Work Out the Percentage of an Amount
Master the universal formula, then practise with real questions
Universal Formula
Value ÷ 100 × The % Required
✏️ Worked Example 1
What is 25% of 800?
- 800 ÷ 100 × 25
- = 8 × 25
= 200
✏️ Worked Example 2
What is 5% of 235?
- 235 ÷ 100 × 5
- = 2.35 × 5
= 11.75
🎯 Now You Try It
Calculate 7% of 340.
Use: 340 ÷ 100 × 7. Divide first, then multiply.
Full Working
340 ÷ 100 = 3.43.4 × 7
= 23.8
Find 56% of $8,200.
8200 ÷ 100 = 82. Now multiply 82 × 56.
Full Working
8200 ÷ 100 = 8282 × 56
= $4,592
Calculate 83% of 9,000.
9000 ÷ 100 = 90. Then 90 × 83.
Full Working
9000 ÷ 100 = 9090 × 83
= 7,470
A bag of sugar contains 420g. A special offer packet contains an extra 15%. How much sugar is in the special offer packet?
g
Find 15% of 420, then add to 420. Or: 420 ÷ 100 × 115 directly.
Full Working
420 ÷ 100 × 15 = 63g extra420 + 63
= 483g
A car costs £7,500. In a sale it is reduced by 20%. What is the new price?
Find 20% of 7500, then subtract. Or multiply by 80%.
Full Working
7500 ÷ 100 × 20 = £1,5007500 − 1500
= £6,000
There are 52,800 fans at a football match. 37% support Rovers. How many fans support City?
63% support City (100−37). Find 63% of 52,800.
Full Working
100% − 37% = 63% support City52800 ÷ 100 × 63
= 33,264 City fans
🎉 Section 1 Complete!
Great work on percentage of an amount!
Express One Amount as a Percentage of Another
Convert a value to a percentage of the whole
Formula
Value ÷ The Whole × 100
✏️ Worked Example
For every 50 students, 29 are girls. Work out 29 as a percentage of 50.
- 29 ÷ 50 × 100
- = 0.58 × 100
= 58%
🎯 Now You Try It
Work out 15 as a percentage of 80.
%
15 ÷ 80 × 100
Full Working
15 ÷ 80 × 100= 18.75%
Express 126 as a percentage of 360.
%
126 ÷ 360 × 100
Full Working
126 ÷ 360 × 100= 35%
Roger scores 6 out of 8 in a quiz. Work out his score as a percentage.
%
6 ÷ 8 × 100
Full Working
6 ÷ 8 × 100= 75%
James scored: Music 30/90, Drama 48/150, Art 35/120. Enter the highest percentage score (to 2 d.p.).
%
Calculate all three. Music=30÷90×100, Drama=48÷150×100, Art=35÷120×100.
Full Working
Music: 30÷90×100 = 33.33%Drama: 48÷150×100 = 32%
Art: 35÷120×100 = 29.17%
✅ Highest = Music (33.33%)
Susan brings 500 flapjacks and sells 450. What percentage did she sell?
450 ÷ 500 × 100
Full Working
450 ÷ 500 × 100= 90%
🎉 Section 2 Complete!
Excellent! Converting amounts to percentages mastered!
Calculate Percentage Change
Increase or decrease — any size
Formula
Difference ÷ Original Value × 100
✏️ Worked Example
A painting rises from £120,000 to £192,000. Work out the percentage increase.
- Difference = 192,000 − 120,000 = 72,000
- 72,000 ÷ 120,000 × 100
= 60% increase
🎯 Now You Try It
Alice buys a book for £19.80 and sells it for £12.87. Calculate the percentage decrease.
%
Difference = 19.80 − 12.87. Divide by ORIGINAL price × 100.
Full Working
19.80 − 12.87 = 6.936.93 ÷ 19.80 × 100
= 35%
A can of juice increases from 250ml to 330ml. Work out the percentage increase.
%
330 − 250 = 80. Then 80 ÷ 250 × 100.
Full Working
330 − 250 = 8080 ÷ 250 × 100
= 32%
Susan buys an antique for £120 and sells it for £216. Work out her percentage profit.
%
216 − 120 = 96. Then 96 ÷ 120 × 100.
