Mathematics • Year 7 • Unit 1 • Lesson 13
Percentages
Build the basics: % means per hundred. Convert between percentages, fractions, and decimals, find a percentage of an amount, and express one number as a percentage of another.
1. I do — fully worked example
Watch a worked "find a percentage of an amount" example, with two methods side by side.
Problem. Find 35% of $80.
Step 1 — Convert the percentage to a decimal.
35% = 35 ÷ 100 = 0.35.
Reason: per cent means "per hundred", so we divide by 100. Move the decimal 2 places left.
Step 2 — Method 1: Multiply the decimal by the amount.
0.35 × 80 = 28.
Reason: "of" means multiply. (35 × 80 = 2800, then 2 d.p. → 28.00 = 28.)
Step 3 — Method 2 (mental): use the 10% trick.
10% of $80 = $8. So 30% = 3 × $8 = $24. 5% = half of 10% = $4. 35% = 30% + 5% = $24 + $4 = $28.
Reason: 10% is just divide by 10. From there you can build any percentage by scaling.
Step 4 — Check both methods agree.
$28 (decimal method) = $28 (mental method) ✓.
Answer: 35% of $80 = $28.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Find 15% of $120.
Step 1 — Convert 15% to a decimal:
15% = 15 ÷ 100 = _______.
Step 2 — Method 1: decimal × amount.
_______ × $120 = $_______.
Step 3 — Method 2: 10% trick. 10% of $120 = $_______ (just divide by 10). 5% of $120 = half of 10% = $_______. 15% = 10% + 5% = $_______ + $_______ = $_______.
Step 4 — Check both methods agree:
Decimal method = $_______ ; Mental method = $_______ ; same? _______
3. You do — independent practice
Show working under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Find 25% of 120. (Hint: 25% = 1/4.) 1 mark
3.2 Convert 0.08 to a percentage. 1 mark
3.3 Convert 60% to a fraction in simplest form and to a decimal. 1 mark
3.4 Find 20% of $150 using the 10% trick. 1 mark
Standard — combine two ideas
3.5 Find 40% of 90. Show two methods: decimal × amount, and the 10% trick. 2 marks
3.6 Express 14 out of 40 as a percentage. Simplify the fraction first if possible. 2 marks
Extension — push your thinking
3.7 Find 150% of 40. (Hint: percentages over 100% mean more than the whole.) Show your working and explain why your answer is larger than 40. 3 marks
3.8 A team won 16 out of 25 games this season. (a) What percentage did they win? (b) What percentage did they lose (assuming no draws)? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (15% of $120)
Step 1: 15 ÷ 100 = 0.15.
Step 2: 0.15 × $120 = $18.
Step 3: 10% of $120 = $12. 5% = $6. 15% = $12 + $6 = $18.
Step 4: $18 = $18 ✓.
3.1 — 25% of 120
25% = 1/4. 120 ÷ 4 = 30. (Or: 0.25 × 120 = 30.)
3.2 — 0.08 as a percentage
Multiply by 100 (move dot 2 places right): 0.08 × 100 = 8%.
3.3 — 60% as a fraction and decimal
Fraction: 60/100 = 3/5 (÷ 20). Decimal: 60 ÷ 100 = 0.6.
3.4 — 20% of $150 (10% trick)
10% of $150 = $15. 20% = 2 × $15 = $30.
3.5 — 40% of 90
Decimal method: 40% = 0.40. 0.40 × 90 = 36.
10% method: 10% of 90 = 9. 40% = 4 × 9 = 36. ✓
3.6 — 14 out of 40 as a %
14/40 = 7/20 (÷ 2). 7/20 × 100 = 700 ÷ 20 = 35%. (Or: 7/20 = 0.35 = 35%.)
3.7 — 150% of 40
150% = 1.5 (as a decimal). 1.5 × 40 = 60. The answer is larger than 40 because 150% means more than the whole (one whole 40, plus another half of 40 = 20, total 60). Whenever the % is greater than 100, the multiplier is greater than 1, so the answer grows.
3.8 — Team won 16 out of 25
(a) 16/25 × 100 = 1600 ÷ 25 = 64% won.
(b) Lost = 25 − 16 = 9 games. 9/25 × 100 = 900 ÷ 25 = 36% lost. (Check: 64% + 36% = 100% ✓.)