claire Roberts
1
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 2
May 2019
© VIDLEARN® 2019
2
CONSIDER…
At this point you should consider the list of session objectives and ask yourself:
How many of the session objectives am I confident with
Could I explain these objectives in relation to teaching and learning
SLIDE NUMBER 3
May 2019
© VIDLEARN® 2019
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Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 4
May 2019
© VIDLEARN® 2019
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Key vocabulary
In mathematics, the natural numbers are those used for counting and ordering. In common language, words used for counting
are cardinal numbers and words used for ordering are ordinal numbers.
The symbol for the set of all natural numbers is shown
An integer is a number that can be written without a fractional component. The set of integers consists of the positive and negative natural numbers and zero.
21, 4, 0, and −2048 are integers, but 9.75, 5 ¹⁄₂, and √2 are not.
The symbol for the set of all integers is shown
(originating from the German word zahlen)
Basics of number
SLIDE NUMBER 5
May 2019
© VIDLEARN® 2019
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Key vocabulary
The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc, are called real numbers. Positive or negative, large or small, whole numbers or decimal numbers are all real numbers, so called because they are not imaginary numbers.
The symbol for the set of all real numbers is shown
An imaginary number is one that when squared gives a negative result. When we square a real number we always get a positive, or zero, result. For example, 2×2=4, and (-2)×(-2)=4 as well. So how can we square a number and get a negative result? Because we "imagine" that we can. The "unit" for imaginary numbers (the same as "1" for real numbers) is √(-1), and its symbol is i or j.
Basics of number
SLIDE NUMBER 6
May 2019
© VIDLEARN® 2019
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Key vocabulary
A rational number is any number that can be expressed as the quotient or fraction of two integers, with a numerator and a non-zero denominator .
Since may be equal to 1, every integer is a rational number.
The set of all rational numbers is shown
(originating from the Italian word quoziente)
Irrational numbers are all the real numbers which are not rational numbers.
The most famous irrational number is , sometimes called Pythagoras’ constant. Other examples include , , , etc
Basics of number
SLIDE NUMBER 7
May 2019
© VIDLEARN® 2019
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Positive and Negative Numbers
In mathematics, direction from zero is indicated by use of positive and negative signs.
Basics of number
SLIDE NUMBER 8
May 2019
© VIDLEARN® 2019
-4 -3 -2 -1 0 1 2 3 4
Negative numbers
Positive numbers
Origin
To denote that a number is negative we use a minus sign in front of
the number, and, on occasion, a plus sign is used to denote a positive number but this is commonly assumed.
-9 denotes “negative nine”; +9 or 9 denotes “positive nine”
8
Greater than, less than, equal to
In mathematics, arrows are used to denote whether a number is greater than, less than or equal to another number.
6 > 3 means that “6 is greater than 3”
-6 < 3 means that “negative 6 is less than 3”
a < b means that “a is less than or equal to b”
b > a means that “b is greater than or equal to a”
It is important to remember that
“ = ” means “equal to”
and not “here’s my next step” or “ the answer is”
Basics of number
SLIDE NUMBER 9
May 2019
© VIDLEARN® 2019
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Review of main ideas from above:
We will use real numbers, rational and irrational numbers but imaginary numbers are only introduced in the Further Mathematics A-level specification, but here’s something to consider
Consider this incorrect use of the = symbol
(3 + 4) x 6 + 7 = 7 = 42 = 49
So now pause the recording to consider, once you have done this play the recording.
