% Percentages

Grade 5 · Number · Cambridge Primary Stage 5

What is a Percentage?

Per hundred; shading grids

FDP Equivalences

Fraction ↔ Decimal ↔ %

Percentage of Amount

Find 10%, then build up

% Problems

What % is A of B?

Ordering Mixed FDP

Convert to % first

1. What is a Percentage?

The word "percent" comes from Latin meaning per hundred. A percentage tells you how many out of 100.

% means "out of 100"
35% = 35 out of 100 = 35/100
Imagine a 10×10 grid with 100 squares. If 35 squares are coloured, that is 35%.
If all 100 are coloured → 100%. If none → 0%.
💡 100% means the whole thing. 50% means half. 25% means a quarter.

2. Fraction ↔ Decimal ↔ Percentage Equivalences

These three forms all show the same amount. You need to know the key ones by heart:

50%1/2 = 0.5
25%1/4 = 0.25
75%3/4 = 0.75
20%1/5 = 0.2
10%1/10 = 0.1
12.5%1/8 = 0.125
33.3%1/3 ≈ 0.333
40%2/5 = 0.4
Fraction → %: divide top by bottom, then ×100
% → Decimal: divide by 100
Decimal → %: multiply by 100

3. Percentage of an Amount

Method 1 (1% then multiply): Find 1% (divide by 100), then multiply.
30% of 80: 1% = 0.8, then 30 × 0.8 = 24
Method 2 (10% shortcut): Find 10% (divide by 10), then build up.
35% of 60: 10% = 6, so 30% = 18, 5% = 3, 35% = 18+3 = 21
Method 3 (multiply by decimal): Convert % to decimal, then multiply.
25% of 48: 0.25 × 48 = 12
💡 Use the 10% shortcut — it's usually the quickest for mental maths!

4. Simple Percentage Problems

What percentage is A of B?
Formula: (A ÷ B) × 100
Example: 15 is what % of 60? → (15 ÷ 60) × 100 = 25%
Percentage increase: Find the increase, then (increase ÷ original) × 100
A price goes from £40 to £50. Increase = £10. % increase = (10 ÷ 40) × 100 = 25%
Percentage decrease: Find the decrease, then (decrease ÷ original) × 100
Price drops from £80 to £60. Decrease = £20. % decrease = (20 ÷ 80) × 100 = 25%

5. Ordering Fractions, Decimals and Percentages

To put a mix of fractions, decimals and percentages in order, convert them all to percentages first.

Order 3/8, 40%, 0.35, 1/4 from smallest to largest:
3/8 = 37.5%, 40% = 40%, 0.35 = 35%, 1/4 = 25%
As %: 25%, 35%, 37.5%, 40%
Order: 1/4, 0.35, 3/8, 40%
💡 Convert everything to the same form before comparing — percentages are usually easiest.

Example 1 — FDP Equivalence

What is 3/4 as a percentage?
3 ÷ 4 = 0.75. Then 0.75 × 100 = 75%

Example 2 — Percentage of an Amount

Find 35% of 60.
10% of 60 = 6. 30% = 18. 5% = 3. 35% = 18 + 3 = 21

Example 3 — What % is A of B?

12 is what % of 48?
(12 ÷ 48) × 100 = 0.25 × 100 = 25%

Example 4 — Ordering

Which is bigger: 3/8 or 40%?
3/8 = 37.5%. Compare 37.5% and 40%. So 40% is bigger.

Example 5 — Percentage Increase

A shirt costs £24 and increases in price by 25%. What is the new price?
25% of £24 = £6. New price = £24 + £6 = £30

Percentage Calculator

Find a percentage of an amount, with step-by-step working.

Fraction ↔ Decimal ↔ % Converter

Exercise 1 — FDP Equivalences

Enter the percentage as a whole number (e.g. enter 25 for 25%).

1. 1/2 = ?%

2. 0.25 = ?%

3. 3/4 = ?%

4. 0.1 = ?%

5. 1/5 = ?%

6. 0.4 = ?%

7. 1/4 = ?%

8. 0.75 = ?%

9. 2/5 = ?%

10. 0.2 = ?%

Exercise 2 — Percentage of an Amount

Find the percentage of each amount. All answers are whole numbers.

