Fractions

Fractions

13/04/23 1

13 April 2023

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

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

Equivalent Fractions

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42

21

1643 12

42

21

1612

43

x 2

x 2

x 4

x 4

Equivalent Fractions

6

3285 21

127

x 4

x 4

x 3

x 3

2036

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

Cancelling Fractions

Cancel

HCF = 3 HCF = 4 So,

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1512

3616

54

1512

÷ 3

÷ 394

3616

÷ 4

÷ 4

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

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

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

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

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

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

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

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

Adding Fractions

Denominators must be the sameEg.

Convert to equivalent fractions with same denominator, if necessary

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54

53

51

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

Subtracting Fractions

Subtraction works the sameEg.

Convert to equivalent fractions with same denominator, if necessary

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52

51

53

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

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

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

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

+, -, 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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