SLIDE NUMBER 10
May 2019
© VIDLEARN® 2019
CONSIDER…
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Review of main ideas from above:
Could be interpreted mathematically as
“i eight all of pi” or “I ate all of the pie”
(3 + 4) x 6 + 7 = 7 = 42 = 49
The beginning and end of this are true, (3 + 4) x 6 + 7 = 49
But, 7≠ 42 ≠ 49 We will look at the correct order of operations in the next part
SLIDE NUMBER 11
May 2019
© VIDLEARN® 2019
CONSIDER…
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Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 12
May 2019
© VIDLEARN® 2019
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Order of operations
Calculations should be completed in a specific order remembered by the acronym BODMAS
Basics of number
SLIDE NUMBER 13
May 2019
© VIDLEARN® 2019
rackets
B
O
D
M
A
S
rder (power)
ivision
ultiplication
ddition
ubtraction
These operations are interchangeable
These operations are interchangeable
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BODMAS
First, let’s consider the calculation from earlier
(3 + 4) x 6 + 7
Basics of number
SLIDE NUMBER 14
May 2019
© VIDLEARN® 2019
= 7 x 6 + 7
= 42 + 7
= 49
If we incorporate some more elements of BODMAS, 13 + 12 ÷ (9 - 7)2
= 13 + 12 ÷ (2)2
= 13 + 12 ÷ 4
= 16
= 13 + 3
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Columnar Addition
If we need to evaluate 2746 + 578, we use the columnar addition method
Basics of number
SLIDE NUMBER 15
May 2019
© VIDLEARN® 2019
2746
578
3
+
2
1
4
1
1
3
It is important to ensure that the digits are kept in clear place value columns and the addition sign is included.
Answer: 3324
15
Columnar Subtraction
If we need to evaluate 2746 - 578, we use the columnar subtraction method
Basics of number
SLIDE NUMBER 16
May 2019
© VIDLEARN® 2019
2746
578
1
-
6
8
2
It is important to ensure that the digits are kept in clear place value columns and the subtraction sign is included.
Answer: 2168
3
1
6
1
16
Long Multiplication
If we need to evaluate 274 x 57, we use the columnar multiplication method
Basics of number
SLIDE NUMBER 17
May 2019
© VIDLEARN® 2019
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57
274
19
1
x
5
2
2
0
7
13
0
3
8
6
15
1
1
Answer: 15618
It is important to ensure that the digits are kept in clear place value columns, the multiplication sign is included and you appreciate that in the second line you are multiplying by a multiple of 10, hence the zero.
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Short division
If we need to evaluate 284 ÷ 5, we use the short division method
Basics of number
SLIDE NUMBER 18
May 2019
© VIDLEARN® 2019
284
5
6
5
3
.
0
8
.
4
If you have a remainder at the end you can introduce a decimal point and as many zeros as are needed. Alternatively you could give the answer as a mixed number by putting the remainder as the numerator and the divisor as the denominator,
Answer: 56.8
i.e.
18
Long division
If we need to evaluate 585 ÷ 15, we use the long division method
Basics of number
SLIDE NUMBER 19
May 2019
© VIDLEARN® 2019
585
15
9
3
In long division, the remainder is found and shown underneath as shown
Answer: 39
45
13
5
135
0
19
Review of main ideas from above:
Consider these questions:
17 + (3 x 6) ÷ 32
672 + 384
965 – 739
361 x 39
391 ÷ 17
So now pause the recording to try these calculations , once you have done this play the recording
SLIDE NUMBER 20
May 2019
© VIDLEARN® 2019
CONSIDER…
20
Review of main ideas from above:
Consider these questions:
17 + (3 x 6) ÷ 32 19
672 + 384 1056
965 – 739 226
361 x 39 14079
391 ÷ 17 23
SLIDE NUMBER 21
May 2019
© VIDLEARN® 2019
CONSIDER…
21
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 22
May 2019
© VIDLEARN® 2019
22
Powers
Powers are used when a number is multiplied by itself a number of times.
For example,
3 x 3 x 3 x 3 = 34 = 81
They can also be used for reciprocals and roots.
and
The rules of indices (or powers) will be covered in more detail in Session 2 – Indices, roots and surds
Basics of number
SLIDE NUMBER 23
May 2019
© VIDLEARN® 2019
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Common Powers and Roots
Basics of number
SLIDE NUMBER 24
May 2019
© VIDLEARN® 2019
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Review of main ideas from above:
Powers are very powerful in mathematics
Modern scientific calculators can find any power of any number – do you know how to do this on yours? https://www.youtube.com/results?search_query=how+to+use+a+scientific+calculator+for+powers
So now pause the recording to consider the use of your calculator, once you have done this play the recording
SLIDE NUMBER 25
May 2019
© VIDLEARN® 2019
CONSIDER…
25
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 26
May 2019
© VIDLEARN® 2019
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Rounding
Numbers can be rounded to a given number of decimal places or to a given number of significant figures.