1. 50% of 80

2. 25% of 48

3. 10% of 70

4. 30% of 60

5. 75% of 40

6. 20% of 55

7. 40% of 90

8. 15% of 80

9. 60% of 70

10. 5% of 120

Exercise 3 — What Percentage is A of B?

Enter the percentage as a whole number.

1. 15 is what % of 60?

2. 12 is what % of 48?

3. 20 is what % of 80?

4. 9 is what % of 36?

5. 30 is what % of 50?

6. 7 is what % of 70?

7. 18 is what % of 90?

8. 5 is what % of 20?

9. 24 is what % of 40?

10. 35 is what % of 140?

Exercise 4 — Ordering Mixed FDP

Enter 1 if the first value is bigger, enter 2 if the second value is bigger.

1. Is 3/8 bigger or smaller than 40%? (1 = 3/8 is bigger, 2 = 40% is bigger)

2. Is 0.3 bigger or smaller than 25%? (1 = 0.3 is bigger, 2 = 25% is bigger)

3. Is 1/2 bigger or smaller than 45%? (1 = 1/2 is bigger, 2 = 45% is bigger)

4. Is 0.65 bigger or smaller than 3/5? (1 = 0.65 bigger, 2 = 3/5 bigger)

5. Is 1/4 bigger or smaller than 30%? (1 = 1/4 bigger, 2 = 30% bigger)

6. Is 0.7 bigger or smaller than 3/4? (1 = 0.7 bigger, 2 = 3/4 bigger)

7. Is 4/5 bigger or smaller than 78%? (1 = 4/5 bigger, 2 = 78% bigger)

8. Is 0.33 bigger or smaller than 1/3? (1 = 0.33 bigger, 2 = 1/3 bigger)

9. Is 60% bigger or smaller than 0.6? (1 = 60% bigger, 2 = 0.6 bigger)

10. Is 9/10 bigger or smaller than 85%? (1 = 9/10 bigger, 2 = 85% bigger)

Exercise 5 — Percentage Increase and Decrease

Find the new price after the increase or decrease.

1. A coat costs £40. Price increases by 25%. New price?

2. A game costs £60. Price decreases by 10%. New price?

3. A book costs £20. Price increases by 50%. New price?

4. A TV costs £300. Price decreases by 20%. New price?

5. A shirt costs £24. Price increases by 25%. New price?

6. Tickets cost £80. Price decreases by 15%. New price?

7. A phone costs £200. Price increases by 30%. New price?

8. Food bill is £50. 10% off. New price?

9. Shoes cost £90. 20% increase. New price?

10. Rent is £600. 5% increase. New rent?

🏋️ Practice — Mixed Percentages (20 Questions)

1. 1/2 as a percentage?

2. 25% of 80 = ?

3. 18 is what % of 72? (enter whole number)

4. 0.6 as a percentage?

5. 40% of 55 = ?

6. Price is £50. Decreases 20%. New price?

7. 3/4 as a percentage?

8. 10% of 340 = ?

9. 5 is what % of 25?

10. 75% of 200 = ?

11. 0.05 as a percentage?

12. 35% of 60 = ?

13. 24 is what % of 60?

14. Price is £80. Increases 25%. New price?

15. 2/5 as a percentage?

16. 60% of 90 = ?

17. 16 is what % of 80?

18. Price is £120. Decreases 30%. New price?

19. 1/10 as a percentage?

20. 80% of 45 = ?

🏆 Challenge — Multi-Step Percentage Problems (8 Questions)

1. A jacket is £80. It is reduced by 30%, then reduced by a further 10% of the new price. What is the final price?

2. 45 out of 180 students walk to school. What percentage walk? (enter whole number)

3. A shop sells 600 items. 35% are clothes, 45% are electronics. How many items are neither? (enter the number)

4. A price increases from £40 to £52. What is the % increase?

5. 15% of a number is 12. What is the full number?

6. Order these from smallest: 3/8, 40%, 0.35. Which has the smallest value — enter 1 for 3/8, 2 for 40%, 3 for 0.35.

7. Sam scores 36 out of 48 on a test. What is his percentage score?

8. A school has 400 pupils. 55% are girls. How many boys are there?