Year 6 Maths reasoning (SATs): Fractions, decimals and percentages

Method. Think of 3/4 as 3 quarters.

1. Use a quarter. 1/4 = 0.25.
   0.25
2. Multiply by 3. 3 x 0.25 = 0.75.
   0.75
3. Write the answer.
   0.75

Check. 0.75 = 75/100 = 3/4. ✓

Method. A percentage is out of 100.

1. Write as hundredths. 0.2 = 0.20 = 20/100.
   20/100
2. Write as a percentage. 20 hundredths is 20%.
   20%
3. Write the answer.
   20%

Check. 20 out of 100 is 20%. ✓

Method. Write as a decimal, then multiply by 100.

1. Write as a decimal. 3/5 = 0.6.
   0.6
2. Multiply by 100. 0.6 x 100 = 60, so 60%.
   60%
3. Write the answer.
   60%

Check. 60% of 100 = 60, and 0.6 = 60/100. ✓

Method. Find 1% first, then multiply.

1. Find one per cent. Divide 84 by 100.
   84 / 100 = 0.84
2. Multiply by the number of per cent. Multiply the answer by 25.
   0.84 x 25 = 21
3. Write the answer. 25% of 84 is 21.
   21
4. Write the answer.
   21

Check. 1% of 84 is 0.84, so 25% is 21. ✓

Method. Find 1% first, then multiply.

1. Find one per cent. Divide 300 by 100.
   300 / 100 = 3
2. Multiply by the number of per cent. Multiply the answer by 7.
   3 x 7 = 21
3. Write the answer. 7% of 300 is 21.
   21
4. Write the answer.
   21

Check. 1% of 300 is 3, so 7% is 21. ✓

Method. Find 1% first, then multiply.

1. Find one per cent. Divide 60 by 100.
   60 / 100 = 0.6
2. Multiply by the number of per cent. Multiply the answer by 35.
   0.6 x 35 = 21
3. Write the answer. 35% of 60 is 21.
   21
4. Write the answer.
   21

Check. 1% of 60 is 0.6, so 35% is 21. ✓

Method. Divide by 10.

1. Divide by 10. 350 / 10 = 35.
   35
2. Write the answer.
   35

Check. 35 x 10 = 350. ✓

Method. Divide by 4, then multiply by 3.

1. Divide by 4. 48 / 4 = 12.
   12
2. Multiply by 3. 12 x 3 = 36.
   36
3. Write the answer.
   36

Check. 36 / 3 = 12, and 12 x 4 = 48. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. 0.25, 1/4 and 25/100 are all a quarter, which is 25%.
   0.25, 1/4, 25/100
3. Leave the others unticked. These do not match.
   2.5, 1/5 are not ticked
4. Write the answer.
   0.25, 1/4, 25/100

Check. Each ticked option is true. ✓

Watch out. 2.5 is 250%, not 25%, and 1/5 is 20%.

Method. Write 0.6 as a fraction and compare.

1. Write 0.6 as a fraction. 0.6 = 6/10 = 3/5.
   3/5
2. Compare. They are equal, so Ali is not right.
   equal
3. Write the answer.
   no

Check. 0.6 = 3/5. ✓

Method. Find 40% of 30.

1. Find 1%. 30 / 100 = 0.3.
   0.3
2. Find 40%. 0.3 x 40 = 12.
   12
3. Write the answer.
   12

Check. 12 out of 30 is 40%. ✓

Method. Find each part, then add.

1. Car. 30 / 5 = 6 pupils.
   6
2. Bus. 30 / 3 = 10 pupils.
   10
3. Add. 6 + 10 = 16 pupils.
   16
4. Write the answer.
   16

Check. 16 + 14 = 30. ✓

Method. Work out both amounts, then compare.

1. Work out 60% of 80. 80 / 100 = 0.8, and 0.8 x 60 = 48.
   48
2. Work out 3/4 of 60. 60 / 4 = 15, and 15 x 3 = 45.
   45
3. Compare. 48 is more than 45.
   48 > 45
4. Write the answer.
   60% of 80 is 48, and 3/4 of 60 is 45, so 60% of 80 is more.

Check. 48 > 45. ✓

Method. Write 0.4 as tenths.

1. Write as a fraction. 0.4 = 4/10 = 2/5.
   2/5
2. Write as a percentage. 0.4 = 40 hundredths = 40%.
   40%
3. Write the answer.
   2/5, 0.4 and 40%.

Check. 2/5 = 0.4 = 40%. ✓

Method. Find 1% and multiply by 15.

1. Find 1%. 240 / 100 = 2.4.
   2.4
2. Multiply by 15. 2.4 x 15 = 36.
   36
3. Write the answer.
   36

Check. 36 is 15% of 240. ✓

Method. Find 1/5 of 45.

1. Divide by 5. 45 / 5 = 9.
   9
2. Write the reduction. The reduction is 9 pounds.
   9 pounds
3. Write the answer.
   9

Check. 9 x 5 = 45. ✓