Fractions & Percentages

19/04/23 1

19 April 2023

Contents

Fractions – the Language ofEquivalent Fractions and Cancelling

FractionsTop Heavy Fractions and Mixed NumbersOrdering FractionsFinding a Fraction

19/04/23 2

What are Fractions ?

Parts of a wholeEg.

Numerator

Denominator

Unit Fractions

19/04/23 3

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

19/04/23 4

21

43

Equivalent Fractions

19/04/23 5

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

19/04/23 7

105

5

21

105

÷ 5

÷ 5

Cancelling Fractions

Cancel

HCF = 3 HCF = 4 So,

19/04/23

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

19/04/23 9

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

19/04/23 10

326

32

533

518

328

Top Heavy Fractions & Mixed Numbers

Convert into a top heavy fraction

So = =

Try

= =

19/04/23 11

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)

19/04/23 12

51

54

52

53

53

85

2011

40

Ordering Fractions

Now put them in order …

So, then answer the question

19/04/23 13

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

19/04/23 14

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

19/04/23 15

52

51 25

1255 25x 250

52

Contents - Percentages

What are Percentages ?Converting between Fractions and

PercentagesFinding a Percentage

19/04/23 16

What are Percentages ?

They are just like fractionsThe whole is always split into 100 partsSo 35% means 35 out of the 100 parts

19/04/23 17

10035

Converting between F, D & P

Converting a percentage to a fraction40% means 40 out of every 100

Don’t forget to cancel down, if possible

10040

52

Converting between F, D & P

Converting a fraction to a percentageYou need to find the equivalent fraction

which has 100 as the denominator

___ 1005

3 x 20

x 20

60 So 60%

Finding a Percentage -

Remember, 10% =

To find we by 10

101

10010

101

Without aCalculator

Finding a Percentage -

Use this info to find any percentagei.e. Find 30% of £24010% = £24So, 30% = 3 x £24 = £72

30% = £72.00

Without aCalculator

Finding a Percentage -

45% of 120 children at the theatre were boys, how many were boys ?

10% = 12 so 5% = 6 (half of 10%)So, 40% = 4 x 12 = 48and 5% = 6

45% = 48 + 6 = 54 boys

Without aCalculator