The basic rules are the same for both:
Find the digit that will be the new final digit
Look at the digit that follows it
If it is less than 5, the final digit remains unchanged
If it is 5 or more, then the final digit must be increased by one. If the final digit is 9, then the number before is increased by one, and so on.
See the next slide for examples
Basics of number
SLIDE NUMBER 27
May 2019
© VIDLEARN® 2019
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Rounding to a given number of decimal places
Rounding 34.6456 to one decimal place (1dp) will give 34.6
Rounding 67.6563 to 2dp will give 67.66
Rounding 8.0998 to 3dp will give 8.100
Note on example 3 that, despite the zeros having no value, they are required to meet the degree of accuracy
Basics of number
SLIDE NUMBER 28
May 2019
© VIDLEARN® 2019
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Rounding to a given number of significant figures
Rounding 34.6456 to one significant figure (1sf) will give 30
Rounding 67.6563 to 2sf will give 68
Rounding 8.0998 to 3sf will give 8.10
Rounding 0.030456 to 3sf will give 0.0305
Notes
Example 1 – the zero is included as a place value holder
Example 3 – the zero is include to meet the degree of accuracy
Example 4 – the first significant figure is the 3, preceding zeros are not counted but subsequent zeros are
Basics of number
SLIDE NUMBER 29
May 2019
© VIDLEARN® 2019
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Estimation
It is useful to be able to estimate the value of a calculation, even if you have access to a calculator.
Consider the following, quite complex calculation,
Basics of number
SLIDE NUMBER 30
May 2019
© VIDLEARN® 2019
The exact answer is 20.2 (3sf)
If you were to accidentally type 193 instead of 19.3,
the calculator would give the answer 2020 (3sf) which you would know was wrong if you had estimated first
30
Review of main ideas from above:
Round the following numbers to the degree of accuracy given in brackets:
6.7083 (2dp)
3091.87 (3sf)
0.004001 (2sf)
For the following calculation, first find an estimate then use your calculator to find the exact answer to 3sf
So now pause the recording to consider the questions, once you have done this play the recording
SLIDE NUMBER 31
May 2019
© VIDLEARN® 2019
CONSIDER…
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Review of main ideas from above:
6.7083 (2dp) = 6.71
3091.87 (3sf) = 3090
0.004001 (2sf) = 0.0040
Exact answer = 1.65 (3sf)
SLIDE NUMBER 32
May 2019
© VIDLEARN® 2019
CONSIDER…
32
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 33
May 2019
© VIDLEARN® 2019
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Factors and Multiples
Factors are numbers which can be multiplied together to give the original number. They are usually found in pairs, except in the case of square numbers which always have an odd number of factors.
For example,
Factors of 24 are 1 and 24, 2 and 12, 3 and 8, 4 and 6
Factors of 16 are 1 and 16, 2 and 8, 4 (and 4)
Multiples are numbers that are generated by multiplying by integers. Basically they are the numbers found in the times tables.
For example,
The first 10 multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20
The first 5 multiples of 100 are 100, 200, 300, 400 and 500
Basics of number
SLIDE NUMBER 34
May 2019
© VIDLEARN® 2019
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Prime numbers
Prime numbers are special numbers which have exactly two factors – itself and one.
A common misconception is that 1 is a prime number, but it only has one factor.
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit.
It is completed by marking the multiples
of each prime, starting with the
first prime number, 2, on a number grid.
The numbers left unmarked are
the prime numbers.
Basics of number
SLIDE NUMBER 35
May 2019
© VIDLEARN® 2019
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Prime Factor Decomposition
Any integer can be written as a product of its prime factors which can be found by Prime Factor Decomposition
Let’s write 420 as a product of its prime factors,
Basics of number
SLIDE NUMBER 36
May 2019
© VIDLEARN® 2019
420
2
2
210
105
35
3
5
7
Answer: 2 x 2 x 3 x 5 x 7
or 22 x 3 x 5 x 7
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Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
If we need to find the HCF or LCM of two or more integers we can use prime factor decomposition.
