Fractions Year 6 www.KeyStage2Maths.com

÷2 ÷3 6 3 1 = = 18 9 3 ÷2 ÷3

÷6 6 1 = 18 3 ÷6

6 18 1 3

÷2 ÷2 8 4 2 = = 12 6 3 ÷2 ÷2

÷4 8 2 = 12 3 ÷4

8 eight twelfths 12 2 3 two thirds

÷2 ÷2 12 6 3 = = 20 10 5 ÷2 ÷2

÷4 12 3 = 20 5 ÷4

12 twelve twentieths 20 3 three fifths 5

÷7 ÷7 ÷5 14 2 7 1 25 5 = = = 35 5 28 4 30 6 ÷7 ÷7 ÷5

= = 10 ? 12 ? 2 3 4 5 15 15 Which fraction is larger: or ? x5 x3 x5 x3 When one denominator is not a multiple of another, you need to convert both fractions. x5 x3 10 ? 12 ? 2 3 4 5 = = 15 15 15 is a multiple of both 3 and 5, so we can find two equivalent fractions with a denominator of 15. x5 x3

Which fraction is larger: or ? 2 3 4 5 Which fraction is larger: or ?

= = 9 ? 10 ? 3 4 5 6 12 12 Which fraction is larger: or ? x3 x2 x3 x2 12 is a multiple of both 4 and 6, so we can find two equivalent fractions with a denominator of 12. 9 ? 10 ? 3 4 5 6 = = 12 12 x3 x2

Which fraction is larger: or ? 3 4 5 6 Which fraction is larger: or ?

= = 15 ? 14 ? 5 6 7 9 18 18 Which fraction is larger: or ? x3 x2 x3 x2 18 is a multiple of both 6 and 9, so we can find two equivalent fractions with a denominator of 18. 15 ? 14 ? 5 6 7 9 = = 18 18 x3 x2

Which fraction is larger: or ? 5 6 7 9 Which fraction is larger: or ?

Order these fractions from smallest to largest. 3 5 11 20 1 2 7 10 3 4 12 11 14 15 20 20 10 20 20 20 1 2 11 20 3 5 7 10 3 4

1/2 10/20 11/20 11/20 3/5 12/20 7/10 14/20 3/4 15/20

Order these fractions from smallest to largest. 3 4 2 3 1 2 1 3 5 6 9 10 8 4 12 12 6 12 12 12 1 3 1 2 2 3 3 4 5 6

1/3 4/12 1/2 6/12 2/3 8/12 3/4 9/12 5/6 10/12

2 3 1 4 8 12 3 12 11 12 + = + = x4 x3 ? 8 3 ? 2 3 1 4 = = 12 12 x4 x3

2 3 1 4 8 12 3 12 11 12 + = + =

1 2 2 5 5 10 4 10 1 10 - = - = x5 x2 ? 5 4 ? 1 2 2 5 = = 10 10 x5 x2

1 2 2 5 5 10 4 10 1 10 - = - =

3 4 1 5 15 20 4 20 19 20 + = + = x5 x4 15 ? 4 ? 3 4 1 5 = = 20 20 x5 x4

3 4 1 5 15 20 4 20 19 20 + = + =

3 5 3 4 12 20 15 20 27 20 7 20 + = + = = 1 x4 x5 27 ÷ 20 = 12 ? 15 ? 3 5 3 4 = = 7 20 1 r 7 = 1 20 20 x4 x5

3 5 3 4 12 20 15 20 27 20 7 20 + = + = = 1

1 3 5 12 4 12 5 12 9 12 3 + 2 = 3 + 2 = 5 x3 4 ? 1 3 = 12 x3

1 3 1 5 5 15 3 15 8 15 3 + 3 = 3 + 3 = 6 x5 x3 5 ? 3 ? 1 3 1 5 = = 15 15 x5 x3

5 8 1 8 6 8 3 4 3 + 2 = 5 = 5

5 6 5 6 10 6 4 6 4 6 2 3 4 + 2 = 6 + = 6 + 1 = 7 = 7

3 7 5 7 8 7 1 7 1 7 3 + 1 = 4 + = 4 + 1 = 5

2 5 3 5 5 4 + 3 = 7 + = 7 + 1 = 8

1 2 7 10 5 10 7 10 12 10 4 + 2 = 4 + 2 = 6 + = x5 2 10 2 10 6 + 1 = 7 5 ? 1 2 = 10 x5

2 3 3 5 10 15 9 15 19 15 4 + 3 = 4 + 3 = 7 + = x5 x3 4 15 4 15 7 + 1 = 8 10 ? ? 9 2 3 3 5 = = 15 15 x5 x3

3 2 7 10 15 10 7 10 8 10 - = - = x5 15 ? 3 2 = 10 x5

3 2 7 10 15 10 7 10 8 10 - = - =

7 5 3 4 28 20 15 20 13 20 - = - = x4 x5 28 ? 15 ? 7 5 3 4 = = 20 20 x4 x5

7 5 3 4 13 20 - =

7 5 3 4 28 20 15 20 13 20 - = - =

3 4 7 8 14 8 7 8 7 8 1 - = - = x2 3 4 7 4 1 = 14 ? 7 4 = (1 x 4) + 3 = 7 8 x2

3 4 7 8 14 8 7 8 7 8 1 - = - =

1 3 1 2 8 6 3 6 5 6 1 - = - = x2 x3 1 3 4 3 1 = 8 ? 3 ? 4 3 1 2 = = (1 x 3) + 1 = 4 6 6 x2 x3

