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

Percentages of amounts

Converting between fractions, decimals and percentages

This topic is relevant for:

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.

**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.

In order to decrease a value by a percentage:

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

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

DOWNLOAD FREEGet your free percentage decrease worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEDecrease

- Calculate
30% of£80

To do this without a calculator, the easiest way is to calculate

2 Subtract it from the initial value

Decrease

Calculate 45% of 250km

Subtract it from the original value

\[250 – 112.5 = 137.5km\]

Decrease

Calculate 39% of 760

This time we are going to use a calculator. When using a calculator we divide the value by

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

** **Subtract it from the original value

\[760 – 296.4 = 463.6\]

A jumper costing

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

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 **decreasing the value** and

2Convert to a decimal

3Multiply the original amount by the decimal

Decrease

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

\[84\times 0.54=45.36m\]

Daniel has

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

\[3600\times 0.725=£ 2610\]

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

Ricky weighed

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

Louise buys a car for

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

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

**Converting between percentages and decimals**

Incorrectly converting percentages to decimals. The most common mistakes are with single digit percentages (e.g.

Remember to divide the percentage by

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

1. Decrease 7500m by 20\%

7480m

7520m

9000m

6000m

20\% of 7500m is 1500m .

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

7500 – 1500 = 6000

2. Decrease 44ml by 82\%

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

3. Use a multiplier to decrease £754 by 23\%

£580.58

£731

£173.42

927.42

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

4. Use a multiplier to decrease 254g by 38.2\%

215.8g

6.65g

97.028g

156.972g

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

5. Find the percentage decrease when 650kg is decreased to 320kg

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

6. Find the percentage loss when Tristan buys a tractor for £11500 and sells the tractor for £9775

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

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)**

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

- Percentage increase
- Compound interest
- Reverse percentages

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