Full Working
216 − 120 = £9696 ÷ 120 × 100
= 80%
A website had 140,000 views in March and 198,800 in April. Work out the percentage increase.
%
198800 − 140000 = 58800. Divide by ORIGINAL (140000) × 100.
Full Working
198,800 − 140,000 = 58,80058,800 ÷ 140,000 × 100
= 42%
Peter's weight decreases from 80kg to 64kg. Calculate the percentage decrease.
80 − 64 = 16. Then 16 ÷ 80 × 100.
Full Working
80 − 64 = 1616 ÷ 80 × 100
= 20%
🎉 Section 3 Complete!
Brilliant — percentage change nailed!
Calculate Original Value After a Change
Reverse / Inverse Percentages
Key Idea
Given amount ÷ % it represents × 100
✏️ Worked Example
After 4% interest, Patrick has £291.20. How much did he invest?
- £291.20 = 104% of original
- 291.20 ÷ 104 × 100
= £280
🎯 Now You Try It
Jennifer has 54 DVDs — 80% MORE than last month. How many did she have last month?
54 = 180% (original + 80% more). So: 54 ÷ 180 × 100.
Full Working
54 = 180%54 ÷ 180 × 100
= 30 DVDs
Lauren gets a 12% pay rise. Her new salary is £24,080. What was her salary before?
£24,080 = 112%. So: 24080 ÷ 112 × 100.
Full Working
24,080 = 112%24,080 ÷ 112 × 100
= £21,500
Jacob pays £84 for a watch including 20% VAT. What is the price without VAT?
£84 = 120% (includes VAT). So: 84 ÷ 120 × 100.
Full Working
84 = 120%84 ÷ 120 × 100
= £70
A fish tank loses 45% of its water, leaving 363 litres. How much water was there before?
l
363 = 55% (lost 45%). So: 363 ÷ 55 × 100.
Full Working
363 = 55% (100−45)363 ÷ 55 × 100
= 660 litres
A limited edition bag of flour (25% more) contains 650g. How much is in the standard bag?
650 = 125%. So: 650 ÷ 125 × 100.
Full Working
650 = 125%650 ÷ 125 × 100
= 520g
🎉 Section 4 Complete!
Superb — reverse percentages mastered!
Simple & Compound Interest
Percentages vs Decimals approach
Simple Interest
Same interest earned each year
Compound Interest
Amount × (1 + rate)ⁿ or multiply each year
✏️ Compound — Worked Example
Fiona invests £1,600 for 4 years at 4% compound interest. Total?
- 1600 × 1.04 × 1.04 × 1.04 × 1.04
= £1,871.77
🎯 Now You Try It
Sebastian leaves £3,000 in the bank for 2 years at 2% compound interest. What is the total?
Year 1: 3000 × 1.02. Year 2: multiply by 1.02 again.
Full Working
Year 1: 3000 × 1.02 = £3,060Year 2: 3060 × 1.02
= £3,121.20
A car worth £18,000 depreciates by 15% each year for 3 years. What is it worth at the end?
Depreciate by 15% = multiply by 0.85 each year, 3 times.
Full Working
Year 1: 18000 × 0.85 = £15,300Year 2: 15300 × 0.85 = £13,005
Year 3: 13005 × 0.85
= £11,054.25
Jenny invests £400 for 2 years at 5% compound interest. Tim says interest will be £40. Enter the actual total interest.
400 × 1.05 × 1.05, then subtract £400 to find interest.
Full Working
400 × 1.05 = £420420 × 1.05 = £441
Interest = 441 − 400
= £41 (Tim is wrong!)
James (100kg) loses 3% per month for 6 months (compound). What does he weigh after 6 months? (2 d.p.) Has he hit his 80kg target?
kg
100 × 0.97⁶ (multiply by 0.97 six times). Is result ≤ 80?
Full Working
100 × 0.97⁶= 83.30kg
❌ James has NOT reached 80kg
🎉 All Sections Complete!
Outstanding — ready to see your final results!
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Section Breakdown
Work Out the Percentage of an Amount
Level 1 · Simple whole-number percentages
Formula
Value ÷ 100 × The % Required
✏️ Worked Example
What is 10% of 350?
