116. Percentage Change

Learning Intentions

• To know the meaning of the terms discount, mark-up, profit, loss, selling price, retail price and wholesale price
• Solve the new value if an amount is increased or decreased by a percentage
• To understand that percentage mark-ups and discounts correspond to increasing and decreasing a price by a percentage

Pre-requisite Summary

• Know that a percentage is a number out of
• Be able to convert a percentage to a decimal or fraction
• Be able to find a percentage of a quantity
• Understand that increasing means making a value larger
• Understand that decreasing means making a value smaller
• Know that money amounts are usually written in dollars and cents
• Be able to add and subtract decimal numbers accurately

Worked Examples

Worked Example 1

State the meaning of each term:

a) discount

b) mark-up

c) profit

Worked Example 2

State the meaning of each term:

a) loss

b) selling price

c) wholesale price

d) retail price

Worked Example 3

Find the new value after an increase:

a) Increase $ by

b) Increase $ by

Worked Example 4

Find the new value after a decrease:

a) Decrease $ by

b) Decrease $ by

Worked Example 5

A shop buys an item for $ wholesale and adds a mark-up.

a) Find the mark-up amount

b) Find the selling price

Worked Example 6

A jacket has a retail price of $ and is sold at a discount of .

a) Find the discount amount

b) Find the new selling price

Problems

Problem 1

State the meaning of each term:

a) discount

b) mark-up

c) profit

Problem 2

State the meaning of each term:

a) loss

b) selling price

c) wholesale price

d) retail price

Problem 3

Find the new value after an increase:

a) Increase $ by

b) Increase $ by

Problem 4

Find the new value after a decrease:

a) Decrease $ by

b) Decrease $ by

Problem 5

A shop buys an item for $ wholesale and adds a mark-up.

a) Find the mark-up amount

b) Find the selling price

Problem 6

A pair of shoes has a retail price of $ and is sold at a discount of .

a) Find the discount amount

b) Find the new selling price

Exercises

Understanding and Fluency

Exercise 1.

Match each term to its meaning:

a) discount

b) mark-up

c) profit

d) loss

Exercise 2.

State whether each situation describes a discount, mark-up, profit or loss:

a) a store reduces the price of a bike by

b) a shop increases the price of a toy by

c) an item is sold for more than it cost

d) an item is sold for less than it cost

Exercise 3.

Find the new value after each increase:

a) $ increased by

b) $ increased by

c) $ increased by

Exercise 4.

Find the new value after each decrease:

a) $ decreased by

b) $ decreased by

c) $ decreased by

Exercise 5.

Find the mark-up amount and the new price:

a) $ marked up by

b) $ marked up by

c) $ marked up by

Exercise 6.

Find the discount amount and the new price:

a) $ discounted by

b) $ discounted by

c) $ discounted by

Exercise 7.

Decide whether the price has increased or decreased, then find the new value:

a) a book costing $ has a discount

b) a chair costing $ has a mark-up

c) a game costing $ has a discount

Exercise 8.

Complete each statement:

a) A mark-up means the price is ______ by a percentage

b) A discount means the price is ______ by a percentage

c) Wholesale price is usually the price paid by the ______

d) Retail price is usually the price paid by the ______

Reasoning

Exercise 9.

Explain why a discount and a mark-up do not have the same effect on a price.

Exercise 10.

A student says that a discount on $ means subtracting $ . Explain the mistake.

Exercise 11.

Noah says that profit means the same as selling price. Is he correct? Explain.

Exercise 12.

Explain why a mark-up corresponds to increasing the original price by a percentage.

Exercise 13.

A student says that if the wholesale price is $ and the selling price is $ , then the profit is . Describe the error.

Problem-solving

Exercise 14.

A store buys a bag for $ wholesale and sells it for $ .

a) Find the profit

b) State whether this is a mark-up or a discount situation

Exercise 15.

A bicycle has a retail price of $ and is on sale for off. What is the sale price?

Exercise 16.

A toy store buys a board game for $ and adds a mark-up of . What is the new selling price?

Exercise 17.

A jacket costs $ and the store offers a discount. How much is the discount, and what is the new price?

Exercise 18.

A café buys mugs for $ each wholesale and sells them for $ each. Find the profit on one mug.

Exercise 19.

A computer monitor has a wholesale price of $ . The shop uses a mark-up. What is the retail price?

Potential Misunderstandings

• Students may think discount means the final price rather than the amount taken off
• Students may think mark-up means subtracting a percentage instead of adding a percentage
• Students may confuse profit with selling price
• Students may confuse wholesale price with retail price
• Students may think a percentage increase means adding the percentage number directly as dollars
• Students may think a percentage decrease means subtracting the percentage number directly as dollars
• Students may calculate the percentage amount correctly but then forget to add or subtract it from the original amount
• Students may confuse the original price with the new price when finding profit or loss
• Students may think all discounted items are sold at a loss
• Students may not recognise that mark-ups and discounts describe percentage increases and decreases in price

Next: 117. Percentage Change, Profit, Loss and Error