1 3 1 2 5 6 1 - =

1 3 1 2 8 6 3 6 5 6 1 - = - =

5 8 3 8 2 8 3 - 1 = 2

1 2 3 8 4 8 3 8 1 8 4 - 2 = 4 - 2 = 2 x4 4 ? 1 2 = 8 x4

2 3 1 4 8 12 3 12 5 12 5 - 3 = 5 - 3 = 2 x4 x3 8 ? 3 ? 2 3 1 4 = = 12 12 x4 x3

5 8 3 8 2 8 1 4 4 - 2 = 2 = 2

1 6 5 6 7 6 5 6 2 6 1 3 4 - 2 = 3 - 2 = = 1 1

2 7 5 7 9 7 5 7 4 7 3 - 1 = 2 - 1 = 1

2 5 3 5 7 5 3 5 4 5 4 - 3 = 3 - 3 =

1 5 2 5 6 5 2 5 4 5 5 - 2 = 4 - 2 = 2 1 5 6 5 1 =

1 5 1 3 3 15 5 15 18 15 5 15 13 15 4 - 3 = 4 - 3 = 3 - 3 = x3 x5 3 15 18 15 1 = 3 ? 5 ? 1 5 1 3 = = 15 15 x3 x5

3 4 4 5 15 20 16 20 35 20 16 20 19 20 6 - 3 = 6 - 3 = 5 - 3 = 2 x5 x4 15 20 35 20 1 = 15 ? 16 ? 3 4 4 5 = = 20 20 x5 x4

2 7 2 5 10 35 14 35 45 35 14 35 31 35 4 - 2 = 4 - 2 = 3 - 2 = 1 x5 x7 10 35 45 35 1 = 10 ? 14 ? 2 7 2 5 = = 35 35 x5 x7

2 5 Count from 0 in steps of . 2 5 4 5 1 1 5 1 3 5 2 2 2 5 2 4 5 3 1 5 3 3 5

2 9 Count from 0 in steps of . 2 9 4 9 6 9 8 9 1 1 9 1 3 9 1 5 9 1 7 9 2

3 4 Count from 0 in steps of . 3 4 1 1 2 2 1 4 3 3 3 4 4 1 2 5 1 4 6 6 3 4

3 4 1 2 Count back from in steps of . 5 5 3 4 5 1 4 4 3 4 4 1 4 3 3 4 3 1 4 2 3 4 2 1 4 1 3 4 1 1 4

2 5 4 Count back from in steps of . 4 3 3 5 3 1 5 2 4 5 2 2 5 2 1 3 5 1 1 5 4 5 2 5

8 9 3 9 Count back from in steps of . 7 7 8 9 7 5 9 7 2 9 6 8 9 6 5 9 6 2 9 5 8 9 5 5 9 5 2 9 4 8 9

1 of 24 = 8 3

1 of 30 = 6 5

1 of 24 = 4 6

1 of 400 = 100 100 x 4 = 400 4 1 of 210 = 70 70 x 3 = 210 3 1 1 of 215 = 43 4 3 x 5 5 2 1 5

3 x 21 63 3 4 3 4 of 21 = = = 15 4 4

2 x 23 46 1 5 2 5 of 23 = = = 9 5 5

2 x 17 34 1 3 2 3 of 17 = = = 11 3 3 3 x 14 42 2 5 3 5 of 14 = = = 8 5 5 5 x 9 45 3 6 5 6 of 9 = = = 7 6 6

3 3 x 5 4 15 4 3 x 5 = = = 3 4 4

2 2 x 6 3 12 3 x 6 = = = 4 3

3 4 9 4 1 1 2 x 3 = 6 + = 6 + 2 = 8 4 4

1 4 6 4 2 1 2 x 6 = 12 + = 12 + 1 = 12 + 1 4 2 1 = 13 2

1 3 7 3 1 1 2 x 7 = 14 + = 14 + 2 = 16 3 3 7 10 14 10 4 2 4 x 2 = 8 + = 8 + 1 = 9 10 5 1 6 9 6 3 1 5 x 9 = 45 + = 45 + 1 = 46 6 2

3 4 11 4 3 1 33 4 1 2 x 3 = x = = 8 4

1 4 9 4 6 1 54 4 2 4 1 2 2 x 6 = x = = 13 = 13 1 3 2 4 4 5 4 1

1 3 7 3 7 1 49 3 1 3 2 x 7 = x = = 16 1 6 1 3 3 4 9 1

7 10 47 10 2 1 94 10 4 2 5 4 x 2 = x = = 9 = 9 10 1 4 7 x 2 9 4

1 6 31 6 9 1 279 6 3 6 1 2 5 x 9 = x = = 46 = 46 3 1 x 9 4 6 3 6 2 7 9 6 2 7 9 2 3

To multiply a mixed number by a whole number, change the mixed number to an improper fraction and put the whole number over 1, then multiply, then change your answer to a mixed number. 3 4 11 4 3 1 33 4 1 4 2 x 3 = x = = 8

When multiplying by a mixed number, you can simplify by ‘cancelling’ a numerator and a denominator, which means finding a factor of both numbers and dividing by that factor. 1 4 9 4 6 1 3 27 2 1 2 2 x 6 = x = = 13 2

1 6 31 6 9 1 3 93 2 1 2 5 x 9 = x = = 46 2 1 3 7 3 7 1 49 3 1 3 2 x 7 = x = = 16 7 10 47 10 2 1 1 47 5 2 5 4 x 2 = x = = 9 5