Percentage decrease

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In order to access this I need to be confident with:

Percentages of an amount Comparing between fractions, decimals and percentages

This topic is relevant for:

GCSE Maths Number FDP Percentages

Percentage Decrease

Here we will learn about percentage decrease including how to decrease a value by a given percentage, how to use multipliers to calculate percentage decrease and how to work out percentage change.

There are also percentage increase and decrease worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is percentage decrease?

Percentage decrease means subtracting a given percentage of a value from the original value. To do this we can either calculate the given percentage of the value and then subtract it from the original or use a percentage multiplier.

What is percentage decrease?

How to decrease a value by a percentage

In order to decrease a value by a percentage:

Calculate the given percentage of the value
Subtract it from the original number

Explain how to decrease a value by a percentage in 2 steps

Percentage increase and decrease worksheet

Get your free percentage increase and decrease worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Percentage increase and decrease worksheet

Get your free percentage increase and decrease worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Percentage decrease examples

Example 1: non-calculator

Decrease £80 by 30%

Calculate 30% of £80

To do this without a calculator, the easiest way is to calculate 10% (by dividing by 10) and then multiply by 3 to get 30%.

10% of £80 = £8

30% of £80 = £24

2 Subtract it from the initial value

£80 – £24 = £56

Example 2: non-calculator

Decrease 250km by 45%

Calculate 45% of 250km

10% of 250km = 25km

40% of 250km = 100km

5% of 250km = 12.5km

45% of 250km = 112.5km

Subtract it from the original value

\[250 – 112.5 = 137.5km\]

Example 3: calculator

Decrease 760 by 39%

Calculate 39% of 760

This time we are going to use a calculator. When using a calculator we divide the value by 100 to find 1% and then multiply by the percentage that we want.

\begin{array}{l} 760 \div 100=7.6 \\\\ 7.6 \times 39=296.4 \end{array}

Subtract it from the original value

\[760 – 296.4 = 463.6\]

Example 4: calculator

A jumper costing £13.20 is reduced by 15% in a sale. Calculate the new price of the jumper.

Calculate 15% of £13.20

\[\begin{array}{l} 13.20 \div 100=0.132 \\\\ 0.132 \times 15= £1.98 \end{array}\]

Subtract it from the original price

£13.20 – £1.98 = £11.22

How to decrease a value by a percentage using a percentage multiplier

We can decrease a value by a percentage using a percentage multiplier. A percentage multiplier is a decimal that is related to the percentage you are trying to find.

Subtract the percentage we are decreasing by from 100%

We subtract it from 100% because we are decreasing the value and 100% represents the original value.

2Convert to a decimal

3Multiply the original amount by the decimal

Example 5: using a multiplier

Decrease 84m by 46%

Here we are calculating a 46 percent decrease so subtract 46% from 100%

\[100\% – 46\% = 54\%\]

Convert to a decimal. To do this we divide the percentage by 100.

\[54\% = 0.54\]

Multiply the starting value by the decimal

\[84\times 0.54=45.36m\]

Example 6: using a multiplier

Daniel has £3600. He spends 27.5% of his money. How much does he have left?

This is a 27.5 percent decrease so subtract 27.5% from 100%

\[100\% – 27.5\% = 72.5\%\]

Convert to a decimal.

\[72.5\% = 0.725\]

Multiply the value by the decimal

\[3600\times 0.725 = £. 2610\]

Calculating percentage decrease

Given two values, we can calculate the percentage difference. This can also be called percentage decrease or percentage loss.

We can calculate percentage change using the percentage change formula:

\[\text { Percentage change }=\frac{\text { Change }}{\text { Original }} \times 100\]

The same formula can be used to calculate percentage increase.

Work out how much the value has changed by subtracting the final value from the original value
Apply the percentage change formula

Example 7: calculating percentage change

Ricky weighed 70kg in March. By June his weight had decreased to 64.4kg. Calculate the percentage decrease in his weight.

His weight has changed from 70kg to 64.4kg. Work out the change:

\[70kg – 64.4kg = 5.6kg\]

Apply the percentage change formula. The change is 5.6kg and the original amount is 70kg.

\[\text { Percentage change }=\frac{5.6}{70} \times 100\]

Percentage decrease = 8%

Example 8: calculating percentage loss

Louise buys a car for £7500 and sells it for £6150. Calculate Louise’s percentage loss.