- 350 ÷ 100 × 10
- = 3.5 × 10
= 35
🎯 Now You Try It
Find 10% of 450.
Divide 450 by 100 to get 1%, then multiply by 10.
Full Working
450 ÷ 100 = 4.54.5 × 10
= 45
Work out 25% of 200.
200 ÷ 100 = 2. Then 2 × 25.
Full Working
200 ÷ 100 = 22 × 25
= 50
A shop has 80 items. 15% are on sale. How many items are on sale?
80 ÷ 100 × 15
Full Working
80 ÷ 100 × 15= 12 items
A meal costs £40. VAT is 20%. What is the VAT amount?
40 ÷ 100 × 20
Full Working
40 ÷ 100 × 20= £8
A worker earns £320 per week. They receive a 5% bonus. How much is the bonus?
320 ÷ 100 × 5
Full Working
320 ÷ 100 × 5= £16
🎉 Section 1 Complete!
Great start!
Percentage Increase & Decrease
Level 1 · Adding and subtracting percentages
Increase
Original + (Original ÷ 100 × %)
Decrease
Original − (Original ÷ 100 × %)
✏️ Worked Example
A TV costs £250. It is reduced by 20%. What is the new price?
- 250 ÷ 100 × 20 = £50 (reduction)
- 250 − 50
= £200
🎯 Now You Try It
A coat costs £60. It is reduced by 10% in a sale. What is the new price?
10% of 60 = £6. Then 60 − 6.
Full Working
60 ÷ 100 × 10 = £660 − 6
= £54
A salary is £18,000 per year. It increases by 5%. What is the new salary?
5% of 18000 = 900. Then 18000 + 900.
Full Working
18000 ÷ 100 × 5 = £90018000 + 900
= £18,900
A phone costs £120. The shop adds 20% profit. What is the selling price?
20% of 120 = £24. Then 120 + 24.
Full Working
120 ÷ 100 × 20 = £24120 + 24
= £144
A class has 30 students. 30% are absent one day. How many students are present?
30% of 30 = 9 absent. Present = 30 − 9.
Full Working
30 ÷ 100 × 30 = 9 absent30 − 9
= 21 present
A house is worth £150,000. Its value increases by 8%. What is the new value?
8% of 150,000 = £12,000. Then add to original.
Full Working
150000 ÷ 100 × 8 = £12,000150,000 + 12,000
= £162,000
🎉 Section 2 Complete!
Excellent work!
Simple Interest & Everyday %
Level 1 · Interest, discounts and real-life problems
Simple Interest
Amount × rate ÷ 100 × years
✏️ Worked Example
£500 in a savings account earns 3% simple interest per year. How much interest after 2 years?
- Interest per year: 500 ÷ 100 × 3 = £15
- Total: 15 × 2
= £30 interest
🎯 Now You Try It
£400 earns 5% simple interest per year. How much interest is earned in 1 year?
400 ÷ 100 × 5
Full Working
400 ÷ 100 × 5= £20
Tom puts £1,200 into an account earning 4% simple interest per year. How much is in the account after 3 years?
Interest per year = 1200 ÷ 100 × 4 = £48. Multiply by 3, then add to original.
Full Working
1200 ÷ 100 × 4 = £48/year48 × 3 = £144 interest
1200 + 144
= £1,344
A jacket costs £85. There is a 20% discount. What is the sale price?
20% of 85 = £17. Then 85 − 17.
Full Working
85 ÷ 100 × 20 = £1785 − 17
= £68
A bricklayer earns £620 per week. He gets a 3% pay rise. What is his new weekly wage?
3% of 620 = £18.60. Add to original.
Full Working
620 ÷ 100 × 3 = £18.60620 + 18.60
= £638.60
A care home has 40 residents. 35% require specialist support. How many do NOT need specialist support?
35% of 40 = 14. Then 40 − 14.
Full Working
40 ÷ 100 × 35 = 1440 − 14
= 26 residents
🎉 All Level 1 Sections Complete!
Fantastic work — ready for your results!
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Section Breakdown
⚡ Challenge Mode
5 worded real-world questions. No hints. Race against the clock!
5Questions
15Pts Available
15 minTotal Time
🧠
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Five real-world percentage problems — worded, timed, no hints allowed!
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