117. Percentage Change, Profit, Loss and Error

Learning Intentions

• To know the meaning of the terms percentage change, percentage profit, percentage loss and percentage error
• Calculate the percentage change (increase or decrease) when prices are increased or decreased

Pre-requisite Summary

• Know that a percentage is a number out of
• Be able to Solve the increase or decrease between two values
• Understand that percentage change compares the change to the original amount
• Know the meaning of increase and decrease
• Be able to subtract decimal numbers accurately
• Be able to divide one quantity by another
• Know the meaning of profit and loss from buying and selling situations
• Understand that an error is the difference between an estimated or measured value and the actual value

Worked Examples

Worked Example 1

State the meaning of each term:

a) percentage change

b) percentage profit

c) percentage loss

d) percentage error

Worked Example 2

Find the percentage increase:

a) a price increases from $ to $

b) a price increases from $ to $

Worked Example 3

Find the percentage decrease:

a) a price decreases from $ to $

b) a price decreases from $ to $

Worked Example 4

Find the percentage profit or percentage loss:

a) cost price $ , selling price $

b) cost price $ , selling price $

Worked Example 5

Find the percentage error:

a) actual value , measured value

b) actual value , measured value

Worked Example 6

A store changes prices. Find the percentage change and state whether it is an increase or decrease:

a) from $ to $

b) from $ to $

c) from $ to $

Problems

Problem 1

State the meaning of each term:

a) percentage change

b) percentage profit

c) percentage loss

d) percentage error

Problem 2

Find the percentage increase:

a) a price increases from $ to $

b) a price increases from $ to $

Problem 3

Find the percentage decrease:

a) a price decreases from $ to $

b) a price decreases from $ to $

Problem 4

Find the percentage profit or percentage loss:

a) cost price $ , selling price $

b) cost price $ , selling price $

Problem 5

Find the percentage error:

a) actual value , measured value

b) actual value , measured value

Problem 6

A store changes prices. Find the percentage change and state whether it is an increase or decrease:

a) from $ to $

b) from $ to $

c) from $ to $

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each term:

a) percentage change

b) percentage profit

c) percentage loss

d) percentage error

Exercise 2.

Find the increase or decrease in each situation first, then find the percentage change:

a) from $ to $

b) from $ to $

c) from $ to $

Exercise 3.

Find the percentage increase:

a) from $ to $

b) from $ to $

c) from $ to $

Exercise 4.

Find the percentage decrease:

a) from $ to $

b) from $ to $

c) from $ to $

Exercise 5.

Find the percentage profit or percentage loss:

a) cost price $ , selling price $

b) cost price $ , selling price $

c) cost price $ , selling price $

Exercise 6.

Find the percentage profit or percentage loss:

a) cost price $ , selling price $

b) cost price $ , selling price $

c) cost price $ , selling price $

Exercise 7.

Find the percentage error:

a) actual , measured

b) actual , measured

c) actual , measured

Exercise 8.

A price changes. State whether it is an increase or decrease, then find the percentage change:

a) from $ to $

b) from $ to $

c) from $ to $

d) from $ to $

Reasoning

Exercise 9.

Explain why percentage change is calculated Use the original value, not the new value.

Exercise 10.

A student says that when a price changes from $ to $ , the percentage change is . Explain the mistake.

Exercise 11.

Noah says that percentage profit is found by dividing the profit by the selling price. Is he correct? Explain.

Exercise 12.

Explain why a decrease from $ to $ is a decrease.

Exercise 13.

A student says that if the measured value is greater than the actual value, then the percentage error must be negative. Describe the error.

Problem-solving

Exercise 14.

A shirt was marked up from $ to $ . Find the percentage increase.

Exercise 15.

A bicycle was on sale, reduced from $ to $ . Find the percentage decrease.

Exercise 16.

A shop bought a lamp for $ and sold it for $ . Find the profit and the percentage profit.

Exercise 17.

A shop bought a game for $ and sold it for $ . Find the loss and the percentage loss.

Exercise 18.

A piece of wood has an actual length of m, but it is measured as m. Find the percentage error.

Exercise 19.

The price of a phone increased from $ to $ , then later decreased to $ .

a) Find the first percentage change

b) Find the second percentage change

Potential Misunderstandings

• Students may think percentage change compares the change to the new value instead of the original value
• Students may confuse the amount of change with the percentage change
• Students may forget to decide first whether the change is an increase or a decrease
• Students may calculate the difference correctly but divide by the wrong amount
• Students may confuse percentage profit with the actual profit amount
• Students may confuse percentage loss with subtracting a percent sign from the loss
• Students may use the selling price instead of the cost price when finding percentage profit or percentage loss
• Students may think percentage error can be found without first finding the error amount
• Students may forget that percentage error compares the error to the actual value
• Students may assume the same dollar change always gives the same percentage change, even when the original amounts are different

Next: 118e. The Unitary Method with Percentages