Mathematics • Year 8 • Unit 1 • Lesson 3
Percentage of a Quantity
Build fluency with the two methods from Lesson 3: the multiplier method (% → decimal → ×) and the unitary method (find 1% first, then scale). One worked example, one guided, then eight independent problems.
1. I do, fully worked example
Read every line. We'll do it two ways, the multiplier method AND the unitary method, and confirm we get the same answer.
Problem. Find 15% of $60.
Method 1, Multiplier method.
Step 1: convert 15% to a decimal → 15% = 0.15.
Step 2: multiply by the quantity → 0.15 × 60 = 9.
Reason: "% of" really means "× (% as a decimal)". This is fastest on a calculator.
Method 2, Unitary method.
Step 1: find 1% of $60 → $60 ÷ 100 = $0.60.
Step 2: scale up to 15% → 15 × $0.60 = $9.
Reason: if you know what ONE percent is worth, you can scale to ANY percent by multiplying. Great for mental maths.
Check both agree.
Both methods give $9. ✓
Answer: 15% of $60 = $9.
2. We do, fill in the missing steps
Use the unitary method for this one. Fill in each blank. 4 marks
Problem. Find 8% of $200.
Step 1, Find 1% of $200:
$200 ÷ 100 = $______
Step 2, Scale up to 8%:
8 × $______ = $______
Step 3, Check using the multiplier method:
8% = ______, then ______ × 200 = $______
Step 4, Final answer:
8% of $200 = $______
3. You do, independent practice
Show your working under each problem. Pick whichever method (multiplier or unitary) you prefer. The first four are foundation (one-step). The middle two are standard. The last two are extension.
Foundation, one-step
3.1 Find 10% of $50. 1 mark
3.2 Find 50% of 80 kg. 1 mark
3.3 Find 25% of $40. 1 mark
3.4 Find 1% of $300 (this is the start of any unitary calculation). 1 mark
Standard, choose your method
3.5 Find 20% of $75. Show which method (multiplier or unitary) you used. 2 marks
3.6 Find 12% of $45. Show working using the multiplier method. 2 marks
Extension, combine building blocks
3.7 Find 17% of $240 using mental maths only (use the building blocks 10%, 5% and 1%). Show how you built it. 3 marks
3.8 Find 7.5% of $80. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (faded 8% of $200)
Step 1: $200 ÷ 100 = $2.
Step 2: 8 × $2 = $16.
Step 3 (check): 8% = 0.08, then 0.08 × 200 = $16. ✓
Step 4: 8% of $200 = $16.
3.1-10% of $50
10% = 0.10. So 0.10 × 50 = $5. (Quick mental trick: 10% is "divide by 10".)
3.2-50% of 80 kg
50% = half. Half of 80 = 40 kg.
3.3-25% of $40
25% = 1/4. One quarter of $40 = $40 ÷ 4 = $10. (Multiplier method: 0.25 × 40 = $10.)
3.4-1% of $300
$300 ÷ 100 = $3.
3.5-20% of $75
Multiplier method: 0.20 × 75 = $15. (Unitary check: 1% = $0.75, then 20 × $0.75 = $15. ✓)
3.6-12% of $45 (multiplier)
12% = 0.12. 0.12 × 45 = $5.40.
3.7-17% of $240 (mental)
Building blocks: 10% of $240 = $24. 5% = half of $24 = $12. 1% of $240 = $2.40.
Then 17% = 10% + 5% + 2 × 1% = $24 + $12 + $4.80 = $40.80.
(Multiplier check: 0.17 × 240 = $40.80. ✓)
3.8-7.5% of $80
7.5% = 0.075. 0.075 × 80 = $6. (Unitary check: 1% = $0.80; 7 × $0.80 = $5.60; 0.5 × $0.80 = $0.40; total $6.)