Year 6 Arithmetic (SATs): Mental calculation with decimals and fractions

Method. Add the tenths: 6 + 8 = 14 tenths.

1. Add the tenths. 6 tenths + 8 tenths = 14 tenths.
   14 tenths
2. Write it as a decimal. 14 tenths is 1 whole and 4 tenths.
   1.4
3. Write the answer.
   1.4

Check. 1.4 - 0.8 = 0.6. ✓

Method. Subtract 2 from 4.2, then add back the 0.1 that was taken too much.

1. Subtract 2. 4.2 - 2 = 2.2.
   2.2
2. Add 0.1. 1.9 is 0.1 more than 2, so add 0.1 back.
   2.3
3. Write the answer.
   2.3

Check. 2.3 + 1.9 = 4.2. ✓

Method. Think of £3.50 + £2.75 in pence.

1. Change to pence. 350p + 275p = 625p.
   625p
2. Change back to pounds. 625p is £6.25.
   6.25
3. Write the answer.
   6.25

Check. 625 - 275 = 350. ✓

Method. Count up from 3.6 to 10.

1. Count up. 3.6 + 0.4 = 4, then 4 + 6 = 10.
   0.4 + 6 = 6.4
2. Write the answer.
   6.4

Check. 3.6 + 6.4 = 10. ✓

Method. Half of 18 is 9.

1. Halve 18. 18 ÷ 2 = 9.
   9
2. Write the answer.
   9

Check. 9 + 9 = 18. ✓

Method. Think of 1.2 as 1 and 0.2.

1. Split. 1 × 5 = 5 and 0.2 × 5 = 1.
   5 + 1
2. Add. 5 + 1 = 6.
   6
3. Write the answer.
   6

Check. 6 ÷ 5 = 1.2. ✓

Method. A quarter of 8 is 2.

1. Find a quarter of 8. 8 ÷ 4 = 2.
   2
2. Write the answer.
   2

Check. 2 × 4 = 8, so 0.25 × 8 = 2. ✓

Method. Divide by the bottom number, then multiply by the top number.

1. Divide the amount by the bottom number. 36 ÷ 3 = 12.
   36 ÷ 3 = 12
2. Multiply by the top number. Take 1 of those parts.
   12 × 1 = 12
3. Write the answer.
   12

Check. One 3th of 36 is 12, and 1 of those is 12. ✓

Method. Divide by the bottom number, then multiply by the top number.

1. Divide the amount by the bottom number. 20 ÷ 4 = 5.
   20 ÷ 4 = 5
2. Multiply by the top number. Take 3 of those parts.
   5 × 3 = 15
3. Write the answer.
   15

Check. One 4th of 20 is 5, and 3 of those is 15. ✓

Method. Divide by the bottom number, then multiply by the top number.

1. Divide the amount by the bottom number. 45 ÷ 5 = 9.
   45 ÷ 5 = 9
2. Multiply by the top number. Take 2 of those parts.
   9 × 2 = 18
3. Write the answer.
   18

Check. One 5th of 45 is 9, and 2 of those is 18. ✓

Method. Divide by the bottom number, then multiply by the top number.

1. Divide the amount by the bottom number. 80 ÷ 8 = 10.
   80 ÷ 8 = 10
2. Multiply by the top number. Take 5 of those parts.
   10 × 5 = 50
3. Write the answer.
   50

Check. One 8th of 80 is 10, and 5 of those is 50. ✓

Method. Add the two prices.

1. Add. £3.50 + £2.75 = £6.25.
   £6.25
2. Write the answer.
   £6.25

Check. £6.25 - £2.75 = £3.50. ✓

Method. Find one fifth of 45, then take two.

1. Divide the amount by the bottom number. 45 ÷ 5 = 9.
   45 ÷ 5 = 9
2. Multiply by the top number. Take 2 of those parts.
   9 × 2 = 18
3. Write the answer.
   18

Check. 18 + 27 = 45. ✓

Method. Subtract 0.9 from 2.4.

1. Subtract. 2.4 - 0.9 = 1.5.
   1.5
2. Write the answer.
   1.5 m

Check. 1.5 + 0.9 = 2.4. ✓

Method. Think of 0.5 as half.

1. Half of 30. 30 ÷ 2 = 15.
   15
2. Compare. 0.5 × 30 = 15 as well.
   15
3. Write the answer.
   Yes, because multiplying by 0.5 is the same as halving, and half of 30 is 15.

Check. 15 + 15 = 30. ✓

Method. Find 3/4 of 60, then add 0.5.

1. Find 3/4 of 60. 60 ÷ 4 = 15, then 15 × 3 = 45.
   45
2. Add 0.5. 45 + 0.5 = 45.5.
   45.5
3. Write the answer.
   45.5

Check. 45.5 - 0.5 = 45. ✓