Percentage Price Play

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📖 Before You Begin: Percentage Multipliers

A multiplier is a number that tells you what to multiply an original amount by to find a new amount. We use multipliers because they combine the original amount and the percentage change in one calculation.

To find a multiplier for an increase, add the percentage to 100%, then change the result to a decimal:

Increase by 20%: 100% + 20% = 120% = 1.20

To find a multiplier for a decrease, subtract the percentage from 100%, then change the result to a decimal:

Decrease by 20%: 100% − 20% = 80% = 0.80

Always multiply the original amount by the multiplier:

New amount = original amount × multiplier

For example, to increase $50 by 20%, multiply $50 × 1.20. To decrease $50 by 20%, multiply $50 × 0.80. The amount you multiply is the original price or amount, unless the question says to use a new or discounted amount.

Warm-up A. A game costs $60 and its price increases by 25%. What multiplier should you use, and what should you multiply by it?

Warm-up B. A backpack costs $80 and is reduced by 15%. What multiplier should you use? Write the calculation you would do to find the sale price.

📚 Part 1: Quick Check (Multiple Choice)

1. A shirt costs $40 and is 25% off. What is the sale price?

$30

$35

$10

$25

2. A laptop costs $1,200. The store increases the price by 10%. New price is:

$1,320

$120

$1,202

$13,200

3. Which multiplier matches "increase by 20%"?

1.20

0.80

1.02

4. Check all that apply: Which are correct multipliers for "decrease by 30%"?

0.70

1.30

0.30

✏️ Part 2: Sale Price Calculations

Quick tip: To increase by 20% use multiplier 1.20 because 100% + 20% = 120% → 1.20. To decrease by 20% use 0.80 because 100% − 20% = 80% → 0.80. Multiply the original price by the multiplier to get the new price.

5. A jacket is $85. It's 20% off. Work out the sale price.

6. A bike is $350. The shop increases the price by 15% for a new model. Work out the new price.

7. Headphones are $220. Clearance: 35% off. Work out the sale price.

8. Sneakers cost $95. Price rises by 8% because of a supplier cost increase. Work out the new price.

9. A table is $460. First it is discounted 12%, then there is an extra 10% off the discounted price. Work out the final price.

📝 Part 3: Explain & Reflect

10. In your own words, explain why we multiply when we increase or decrease an amount by a percentage. Use an example if it helps.

11. Choose one product above. Show your step-by-step calculation and explain why you used the multiplier(s) you did.

✅ Answer Key: Percentage Multipliers

Warm-Up Solutions

Warm-up A: Increase by 25%: 100% + 25% = 125% = 1.25. Multiply the original price by the multiplier: $60 × 1.25 = $75.

Warm-up B: Decrease by 15%: 100% − 15% = 85% = 0.85. Calculation: $80 × 0.85 = $68.

Part 1 Solutions

1. $30. A 25% discount uses the multiplier 0.75: $40 × 0.75 = $30.

2. $1,320. A 10% increase uses the multiplier 1.10: $1,200 × 1.10 = $1,320.

3. 1.20. An increase of 20% means 100% + 20% = 120% = 1.20.

4. 0.70. A decrease of 30% means 100% − 30% = 70% = 0.70.

Part 2 Solutions

5. 20% off uses 0.80: $85 × 0.80 = $68.

6. A 15% increase uses 1.15: $350 × 1.15 = $402.50.

7. 35% off uses 0.65: $220 × 0.65 = $143.

8. An 8% increase uses 1.08: $95 × 1.08 = $102.60.

9. A 12% discount uses 0.88, followed by a 10% discount using 0.90: $460 × 0.88 × 0.90 = $364.32.

Part 3 Sample Solutions

10. Multiplication applies the percentage change to the original amount in one step. For example, increasing $50 by 20% means multiplying by 1.20, while decreasing $50 by 20% means multiplying by 0.80.

11. Sample answer using the jacket: 20% off means the multiplier is 0.80 because 100% − 20% = 80%. Then $85 × 0.80 = $68. The sale price is $68.