REVERSE PERCENTAGES (YEAR 9)

Reverse Percentages 27.02.2025

I can:
1) convert between decimals & %ages
2) find %age of an amount
3) increase or decrease a quantity by a certain %age

Prior Knowledge

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

Complete the quizizz titled "Starter for Reverse Percentages" by clicking on the link below.

Starter

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

A multiplier is a number you can multiply by to quickly calculate a %age increase or decrease.

Multiplier (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Multiplier for a %age increase (note this)

When something increases by a %age, the new amount is more than the original. To find the multiplier for a %age increase, add the % to 100% and change the result to decimal

Reverse Percentages 27.02.2025

A multiplier is a number you can multiply by to quickly calculate a %age increase or decrease.

Multiplier (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Multiplier for a %age decrease (note this)

When something decreases by a %age, the new amount is less than the original. To find the multiplier for a %age decrease, subtract the % to 100% and change the result to decimal

Reverse Percentages 27.02.2025

To increase/decrease a quantity by a %age, convert the %age to the appropriate multiplier and multiply the quantity by the multiplier.

Class Activity (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Question-1
Use the multiplier method to:
increase £50 by 20%
decrease £80 by 25%

Reverse Percentages 27.02.2025

A multiplier can be converted back to a percentage. To change a multiplier to %age, first multiply it by 100, then
(a) subtract it from 100 if the result is less than 100. This is a %age decrease
(b) subtract 100 if the result is more than 100. This is a %age increase

Converting Multiplier to a %age (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

Class Activity (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Question-2
Convert the following multipliers to the appropriate percentages.
(a) 1.15 (f) 0.015
(b) 1.07 (g) 0.215
(c) 1.025 (h) 0.12
(d) 2.15 (i) 0.175
(e) 1. 0025 (j) 0.2565

Reverse Percentages 27.02.2025

Sometimes, we know the new amount after a percentage increase or decrease, and we need to work backwards to find the original amount. Use this formula:

original amount = new amount ÷ multiplier

To find an original amount after a %age increase/decrease (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

Class Activity (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Question-5
A car was originally worth £12,000, but its value dropped to £9,000. Find the percentage decrease.
Question-6
A house was originally worth £150,000, but its value increased to £180,000. Find the percentage increase.

Reverse Percentages 27.02.2025

Class Activity (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Question-3
A jacket costs £72 after a 20% increase. What was the original price?
Question-4
A phone now costs £255 after a 15% decrease. What was the original price?

Reverse Percentages 27.02.2025

When a quantity changes by a %age multiple times we use multipliers repeatedly. To find the overall %age change, multiply the individual multipliers and convert your answer to %age (stating whether an increase or a decrease).

To find an amount after a repeated %age increase/decrease (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

Example
An increase of 20% is followed by another increase of 20% and then a decrease of 40%. Find the total percentage change.
Solution
1.2 x 1.2 x 0.6 = 0.864. Thus, 13.6% decrease

To find an amount after a repeated %age increase/decrease (note this)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Reverse Percentages 27.02.2025

Class Activity (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

Question-7
Find the total percentage change when an increase of 60% is followed by a decrease of 50% and then a decrease of 10%.
Question-8
After a discount of 20% followed by another discount of 25%, Eliah bought a laptop for £600. What was the original price of the laptop before the discounts?

Reverse Percentages 27.02.2025

Reflection (in your notebook)

To find an original amount after a %age increase or decrease

Lesson Objective

Solve complex problems involving reverse %ages

Extension

• How can reverse percentages be useful in real life (e.g. working out original prices, taxes, salary deductions)?

• Can you think of a situation where you might need to find an original amount before a percentage change?

• Think of a situation in which a percentage increase is the same over a period of time.