GM Lesson 012 Percentage Increase and Decrease

Learning Intentions

• Apply percentage increase in practical contexts.
• Apply percentage decrease in practical contexts.
• Calculate new values after a percentage change.

Prerequisites

Students should already be able to:

• Convert percentages to decimals.
• Find a percentage of a quantity.
• Interpret percentages in money contexts.
• Use the unitary method for simple percentage calculations.
• Perform multiplication involving decimals.

Key Idea Summary

A percentage change compares the change in a quantity to the original quantity.

For a percentage increase:

For a percentage decrease:

The multiplier is often the most efficient method.

Examples:

• A increase uses the multiplier .
• A decrease uses the multiplier .
• A increase uses the multiplier .
• A decrease uses the multiplier .

Important distinction:

• The original value represents .
• After a increase, the new value is of the original.
• After a decrease, the new value is of the original.

Direct Instruction and Worked Examples

Timing Guide

• Introduction and key idea: minutes
• Direct instruction and worked examples: minutes
• Understanding checks: minutes
• Exercises: minutes

Direct Instruction

A percentage increase means that the final amount is larger than the original amount.

For example, if a price increases by , then the new price is:

So the multiplier is:

A percentage decrease means that the final amount is smaller than the original amount.

For example, if a price decreases by , then the new price is:

So the multiplier is:

Worked Example 1: Percentage Increase Using the Percentage Amount

A gym membership costs $48 per month. The price increases by . Find the new monthly cost.

First calculate of $48:

So the increase is $4.80.

Add the increase to the original amount:

The new monthly cost is $52.80.

Worked Example 2: Percentage Increase Using a Multiplier

A phone plan costs $35 per month. The cost increases by . Find the new monthly cost.

After an increase, the new amount is:

Convert to a decimal:

Multiply the original amount by the multiplier:

The new monthly cost is $37.80.

Worked Example 3: Percentage Decrease Using the Percentage Amount

A jacket originally costs $120. It is reduced by . Find the sale price.

First calculate of $120:

So the decrease is $30.

Subtract the decrease from the original price:

The sale price is $90.

Worked Example 4: Percentage Decrease Using a Multiplier

A second-hand laptop is valued at $900. Its value decreases by over one year. Find its value after one year.

After an decrease, the new amount is:

Convert to a decimal:

Multiply the original amount by the multiplier:

The value after one year is $738.

Worked Example 5: Comparing an Increase and a Decrease

A concert ticket originally costs $80. The price first increases by . Later, the increased price is reduced by . Is the final price $80?

First apply the increase:

The increased price is $92.

Now apply the decrease to $92:

The final price is $78.20.

The final price is not $80 because the decrease was applied to the increased price, not the original price.

Understanding Checks

Check 1

A price increases by .

What multiplier should be used?

Check 2

A price decreases by .

What multiplier should be used?

Check 3

A bicycle costs $420. Its price increases by .

Set up the calculation using a multiplier.

Check 4

A television costs $760. Its price decreases by .

Set up the calculation using a multiplier.

Check 5

Explain why a increase followed by a decrease does not return a value to its original amount.

Exercises

Simple Familiar Exercises

Exercise 1

Write the multiplier for each percentage increase.

a.

b.

c.

d.

Exercise 2

Write the multiplier for each percentage decrease.

a.

b.

c.

d.

Exercise 3

Calculate the new value after each percentage increase.

a. $50 increased by

b. $80 increased by

c. $240 increased by

d. $1200 increased by

Exercise 4

Calculate the new value after each percentage decrease.

a. $50 decreased by

b. $80 decreased by

c. $240 decreased by

d. $1200 decreased by

Complex Familiar Exercises

Exercise 5

A phone bill of $64 increases by .

Calculate the new phone bill.

Exercise 6

A pair of shoes originally costs $150. The price is reduced by .

Calculate the sale price.

Exercise 7

A casual worker earns $28 per hour. Their hourly rate increases by .

Calculate the new hourly rate.

Exercise 8

A car is valued at $18 500. Its value decreases by over one year.

Calculate the value of the car after one year.

Exercise 9

A weekly grocery bill of $185 increases by .

Calculate the new weekly grocery bill.

Exercise 10

A store reduces the price of a washing machine from $840 by .

Calculate the reduced price.

Homework Problems

Problem 1

Write the multiplier for each percentage change.

a. Increase by

b. Decrease by

c. Increase by

d. Decrease by

Problem 2

A streaming subscription costs $17 per month. It increases by .

Calculate the new monthly cost.

Problem 3

A bicycle costs $680. It is discounted by .

Calculate the discounted price.

Problem 4

A worker earns $950 per week. Their wage increases by .

Calculate their new weekly wage.

Problem 5

A phone is bought for $1400. Its value decreases by after one year.

Calculate its value after one year.

Problem 6

A school camp originally costs $520 per student. The cost increases by due to transport costs.

Calculate the new cost per student.

Problem 7

A jacket is reduced by from its original price of $220.

Calculate the sale price.

Problem 8

A quantity is increased by and then decreased by .

Use an original value of $100 to show that the final value is not $100.

Problem 9

A gym membership costs $60 per month. It increases by in one year and then increases by another the next year.

Calculate the monthly cost after two years.

Problem 10

A car worth $24 000 decreases in value by each year for two years.

Calculate the value of the car after two years.

Next: GM Lesson 013 Inflation and Wage Changes