Year 6 Arithmetic (SATs): Fractions, decimals, percentages and amounts
Part of the Year 6 Arithmetic (SATs) decimals and percentages chapter. Chapter overview · whole chapter on one page
Fractions, decimals, percentages and amounts
Rule
A percentage means "out of 100". 25% = 25/100 = 0.25 = 1/4.
To find a percentage of an amount, find 1% first (divide by 100), then multiply by the percentage.
Common equivalents: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
Key ideas
- A percentage is out of 100: 25% = 25/100.
- 1% of an amount is the amount divided by 100.
- Use fractions, decimals and percentages to compare values.
Method. Find 1% first, then multiply by 15.
- Find 1%. 1% is one hundredth, so divide the amount by 100.360 ÷ 100 = 3.6
- Multiply by 15. 15% is 15 lots of 1%.3.6 × 15 = 54
- Write the answer. 54
Check. 10% of 360 is 36, and 5% is 18, so 15% is 54. ✓
Method. Find 1%, then multiply by 20.
- Find 1%. 1% is one hundredth, so divide the amount by 100.85 ÷ 100 = 0.85
- Multiply by 20. 20% is 20 lots of 1%.0.85 × 20 = 17
- Write the answer. 17
Check. 20% is one fifth of 85, and 85 ÷ 5 = 17. ✓
Method. Work out both amounts, then compare.
- Work out 40% of 80. 1% of 80 is 0.8, so 40% is 32.32
- Work out 1/3 of 90. 90 ÷ 3 = 30.30
- Compare. 32 is greater than 30.40% of 80 is greater
- Write the answer. 40% of 80
Check. 40% of 80 is 32 and 1/3 of 90 is 30. ✓
Watch out. Compare the amounts you have worked out, not the percentage and the fraction.
Exercise 4E Practice: fractions, decimals, percentages and amounts
Non-calculatorMethod. Make the bottom 10, 100 or 1000 by multiplying.
- Write over 10, 100 or 1000. 3/5 is the same as the decimal over the matching power of 10.3/5
- Write the decimal. Read the top number with the decimal point in place.0.6
- Write the answer. 0.6
Check. 0.6 is 3/5. ✓
Method. Make the bottom 10, 100 or 1000 by multiplying.
- Write over 10, 100 or 1000. 1/8 is the same as the decimal over the matching power of 10.1/8
- Write the decimal. Read the top number with the decimal point in place.0.125
- Write the answer. 0.125
Check. 0.125 is 1/8. ✓
Method. Make the bottom 10, 100 or 1000 by multiplying.
- Write over 10, 100 or 1000. 7/10 is the same as the decimal over the matching power of 10.7/10
- Write the decimal. Read the top number with the decimal point in place.0.7
- Write the answer. 0.7
Check. 0.7 is 7/10. ✓
Method. Make the bottom 10, 100 or 1000 by multiplying.
- Write over 10, 100 or 1000. 3/4 is the same as the decimal over the matching power of 10.3/4
- Write the decimal. Read the top number with the decimal point in place.0.75
- Write the answer. 0.75
Check. 0.75 is 3/4. ✓
Method. Make the bottom 10, 100 or 1000 by multiplying.
- Write over 10, 100 or 1000. 9/20 is the same as the decimal over the matching power of 10.9/20
- Write the decimal. Read the top number with the decimal point in place.0.45
- Write the answer. 0.45
Check. 0.45 is 9/20. ✓
Method. Multiply by 100 to get out of 100.
- Multiply by 100. 3/5 × 100 = 60.3/5 × 100 = 60
- Write it as a percentage. That many out of 100 is the percentage.60%
- Write the answer. 60%
Check. 0.6 = 60%. ✓
Method. Multiply by 100 to get out of 100.
- Multiply by 100. 1/4 × 100 = 25.1/4 × 100 = 25
- Write it as a percentage. That many out of 100 is the percentage.25%
- Write the answer. 25%
Check. 0.25 = 25%. ✓
Method. Multiply by 100 to get out of 100.
- Multiply by 100. 9/20 × 100 = 45.9/20 × 100 = 45
- Write it as a percentage. That many out of 100 is the percentage.45%
- Write the answer. 45%
Check. 0.45 = 45%. ✓
Method. Multiply by 100 to get out of 100.
- Multiply by 100. 7/10 × 100 = 70.7/10 × 100 = 70
- Write it as a percentage. That many out of 100 is the percentage.70%
- Write the answer. 70%
Check. 0.7 = 70%. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.360 ÷ 100 = 3.6
- Multiply by 15. 15% is 15 lots of 1%.3.6 × 15 = 54
- Write the answer. 54
Check. 15% is about 54. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.85 ÷ 100 = 0.85
- Multiply by 20. 20% is 20 lots of 1%.0.85 × 20 = 17
- Write the answer. 17
Check. 20% is about 17. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.240 ÷ 100 = 2.4
- Multiply by 35. 35% is 35 lots of 1%.2.4 × 35 = 84
- Write the answer. 84
Check. 35% is about 84. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.60 ÷ 100 = 0.6
- Multiply by 5. 5% is 5 lots of 1%.0.6 × 5 = 3
- Write the answer. 3
Check. 5% is about 3. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.250 ÷ 100 = 2.5
- Multiply by 12. 12% is 12 lots of 1%.2.5 × 12 = 30
- Write the answer. 30
Check. 12% is about 30. ✓
Method. Find 1% by dividing by 100, then multiply by the percentage.
- Find 1%. 1% is one hundredth, so divide the amount by 100.300 ÷ 100 = 3
- Multiply by 7. 7% is 7 lots of 1%.3 × 7 = 21
- Write the answer. 21
Check. 7% is about 21. ✓
Method. Find 35% of 240.
- Find 1%. 1% is one hundredth, so divide the amount by 100.240 ÷ 100 = 2.4
- Multiply by 35. 35% is 35 lots of 1%.2.4 × 35 = 84
- Write the answer. 84
Check. Half of 240 is 120, and 35% is a bit less, so 84. ✓
Method. Work out both amounts, then compare.
- 40% of 80. 1% is 0.8, so 40% is 32.32
- 1/3 of 90. 90 ÷ 3 = 30.30
- Compare. 32 is more than 30.40% of 80
- Write the answer. 40% of 80
Check. 32 > 30. ✓
Method. Work out both amounts.
- 50% of 30. Half of 30 is 15.15
- 25% of 60. A quarter of 60 is 15.15
- Write the answer. Yes
Check. Both amounts are 15. ✓
Method. Find 45% of 80.
- Find 1%. 1% is one hundredth, so divide the amount by 100.80 ÷ 100 = 0.8
- Multiply by 45. 45% is 45 lots of 1%.0.8 × 45 = 36
- Write the answer. 36
Check. Half of 80 is 40, and 45% is a little less, 36. ✓
Method. Convert each score to a percentage.
- Ali. 18/20 = 9/10 = 90%.90%
- Priya. 45/50 = 9/10 = 90%.90%
- Write the answer. Both score 90%: Ali scored 90% and so did Priya, because 18/20 and 45/50 both equal 9/10.
Check. 18/20 and 45/50 are both 0.9. ✓