Grade 8 Applying Percent Decrease: Unit Mastery Quiz

Position in the learning sequence

Use this quiz after instruction and practice on applying percent decrease. It assumes the learner already understands:

• percent as a number out of 100: see rea.m08.number.decimals-and-percents.percent-basics.unit-mastery-quiz
• finding a percent of a quantity: see rea.m08.number.decimals-and-percents.percent-quantity.unit-mastery-quiz
• decimal arithmetic accuracy: see rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz

This record does not reteach those topics; it checks whether the learner can combine them to solve percent decrease problems efficiently and correctly.

Assessment focus

A learner demonstrates mastery by being able to:

• identify a percent decrease situation
• convert the decrease percent into a decrease multiplier
• apply the multiplier accurately
• interpret answers in context, including money and measurement
• distinguish the new amount from the amount decreased by

Quiz instructions

• Total marks: 20
• Suggested time: 25 to 35 minutes
• Show working.
• Unless a question says otherwise, give exact decimal answers.
• For money, round to the nearest cent.

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Questions

1. Basic numeric decrease

Decrease 80 by 15%.

[2 marks]

2. Decimal quantity

Decrease 46.5 by 20%.

[2 marks]

3. Multiplier identification

A quantity is decreased by 37%.

1. Write the decrease multiplier.
2. Find the new value if the original amount was 240.

[2 marks]

4. Sale price

A jacket costs $72.00. It is on sale for 25% off. What is the sale price?

[2 marks]

5. Consecutive decreases

A phone plan costs $50.00 per month. First it is reduced by 10%, then the reduced price is decreased by another 20%.

What is the final monthly cost?

[2 marks]

6. Error analysis

A student says:

"To decrease 150 by 12%, I did 150 x 0.12 = 18, so the new amount is 18."

Explain the mistake and find the correct new amount.

[2 marks]

7. Measurement context

A rope is 18.4 m long. Its length decreases by 5% after being cut.

What is the new length?

[2 marks]

8. Reverse-structure without reverse-percent algebra

A store advertises "30% off" on a bicycle with an original price of $640.

1. How much is the discount?
2. What is the sale price?

Then explain why multiplying by 0.70 gives the sale price directly.

[2 marks]

9. Comparison of methods

Decrease 96 by 35%.

Solve it using:

1. the "find the decrease, then subtract" method
2. the multiplier method

Your two answers should match.

[2 marks]

10. Mixed application problem

A town had a population of 12,500. Over one year, the population decreased by 8%.

1. What was the population decrease?
2. What was the new population?
3. Is 0.08 or 0.92 the better multiplier for finding the new population directly? Explain.

[2 marks]

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Full marking solutions

1. Basic numeric decrease

Decrease 80 by 15%.

15% = 0.15, so the decrease multiplier is:

1 - 0.15 = 0.85

New amount:

80 x 0.85 = 68

Answer: 68

Marking guide:

• 1 mark for correct multiplier or correct decrease amount of 12
• 1 mark for correct final answer 68

2. Decimal quantity

Decrease 46.5 by 20%.

20% = 0.20, so the multiplier is:

1 - 0.20 = 0.80

New amount:

46.5 x 0.80 = 37.2

Answer: 37.2

Marking guide:

• 1 mark for using 0.80 or finding the decrease 9.3
• 1 mark for correct final answer 37.2

3. Multiplier identification

A quantity is decreased by 37%.

1. Decrease multiplier:

1 - 0.37 = 0.63

2. New value for 240:

240 x 0.63 = 151.2

Answers:

• multiplier = 0.63
• new value = 151.2

Marking guide:

• 1 mark for 0.63
• 1 mark for 151.2

4. Sale price

A jacket costs $72.00. It is on sale for 25% off.