The value has changed from £7500 to £6150. Work out the change:

£7500 – £6150 = £1350

Apply the percentage change formula. The change is £1350 and the original amount is £7500.

\begin{array}{l} \text { Percentage change }=\frac{\text { Change }}{\text { Original }} \times 100 \\\\ \text { Percentage change }=\frac{1350}{7500} \times 100 \end{array}

Percentage loss = 18%

Percentage decrease is part of our series of lessons to support revision on percentages. You may find it helpful to start with the main percentages lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Common misconceptions

Converting between percentages and decimals

Incorrectly converting percentages to decimals. The most common mistakes are with single digit percentages (e.g. 5%), multiples of 10 (e.g. 40%) and decimal percentage (e.g. 3.2%)

Remember to divide the percentage by 100 to find the decimal.

E.g.

\[5 \%=0.05,\\ 40 \%=0.4,\\ 3.2 \%=0.032,\\ 106.5 \%=1.065\]

Using an incorrect value for the denominator in the percentage decrease formula

Using the new value instead of the original value for the denominator when calculating percentage change

Practice percentage decrease questions

$7480m$

$7520m$

$9000m$

$6000m$

$20\%$ of $7500m$ is $1500m$ .

As this is a decrease we subtract from the original amount.

7500 - 1500 = 6000

$7.92ml$

$36.08ml$

$80.08ml$

$51.92ml$

$82\%$ of $44ml$ is $36.08ml$ .

As this is a decrease we subtract from the original amount.

44 - 36.08 = 7.92

$£580.58$

$£731$

$£173.42$

$927.42$

The multiplier for this decrease is $0.77$ , so the correct calculation is $0.77\times754$

$215.8g$

$6.65g$

$97.028g$

$156.972g$

The multiplier for this decrease is $0.618$ , so the correct calculation $0.618\times254$

$330\%$

$50.77\%$

$49.23\%$

$203.125\%$

The actual decrease is $330kg$ .

To calculate the percentage decrease we divide this by the original amount and multiply by $100$

\frac{650-320}{650}\times100

$17.25\%$

$85\%$

$15\%$

$82.25\%$

The actual loss is $£1725$ .

To calculate the percentage loss we divide this by the original amount and multiply by $100$ .

\frac{11500-9775}{11500}\times100

Percentage decrease GCSE questions

1. (a) A pair of trainers costing £35 are in a $25\%$ off sale. Calculate the sale price of the trainers.

(b) During the last week of the sale the trainers are reduced to $£21$ . Calculate the percentage decrease from the original price.

(4 marks)

Show answer

(a)

$25\%$ of $£35 = £8.75$

(1)

$£35 - £8.75 = £26.25$

(1)

(b)

$£35 - £21 = £14$

(1)

\frac{14}{35} \times 100=40\%

(1)

2. In $2018$ a supermarket chain produced $308900$ tonnes of packaging for its products. In $2019$ they reduced the amount of packaging used by $4.7%$ .

Calculate the amount of packaging used in $2019$ .

(2 marks)

Show answer

$4.7\%$ of $308900 = 14518.3$

(1)

$308900-14518.3 = 294381.7$ tonnes

(1)

3. Samira wants to book a holiday for herself, her husband and their one child. There are two companies that she can book the holiday with. The prices of the holiday are shown below.

Travel Stars

£ $400$ per adult

£ $200$ per child

Ready Jet Go

£ $500$ per adult

£ $100$ per child

$10$ % discount on early bookings

Samira is going to make an early booking. With which company would she get a better deal?

You must show your working.

(5 marks)

Show answer

Travel Stars: $£400+£400+200 = £1000$

(1)

Ready Jet Go: $£500+£500+£100 = £1100$

(1)

$10\%$ of $£1100 = £110$

(1)

$£1100-£110 = £990$

(1)

Better deal with Ready Jet Go

(1)

Learning checklist

You have now learned how to:

Decrease a value by a given percentage

Use a percentage multiplier to decrease a value by a percentage

Calculate percent decrease between two values

The next lessons are

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