Let’s find the HCF and LCM of 420 and 66
Basics of number
SLIDE NUMBER 37
May 2019
© VIDLEARN® 2019
66
2
3
33
11
Answer: 2 x 3 x 11
If we now write both numbers as their products one above the other,
420 = 2 x 2 x 3 x 5 x 7
66 = 2 x 3 x 11
HCF = 2 x 3 = 6
LCM = 2 x 2 x 3 x 5 x 7 x 11 = 4620
37
Review of main ideas from above:
This youtube video is a quirky explanation of the Sieve of Eratosthenes https://www.youtube.com/watch?v=V08g_lkKj6Q
Find the HCF and LCM of these pairs of numbers using prime factor decomposition:
1. 24 and 60
2. 48 and 72
So now pause the recording to watch the youtube video and to try the technique, once you have done this play the recording
SLIDE NUMBER 38
May 2019
© VIDLEARN® 2019
CONSIDER…
38
Review of main ideas from above:
Find the HCF and LCM of these pairs of numbers using prime factor decomposition:
1. 24 and 60
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
HCF = 2 x 2 x 3 = 12; LCM = 2 x 2 x 2 x 3 x 5 = 120
2. 48 and 72
48 = 2 x 2 x 2 x 2 x 3
72 = 2 x 2 x 2 x 3 x 3
HCF = 2 x 2 x 2 x 3 = 24; LCM = 2 x 2 x 2 x 2 x 3 x 3 = 144
SLIDE NUMBER 39
May 2019
© VIDLEARN® 2019
CONSIDER…
39
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 40
May 2019
© VIDLEARN® 2019
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The Product Rule for Counting
To find the total number of outcomes for two or more events, we can use the product rule for counting in which we multiply the number of outcomes for each event together.
For example, if we wanted to know the total number of combinations on a menu with 5 starters, 3 main courses and 4 desserts we could use the product rule,
5 x 3 x 4 = 60 different meal combinations
Basics of number
SLIDE NUMBER 41
May 2019
© VIDLEARN® 2019
This will be explained again in more detail in Session 18 – Probability
41
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 42
May 2019
© VIDLEARN® 2019
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Simplifying Fractions
To simplify a fraction you need to find the HCF of both the numerator and denominator and divide both by this factor. Once a fraction has been simplified in this way it is said to be in its lowest or simplest terms.
For example, to simplify ,we find that the HCF of the numerator and denominator is 9, so dividing both by 9 will give
Basics of number
SLIDE NUMBER 43
May 2019
© VIDLEARN® 2019
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Adding Fractions
To add a pair of fractions with different denominators you need to:
Find the LCM of both the two denominators
Multiply the numerator by the same factor as the denominator would be multiplied by to make the LCM; do this to both fractions
Add the numerators of the two fractions, leaving the denominator unchanged as the LCM
Simplify the new fraction if possible, or convert to a mixed number if the fraction is improper.
For example,
Basics of number
SLIDE NUMBER 44
May 2019
© VIDLEARN® 2019
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Subtracting Fractions
To subtract a fraction from another with a different denominator you need to:
Find the LCM of both the two denominators
Multiply the numerator by the same factor as the denominator would be multiplied by to make the LCM; do this to both fractions
Subtract the second numerator from the first, leaving the denominator unchanged as the LCM
Simplify the new fraction if possible, or convert to a mixed number if the fraction is improper.
For example,
Basics of number
SLIDE NUMBER 45
May 2019
© VIDLEARN® 2019
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Adding or Subtracting Mixed Numbers
Convert the mixed numbers to improper fractions and then follow the process as previously described.
For example,
Basics of number
SLIDE NUMBER 46
May 2019
© VIDLEARN® 2019
The same method is used when subtracting mixed numbers
46
Multiplying Fractions and Mixed Numbers
To multiply a pair of fractions you need to:
Multiply the two numerators to give the new numerator
Multiply the two denominators to give the new denominator
Simplify the new fraction if possible, or convert to a mixed number if the fraction is improper.
For example,
If you need to multiply a pair of mixed numbers you need to first convert to improper fractions, then follow the method above.
Basics of number
SLIDE NUMBER 47
May 2019
© VIDLEARN® 2019
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Dividing Fractions and Mixed Numbers
To divide a pair of fractions you need to:
Convert the fractions so that they have common denominators
Divide the first numerator by the second numerator
Simplify the new fraction if possible, or convert to a mixed number if the fraction is improper.
For example,
If you need to divide a pair of mixed numbers you need to first convert to improper fractions, then follow the method above.