25% = 0.25, so the multiplier is:

1 - 0.25 = 0.75

Sale price:

72.00 x 0.75 = 54.00

Answer: $54.00

Marking guide:

• 1 mark for correct setup
• 1 mark for $54.00

5. Consecutive decreases

Original price: $50.00

First decrease: 10%

Multiplier = 0.90

50.00 x 0.90 = 45.00

Second decrease: 20%

Multiplier = 0.80

45.00 x 0.80 = 36.00

Answer: $36.00

A one-step equivalent is:

50.00 x 0.90 x 0.80 = 36.00

Marking guide:

• 1 mark for correct first or combined setup
• 1 mark for $36.00

6. Error analysis

The student found 12% of 150:

150 x 0.12 = 18

But 18 is the amount of the decrease, not the new amount.

To get the new amount, subtract the decrease from the original:

150 - 18 = 132

Or use the multiplier directly:

1 - 0.12 = 0.88

150 x 0.88 = 132

Answer: The mistake is confusing the decrease amount with the new amount. The correct new amount is 132.

Marking guide:

• 1 mark for correctly explaining the mistake
• 1 mark for correct new amount 132

7. Measurement context

Original rope length: 18.4 m

Decrease: 5%

Multiplier:

1 - 0.05 = 0.95

New length:

18.4 x 0.95 = 17.48

Answer: 17.48 m

Marking guide:

• 1 mark for correct setup
• 1 mark for 17.48 m

8. Reverse-structure without reverse-percent algebra

Original price: $640

1. Discount amount:

30% of 640 = 0.30 x 640 = 192

2. Sale price:

640 - 192 = 448

Direct multiplier explanation:

If 30% is removed, then 70% remains. Since 70% = 0.70, multiplying by 0.70 gives the remaining price directly:

640 x 0.70 = 448

Answers:

• discount = $192
• sale price = $448
• explanation: 0.70 represents the part that remains after a 30% decrease

Marking guide:

• 1 mark for both numerical answers
• 1 mark for correct explanation of 0.70 as the remaining proportion

9. Comparison of methods

Decrease 96 by 35%.

Method 1: find the decrease, then subtract

35% of 96 = 0.35 x 96 = 33.6

New amount:

96 - 33.6 = 62.4

Method 2: multiplier method

1 - 0.35 = 0.65

96 x 0.65 = 62.4

Both methods match.

Answer: 62.4

Marking guide:

• 1 mark for one correct complete method
• 1 mark for second correct method and matching answer 62.4

10. Mixed application problem

Original population: 12,500

1. Population decrease:

8% of 12,500 = 0.08 x 12,500 = 1,000

2. New population:

12,500 - 1,000 = 11,500

3. Better multiplier:

0.92 is better for finding the new population directly, because after an 8% decrease, 92% remains.

Check:

12,500 x 0.92 = 11,500

Answers:

• decrease = 1,000
• new population = 11,500
• better multiplier = 0.92

Marking guide:

• 1 mark for both correct numerical answers
• 1 mark for identifying and explaining 0.92

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Answer key summary

1. 68
2. 37.2
3. 0.63; 151.2
4. $54.00
5. $36.00
6. Correct new amount: 132; error was confusing the decrease with the final amount
7. 17.48 m
8. $192 discount; $448 sale price; 0.70 is the remaining proportion
9. 62.4
10. 1,000; 11,500; multiplier 0.92

Common misconceptions to watch for

• Using the percent itself as the final multiplier. Repair: after a decrease of p%, the multiplier is 1 - p written as a decimal.

• Finding the decrease amount and stopping there. Repair: decide whether the question asks for the amount removed or the new amount remaining.

• Adding decrease multipliers in consecutive-change questions. Repair: successive decreases are applied by multiplying each new multiplier in turn.

• Rounding too early in money questions. Repair: keep full precision until the final cent value.

Recommended mastery threshold

Recommend 16/20 or higher for mastery, with at least these essential indicators:

• the learner correctly uses a decrease multiplier in most questions
• the learner distinguishes between the decrease amount and the final amount
• the learner can solve both bare-number and contextual problems

A score of 18/20 or higher suggests strong readiness to move on to reverse percent change. A score below 16/20 suggests reviewing linked prerequisite records, especially rea.m08.number.decimals-and-percents.percent-basics.unit-mastery-quiz, rea.m08.number.decimals-and-percents.percent-quantity.unit-mastery-quiz, and rea.m08.number.decimals-and-percents.decimal-operations.unit-mastery-quiz.