Use 50%, 25%, 10%, 5% and 1% as building blocks to find percentages without a calculator
Combine building blocks to find any percentage (e.g. 35% = 30% + 5%)
Calculate complex percentages such as 17.5% and 12.5%
Apply percentage methods to real-life contexts including VAT and discounts
Real-World Applications
Shopping: Calculating a 10% discount quickly — divide by 10 mentally — helps you check whether a sale price is correct without reaching for a calculator.
Finance: Mental maths for tips and tax — finding 20% (double 10%) or 15% (10% + half of 10%) are everyday skills for managing money.
Everyday life: Estimating percentages without a calculator — such as working out a rough tip or a quick discount check — is a core life skill.
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Key rule: Always find 10% first (move decimal one place left), then halve it to get 5%. These two steps unlock almost every percentage you need!
✓ Quick Check 1 — Building blocks: 50%, 25%, 10%
Question 1 of 10
Combining Building Blocks
Once you have the building blocks, add them together to reach any percentage. Think of it like making change with coins — use the largest blocks first.
Example 3 — Find 35% of £80
Step 1
Break 35% into: 30% + 5%
Step 2
10% of £80 = £8, so 30% = 3 × £8 = £24
Step 3
5% = £8 ÷ 2 = £4
Step 4
35% = £24 + £4 = £28
Example 4 — Find 15% of £260
Step 1
15% = 10% + 5%
Step 2
10% of £260 = £26
Step 3
5% = £26 ÷ 2 = £13
Step 4
15% = £26 + £13 = £39
Example 5 — Find 45% of £360
Step 1
45% = 50% − 5% (subtraction trick)
Step 2
50% of £360 = £180
Step 3
5% = 10% ÷ 2 = £36 ÷ 2 = £18
Step 4
45% = £180 − £18 = £162
Subtraction trick: For percentages just below a round number (e.g. 45%, 95%), it is often faster to find the round percentage and subtract. 45% = 50% − 5%.
✓ Quick Check 2 — Combining building blocks
Question 1 of 10
More Complex Percentages: 17.5%, 12.5% and VAT
Percentages like 17.5% (old UK VAT) and 12.5% (common tip) are still just combinations of building blocks. The key is extending the chain: 10% → 5% → 2.5%.
Example 6 — Find 17.5% of £160
Step 1
17.5% = 10% + 5% + 2.5%
Step 2
10% of £160 = £16
Step 3
5% = £16 ÷ 2 = £8
Step 4
2.5% = £8 ÷ 2 = £4
Step 5
17.5% = £16 + £8 + £4 = £28
Example 7 — Find 12.5% of £240
Step 1
12.5% = 10% + 2.5%
Step 2
10% of £240 = £24
Step 3
5% = £12, so 2.5% = £12 ÷ 2 = £6
Step 4
12.5% = £24 + £6 = £30
Shortcut
12.5% = \(\frac{1}{8}\), so £240 ÷ 8 = £30 ✓
Example 8 — A meal costs £46. Add 20% VAT. What is the total?
Step 1
10% of £46 = £4.60
Step 2
20% = 2 × £4.60 = £9.20
Step 3
Total = £46 + £9.20 = £55.20
Fraction shortcut: \(12.5\% = \tfrac{1}{8}\) and \(37.5\% = \tfrac{3}{8}\). Dividing by 8 is often faster than doing all the building blocks step by step.
✓ Quick Check 3 — Complex percentages and real-life contexts
Question 1 of 10
Practice: Non-Calculator Percentage Problems
Use the building-block method. Type your numerical answer (e.g. 24), then click Check All.
#
Question
Answer
Result
1
10% of £90
2
25% of £120
3
5% of £60
4
35% of £80
5
15% of £140
6
20% of £75
7
12.5% of £160
8
17.5% of £200
9
75% of £320
10
65% of £40
⚠ Things to Watch Out For
Finding 10% by dividing by other numbers: 10% = ÷10 always. 50% = ÷2. 25% = ÷4. These are the only correct non-calculator shortcuts — never divide by 10 to find 50%.
Building blocks in wrong order: For 35%: find 10% first (÷10), then multiply by 3 for 30%, then add 5% (half of 10%). Always work from 10% downwards.
5% is half of 10%, not ÷5: If 10% of £80 = £8, then 5% = £4 (half of £8). Students often try to divide by 5 directly, which works but is slower non-calculator.
Adding percentages before finding amounts: For 35%, do NOT find 3% and 5% separately. Build from 10% blocks: 30% + 5%.
Percentage of a percentage: 15% of 30% of £200 ≠ 45% of £200. Each percentage applies to the RESULT of the previous one.