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% ✓.)