Mathematics • Year 8 • Unit 1 • Lesson 5
Percentage Increase
Build fluency with the two methods from Lesson 5 — the add-the-increase method and the faster multiplier method (new = original × (1 + P/100)). One worked example, one guided, then eight independent problems.
1. I do — fully worked example
Read every line. We'll solve the same problem two ways — add method AND multiplier method — and check they match.
Problem. A job pays $18/hour. You get a 12% pay rise. What is your new hourly rate?
Method 1 — Add the increase.
Step 1: find 12% of $18 → 0.12 × 18 = $2.16 (this is the dollar increase).
Step 2: add the increase to the original → $18 + $2.16 = $20.16.
Reason: a percentage INCREASE adds a percentage of the original to itself. The increase tells you HOW MUCH it went up.
Method 2 — Multiplier method.
Step 1: the new wage is 100% + 12% = 112% of the old → multiplier = 1.12.
Step 2: new = original × multiplier → 1.12 × 18 = $20.16.
Reason: the multiplier formula is new = original × (1 + P/100). One multiplication does the whole job — fastest with a calculator.
Check.
Both methods give $20.16. ✓
Answer: The new hourly rate is $20.16.
2. We do — fill in the missing steps
Use the multiplier method for this one. Fill in each blank. 4 marks
Problem. A $50 jumper has a 20% markup. Find the new price.
Step 1 — Build the multiplier: 100% + 20% = ______%, so multiplier = ______.
Step 2 — Multiply original by multiplier:
new price = $50 × ______ = $______
Step 3 — Check with the add method:
20% of $50 = $______ , then $50 + $______ = $______
Step 4 — Final answer:
New price of the jumper = $______
3. You do — independent practice
Show your working under each problem. Pick whichever method you prefer. The first four are foundation (single-step, clean numbers). The middle two are standard. The last two are extension.
Foundation — single-step
3.1 Write the multiplier for a 5% increase. 1 mark
3.2 Write the multiplier for a 7.5% increase. 1 mark
3.3 Increase $200 by 10% using any method. 1 mark
3.4 Increase $80 by 25%. 1 mark
Standard — choose your method
3.5 Increase $340 by 15% using the multiplier method. 2 marks
3.6 Increase 80 kg by 7.5%. Show your working. 2 marks
Extension — money + checking
3.7 Increase $1250 by 4%. Solve using BOTH methods (add AND multiplier) and check they agree. 3 marks
3.8 A bike's price has been increased by 8% to $324. (a) Find the dollar increase (8% of the ORIGINAL price). (b) Find the original price. (Hint: $324 = original × 1.08, so original = $324 ÷ 1.08.) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded $50 + 20%)
Step 1: 100% + 20% = 120%, multiplier = 1.20.
Step 2: $50 × 1.20 = $60.
Step 3 (check): 20% of $50 = $10, then $50 + $10 = $60. ✓
Step 4: New price = $60.
3.1 — Multiplier for 5%
1 + 0.05 = 1.05.
3.2 — Multiplier for 7.5%
1 + 0.075 = 1.075.
3.3 — $200 + 10%
$200 × 1.10 = $220. (Or 10% of $200 = $20, $200 + $20 = $220.)
3.4 — $80 + 25%
$80 × 1.25 = $100. (Or 25% of $80 = $20, $80 + $20 = $100.)
3.5 — $340 + 15% (multiplier)
Multiplier = 1.15. $340 × 1.15 = $391.
3.6 — 80 kg + 7.5%
Multiplier = 1.075. 80 × 1.075 = 86 kg. (Add method check: 7.5% of 80 = 6 kg; 80 + 6 = 86. ✓)
3.7 — $1250 + 4% (both methods)
Add method: 4% of $1250 = 0.04 × 1250 = $50. New = $1250 + $50 = $1300.
Multiplier method: $1250 × 1.04 = $1300. ✓ Both match.
3.8 — Reverse 8% increase
(b) Original = $324 ÷ 1.08 = $300.
(a) Dollar increase = 8% of $300 = 0.08 × 300 = $24. (Check: $300 + $24 = $324. ✓)