Mathematics • Year 8 • Unit 1 • Lesson 6
Percentage Decrease
Build fluency with shrinking a value by a percentage — using both the subtract method and the decrease multiplier (× (1 − rate)). One worked example, one guided example with blanks, then eight independent problems.
1. I do — fully worked example
Read every line. Each step has a short reason so you can see why, not just what.
Problem. A $250 pair of shoes is 30% off. Find the sale price using BOTH methods.
Step 1 — Method 1: find the discount in dollars first.
Discount = 30% of $250 = 0.30 × 250 = $75
Reason: "30% of" means multiply by the decimal 0.30. This gives the savings.
Step 2 — Subtract the discount from the marked price.
Sale = 250 − 75 = $175
Reason: original price minus the savings = what you actually pay.
Step 3 — Method 2: use the decrease multiplier.
Multiplier = 1 − 0.30 = 0.70
Reason: 30% off means you PAY 70%. The multiplier for "70% of" is 0.70.
Step 4 — Multiply.
Sale = 250 × 0.70 = $175
Reason: one calculator step instead of two. Same answer.
Answer: Sale price = $175. Method 2 is faster (one step vs two).
2. We do — fill in the missing steps
Same shape as Section 1, but with the working faded. Fill in each blank. 4 marks
Problem. An $80 backpack has 15% off. Find the sale price using the multiplier method.
Step 1 — What % do you actually pay? You pay ______% (i.e. 100 − 15).
Step 2 — Convert pay-% to a multiplier:
Multiplier = 1 − 0.15 = ______
Step 3 — Multiply the marked price by the multiplier:
Sale = 80 × ______ = $______
Step 4 — Check with the subtract method:
Discount = 0.15 × 80 = $______ Sale = 80 − ______ = $______
3. You do — independent practice
Show your working under each problem. The first four are foundation (single round-number discount). The middle two are standard (awkward % or two-step). The last two are extension (depreciation and chained discounts).
Foundation — single round-number discount
3.1 Decrease $160 by 25%. Use the multiplier method. 1 mark
3.2 A $45 shirt has 20% off. What is the sale price? 1 mark
3.3 Decrease 400 kg by 15%. 1 mark
3.4 Write the decrease multiplier for: (a) 40% off (b) 5% off (c) 50% off. 1 mark
Standard — awkward percentage or two-step
3.5 A $300 microwave is reduced by 22%. Find (a) the discount in dollars, and (b) the sale price. 2 marks
3.6 A $1500 fridge is reduced by 7.5%. Find the sale price. 2 marks
Extension — depreciation and chained discounts
3.7 A $30 000 car loses 20% of its value in the first year. What is it worth at the end of year 1? 2 marks
3.8 A $200 jacket is reduced by 25%, then a further 10% comes off the new price at the checkout. Find the final price using two separate multiplications. (Is this the same as "35% off"? Briefly state yes/no.) 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do ($80 at 15% off)
Step 1: You pay 85%.
Step 2: Multiplier = 1 − 0.15 = 0.85.
Step 3: Sale = 80 × 0.85 = $68.
Step 4 check: Discount = 0.15 × 80 = $12; Sale = 80 − 12 = $68. ✓
3.1 — Decrease $160 by 25%
Multiplier = 1 − 0.25 = 0.75. Sale = 160 × 0.75 = $120.
3.2 — $45 shirt, 20% off
Multiplier = 0.80. Sale = 45 × 0.80 = $36.
3.3 — 400 kg less 15%
Multiplier = 0.85. New = 400 × 0.85 = 340 kg.
3.4 — Decrease multipliers
(a) 40% off ⇒ 0.60. (b) 5% off ⇒ 0.95. (c) 50% off ⇒ 0.50.
3.5 — $300 microwave, 22% off
(a) Discount = 0.22 × 300 = $66. (b) Sale = 300 − 66 = $234 (or 300 × 0.78 = $234).
3.6 — $1500 fridge, 7.5% off
Multiplier = 1 − 0.075 = 0.925. Sale = 1500 × 0.925 = $1387.50.
3.7 — $30 000 car, 20% depreciation
Multiplier = 0.80. End of year 1 = 30 000 × 0.80 = $24 000.
3.8 — $200 jacket, 25% then 10%
First reduction: 200 × 0.75 = $150. Second reduction: 150 × 0.90 = $135. Not the same as "35% off" — that would give 200 × 0.65 = $130, $5 cheaper. The 10% at the checkout was only applied to the already-discounted $150, not the original $200.