# Understand how to Increase or Decrease by a Percentage Using a Multiplier

In this worksheet, students will be able to increase or decrease an amount by using a multiplier. Students will also be able to apply this skill to written problems.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Fractions, Decimals and Percentages

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Percentages

Difficulty level:

### QUESTION 1 of 10

Percentages are all around us...we just don't see it most of the time.

We may need to calculate increases...  these are sometimes good like a pay rise,( i wish)  but can also be bad, like bills rising each year. (to true)

We may also need to calculate percentage decreases ... sometimes good like a tax bill decreasing, or sometimes bad like the value of a car reducing.

Has he got bigger, or have I got smaller?

To find a percentage increase we use a multiplier.

If we want to increase 350 by 22% we use the multiplier 350 x 1.22 which equals 427

(this means we take the whole amount of 350 and add 22% to it).

So if we want to increase 241 by 18% the multiplier is 241 x 1.18 = 284.38.

Decreasing 350 by 22% we just do 350 x 0.22 right? Using 0 because we are decreasing. NO, NO, NO

Care is needed here   Remember percent means 'out of 100'.

To decrease we need a little more work.

We need to take the 22% from 100% first. So, 100 - 22 = 78  (we only want to find the 78% that is left).

To complete the decrease the multiplier is 350 x 0.78 = 273

So decrease 42 by 18% = 100 - 18 = 82% and therefore, 42 x 0.82 = 34.44

Take it slowly and you will get there..

Can you increase each of the following by the percentage given?

Time to try percentage decreases.  Decrease each of the following amounts by the percentage given.

Match the following percentage increases and decreases below.

## Column B

Increase 123 by 23%
54.72
Increase 342 by 61%
151.29
Decrease 72 by 24%
70.225
Increase 53 by 32.5%
553
Decrease 48 by 6%
550.62
Decrease 632 by 12.5%
45.12

Mike's weekly wage of £400 is decreased by 5%.

Margot's weekly wage of £350 is increased by 12%

Choose the two options that show how much Mike and Margot now earn?

£200

£352

£420

£380

£392

£658

You're in charge of making toffee apples for this year's bonfire party.  Last year you made 56 and ran out!

This year you decide to increase the number you make by 23%.  How many toffee apples do you make?

Oh no...your scarf has shrunk 31% in the wash.

Its original length was 120 cm.

What is its new length?

At the start of a car rally, Neil had 8 gallons of fuel in his car and Sarah had 12 gallons of fuel.

During the rally, Neil used 25% of his fuel, and Sarah used 40% of her fuel.

Who had most fuel left at the end of the rally?

A table and chairs cost £850.  In the first week of a sale, they are reduced by 13%.

The following week they are reduced by a further 8% of the new price.

How much are the table and chairs after the first reduction?

How much are the table and chairs after the second reduction?

 Amount First Reduction Second Reduction

A motor insurance company offers discounts on premiums for careful drivers.  Their rates of discount are shown in the table below

 No Claims Discount given: 1 year 15% off the full premium 2 years 25% off the full premium 3 years 45% off the full premium 4 years 60% off the full premium

The Parker family, all use the same firm for their insurance.

Mr. Parker has four years' no-claims discount.

His full premium would be  £550.

Mrs Parker has one year's no-claims discount.

Her full premium would be £345

Jimmy has three years' no -claims discount.

His full premium would be £690

Paul has two years' no-claims discount.

His full premium would be £820

Calculate the amount each family member has to pay for motor insurance.

 Amount First Reduction Second Reduction

Last year John's boss (who as you can see is a bit grumpy) gave John a ten percent pay rise because he said business was doing well.

This year he says that business is not so good, and is decreasing John's wages by ten percent!

John's boss says he's no worse off than he was before the rise.

Who is correct John or his boss? (Write your answer as John or Boss)

• Question 1

Can you increase each of the following by the percentage given?

EDDIE SAYS
This is just a really easy way to increase the percentage using your calculator. Mathematicians are always looking for simple ways to work when possible. Here is what your working out should look like: 320 x 1.11 102 x 1.17 48 x 1.03 remember any percentage less than 10 needs an extra 0. If you had done 48 x 1.30 you would have increased by 30%. Not good (unless you are awarding yourself a pay rise) 82 x 1.23 92 x 1.61 290 x 1.07
• Question 2

Time to try percentage decreases.  Decrease each of the following amounts by the percentage given.

EDDIE SAYS
Did you remember the extra step at the beginning? It's so easy to miss this out. Before you decrease remember to subtract the percentage decrease from 100 to give you the multiplier. Decrease 72 by 6 100 - 6 = 94 72 x 0.94 Decrease 82 by 13 100 - 13 = 87 82 x 0.87= 71.34 Imagine you were selling your i-phone to a friend at a discount of 6% and forgot to take this away from 100 first. You would almost be giving it away!
• Question 3

Match the following percentage increases and decreases below.

