fractions
DESCRIPTION
All you have to know about basics of fractionsTRANSCRIPT
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Fractions
13/04/23 1
13 April 2023
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Contents
Fractions – the Language ofEquivalent Fractions and Cancelling
FractionsTop Heavy Fractions and Mixed NumbersOrdering FractionsFinding a FractionWriting as a Fraction+, -, x and ÷ Fractions
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What are Fractions ?
Parts of a wholeEg.
Numerator
Denominator
Unit Fractions
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76
43
32
21
32
21
31
41
51
501
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Fractions
What do they mean …
We have 1 of those parts
The whole is split into 2 parts
We have 3 of those parts
The whole is split into 4 parts
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21
43
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Equivalent Fractions
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42
21
1643 12
42
21
1612
43
x 2
x 2
x 4
x 4
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Equivalent Fractions
6
3285 21
127
x 4
x 4
x 3
x 3
2036
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Cancelling Fractions
Reducing fractions to their simplest form Equivalent fractions using the smallest
numbers Reduce to simplest form Find HCF of 5 and 10 So divide both numerator & denominator by 5
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105
5
21
105
÷ 5
÷ 5
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Cancelling Fractions
Cancel
HCF = 3 HCF = 4 So,
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1512
3616
54
1512
÷ 3
÷ 394
3616
÷ 4
÷ 4
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Top Heavy Fractions & Mixed Numbers
Convert into a mixed number
1 + 1 + =
12 ÷ 5 = 2 with left over
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37
312
512
52
522
52
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Top Heavy Fractions & Mixed Numbers
Convert into a mixed number
26 ÷ 3 = 8, with left over, so
Convert into a top heavy fraction
How many fifths
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326
32
533
518
328
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Top Heavy Fractions & Mixed Numbers
Convert into a top heavy fraction
So = =
Try
= =
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533
53)5x3(
533 5
18
313 7
35
31)3(3x
73x7)5(
310
738
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Ordering Fractions
Easy !!But what about …..
Convert to equivalent fractions with same denominator first
Find LCM of 5, 8 and 20 (denominators)
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51
54
52
53
53
85
2011
40
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Ordering Fractions
Now put them in order …
So, then answer the question
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4024
53 40
2585 40
222011
4024
4025
4022
53
85
2011
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Finding a Fraction
What is of £50 ?
What about of £100 ?
To find ÷ 5To find ÷ 25
How would we find
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21
41
502
1004
51
251
1571
yes,÷ 157
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Finding a Fraction
What about of £125 ?
Find first –
Then, x by 2
So, of £125 is £50
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52
51 25
1255 25x 250
52
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Writing as a Fraction
Write the fraction in the following form:
and then cancel down to simplest form.Eg. Out of 200 road accidents, 40 involved
pedestrians, what fraction is this ?
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Number of Values that Meet Your RequirementTotal Number of Values
51
20040
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Adding Fractions
Denominators must be the sameEg.
Convert to equivalent fractions with same denominator, if necessary
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54
53
51
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Adding Fractions
Different denominators ? Convert …
Remember LCM ?Find LCM of 5 and 4 (denominators)Convert fractions - 20 as denominator
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43
51
20
204
51
2015
43 20
192015
204
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Subtracting Fractions
Subtraction works the sameEg.
Convert to equivalent fractions with same denominator, if necessary
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52
51
53
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Subtracting Fractions
Different denominators – convert …
Find LCM of 2 and 5 (denominators)Convert fractions - 10 as denominator
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52
21
10
105
21
104
52 10
1104
105
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Adding & Subtracting Fractions
Use the following steps, where relevantConvert to top heavy fractionsConvert to equivalent fractions with
same denominatorAdd or subtract the numeratorsCancel down to simplest termsConvert back to mixed number
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Multiplying Fractions
Easy, convert to top heavy fraction firstMultiply across top and multiply across
bottomEg.
Remember to cancel to lowest terms or convert back to a mixed number
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21
32 6
2 31
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Dividing Fractions
Just as easy ! Again, convert to top heavy fractions first, if necessary.
Rule:- Turn the 2nd fraction upside down and then multiply
Answers must be in their simplest form and as mixed numbers if appropriate
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15168
352 3
852 15
11
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+, -, x and Fractions
Always …Give your answer in its simplest formUse mixed numbers where relevant
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Session Summary
Fractions – the Language ofEquivalent Fractions and Cancelling
FractionsTop Heavy Fractions and Mixed NumbersOrdering FractionsFinding a FractionWriting as a Fraction+, -, x and ÷ Fractions
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