Basics of number
SLIDE NUMBER 48
May 2019
© VIDLEARN® 2019
48
Converting Fractions to Decimals,
and vice versa
A fraction is another way of representing a division,
so means 3 ÷ 4.
Hence, to convert a fraction to a decimal, simply divide the numerator by the denominator, meaning that
If you need to write a decimal as a fraction, you need to consider the meaning of the decimal. For instance, 0.45 means 4 tenths and 5 hundredths, or 45 hundredths,
therefore
Basics of number
SLIDE NUMBER 49
May 2019
© VIDLEARN® 2019
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Writing Recurring Decimals as Fractions
A recurring decimal is one that is non-terminating (unlike 0.45) and has a sequence of digits that repeat infinitely.
Recurring decimals are indicated using small dots over the start and finish of the repeating sequence, for example,
To convert to a fraction,
Let
So
and
Hence
Basics of number
SLIDE NUMBER 50
May 2019
© VIDLEARN® 2019
50
Converting Percentages to Fractions to Decimals, and vice versa
A percentage is simply a proportion given as an amount out of 100
Hence, to convert a percentage to a fraction, simply write the percentage value as the numerator with 100 as the denominator, and then to write as a decimal simply divide.
For example, and
If you need to write a decimal as a percentage, firstly consider how many hundredths it is then write as a fraction and then a percentage.
For example, and
Basics of number
SLIDE NUMBER 51
May 2019
© VIDLEARN® 2019
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Converting Percentages to Fractions, and vice versa
Write the percentage value as the numerator with 100 as the denominator, and then simplify if possible.
For example, and
If you need to write a fraction as a percentage,
divide the numerator by the denominator to give the fraction as a decimal
then convert the decimal as previously discussed
For example,
and
Basics of number
SLIDE NUMBER 52
May 2019
© VIDLEARN® 2019
52
Finding Fractions and Percentages of amounts
To find a fraction of an amount ,divide by the denominator then multiply the result by the numerator.
For example, to find of 64,
first find of 64 = 64 ÷ 8 = 8, then multiply by 7, 8 x 7 = 56
Hence of 64 = 56
If you need to find a percentage of an amount, firstly consider the percentage as a fraction, then follow the same method
For example, to find 6% of £500, ( of 500)
first find of 500 = 500 ÷ 100 = 5, then multiply by 6, 5 x 6 = 30
Hence 6% of £500 = £30
Basics of number
SLIDE NUMBER 53
May 2019
© VIDLEARN® 2019
53
Review of main ideas from above:
Have a go at the following questions:
1. 2. 3. 4.
5. Convert 0.76 to a fraction in its simplest terms
6. Convert to a percentage
7. Write the recurring decimal as a fraction
8. Find 4% of £250
So now pause the recording to consider the questions, once you have done this play the recording
SLIDE NUMBER 54
May 2019
© VIDLEARN® 2019
CONSIDER…
54
Review of main ideas from above:
Have a go at the following questions:
1. 2.
3. 4.
5. Convert 0.76 to a fraction in its simplest terms
6. Convert to a percentage = 62.5%
7. Write the recurring decimal as a fraction
8. Find 4% of £250 = £10
SLIDE NUMBER 55
May 2019
© VIDLEARN® 2019
CONSIDER…
55
Session Objectives
The purpose of the session is to:
Understand notation, vocabulary, positive and negative integers and symbols
Calculate using formal written methods of the four operations including brackets, powers, roots and reciprocals
Recognise and apply positive integer powers and associated real roots (square, cube and higher) powers of 2, 3, 4, 5
Describe estimation of calculations and apply the concept to round numbers and measures
Define factors and multiples and use Prime Factor Decomposition to identify HCF and LCM
Define the product rule for counting (combinations)
Perform a range of calculations using fractions, decimals and percentages
SLIDE NUMBER 56
May 2019
© VIDLEARN® 2019
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SLIDE NUMBER 57
May 2019
© VIDLEARN® 2019
CONSIDER…
End of Presentation
At this point it would be advisable to go back over the presentation. Ensure that you are fully able to deal accurately and effectively with each session objective.
You should supplement the content of this session with suitable reading, research and discussion with others.
Claire Roberts
SLIDE NUMBER 58
May 2019
© VIDLEARN® 2019
GCSE Mathematics – Basics of number
End of presentation
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