## Column B

Increase 123 by 23%
151.29
Increase 342 by 61%
550.62
Decrease 72 by 24%
54.72
Increase 53 by 32.5%
70.225
Decrease 48 by 6%
45.12
Decrease 632 by 12.5%
553
EDDIE SAYS
Sometimes when you get increase and decrease questions together it's easy to forget that extra step with decreasing. Remember ignore the decimal point in the increases and decreases. Top tips... if you are increasing a percentage by 46% it is easy you just use the multiplier 1 (which means just take the whole amount) and increase by 46%. Hence x 1.46. When decreasing, think 'I'm decreasing so I have to take something away' this should start you off. So, to decrease by 24% remember to take 24 away from 100 first. 100 - 24 = 76. Now, you don't want the whole amount this time so your multiplier starts with 0 and you just use the percentage left e.g 76. number x 0.76.
• Question 4

Mike's weekly wage of £400 is decreased by 5%.

Margot's weekly wage of £350 is increased by 12%

Choose the two options that show how much Mike and Margot now earn?

£380
£392
EDDIE SAYS
You are now getting used to using multipliers. So much quicker than trying to work it out the long way isn't it? Us mathematicians love a trick or two. Just to clarify Mikes wage decrease was calculated by 100-5 = 95 £400 x 0.95 = £380 Margot's wage £350 x 1.12 = £392
• Question 5

You're in charge of making toffee apples for this year's bonfire party.  Last year you made 56 and ran out!

This year you decide to increase the number you make by 23%.  How many toffee apples do you make?

68.88
EDDIE SAYS
This is just an example of how a percentage question is presented in a written format. Just look for the keywords i.e percentage, and increase. This should then direct you to 56 x 1.23 = 68.88. Save a toffee apple for me!
• Question 6

Oh no...your scarf has shrunk 31% in the wash.

Its original length was 120 cm.

What is its new length?

82.80cm
EDDIE SAYS
This is just another way of wording a decrease question. This time the key word was shrunk which would lead you to a percentage decrease. 100- 31= 69 120cm x 0.69 = 82.80 Top tip... don't let your little brother wash your scarf!
• Question 7

At the start of a car rally, Neil had 8 gallons of fuel in his car and Sarah had 12 gallons of fuel.

During the rally, Neil used 25% of his fuel, and Sarah used 40% of her fuel.

Who had most fuel left at the end of the rally?

Sarah
EDDIE SAYS
You are used to using these multipliers, so now you should be turning your attention to the wording of the questions. The words increase and decrease are not always used. It can be daunting when faced with worded questions but just take your time and identify words that can help you. In this case, the word used suggests a decrease. You need to show each step of your working out (otherwise an examiner might think you have just guessed, and you don't want to throw away marks after all your hard work) Neil 8 x 0.75 = 6 gallons (remember the extra step at the beginning) Sarah 12 x 0.60 = 7.2 gallons She has the most left. 7.2 - 6 = 1.2 more gallons
• Question 8

A table and chairs cost £850.  In the first week of a sale, they are reduced by 13%.

The following week they are reduced by a further 8% of the new price.

How much are the table and chairs after the first reduction?

How much are the table and chairs after the second reduction?

 Amount First Reduction Second Reduction
EDDIE SAYS
This type of question could easily catch you out. Read it very carefully. The first reduction is straightforward £850 x 0.87 = £739.50 Now this is where you need to be careful. The further reduction of 8% is from the new price of £739.50 not the original price. £739.50 X 0.92= £680.34
• Question 9

A motor insurance company offers discounts on premiums for careful drivers.  Their rates of discount are shown in the table below

 No Claims Discount given: 1 year 15% off the full premium 2 years 25% off the full premium 3 years 45% off the full premium 4 years 60% off the full premium

The Parker family, all use the same firm for their insurance.

Mr. Parker has four years' no-claims discount.

His full premium would be  £550.

Mrs Parker has one year's no-claims discount.

Her full premium would be £345

Jimmy has three years' no -claims discount.

His full premium would be £690

Paul has two years' no-claims discount.

His full premium would be £820

Calculate the amount each family member has to pay for motor insurance.

EDDIE SAYS
Oh my goodness, this seems a lot of work as there is so much information. Deep breath! Read through carefully once. Once you have done this you can see it is not that difficult at all. You're just practising a percentage discount four times. Be careful to pick out the correct information, the questions don't necessarily follow the order of the table. 550 x 0.40 = £220 345 x 0.85 =£293.25 690 x 0.55 = 379.50 820 x 0.25 = £205 Just goes to show how much you can save by careful driving!
• Question 10

Last year John's boss (who as you can see is a bit grumpy) gave John a ten percent pay rise because he said business was doing well.

This year he says that business is not so good, and is decreasing John's wages by ten percent!

John's boss says he's no worse off than he was before the rise.

Who is correct John or his boss? (Write your answer as John or Boss)

John
EDDIE SAYS
This looks tricky because there are no wages given to start with, just the percentage increase/decrease rate. This is where you have to use your creativity. Hint: Keep your numbers simple. Suppose I earn £20, 000 a 10% increase would be 20,000 x 1.10 =£22,000. Looking good. A 10% discount of £22,000 is 22,000 x 0.90 = £19,800. Well and truly robbed!
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