 # Increase or Decrease by a Percentage (using a multiplier)

In this worksheet, students will learn to increase or decrease an amount by using a multiplier, plus 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 them most of the time.

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

We may also need to calculate percentage decreases... sometimes good like a tax bill decreasing, or sometimes bad like the value of a something you own (like a car) reducing. Has he got bigger, or have I got smaller?

To find a percentage increase, we need to use a multiplier.

e.g. Increase 350 by 22%.

As we want to find 22% more than our original value, we need to add our 22% on top of our starting 100%.

So our multiplier in this case will be 1.22, which represents 122% of the original value.

Then we multiply our starting value by this:

350 × 1.22 = 427

But what about if we are looking for a percentage decrease?

e.g. Decrease 350 by 22%.

You may be tempted to think that we need to complete the sum 350 × 0.22, right?

No, no, no! This tells us what 22% of 350 is, not how much remains after a 22% decrease

Care is needed hereRemember that 'percent' means out of 100

So we need to take the 22% from 100% first.

This makes sense if we give it some thought - we want to have 22% less than the value we started with, which represented 100%.

100 - 22 = 78

We only want to find the 78% that is left.

To complete the decrease, we calculate:

350 x 0.78 = 273 Take it slowly and we will get there...

In this activity, we will calculate percentage increases and decreases using raw numbers and in real-life situations.

You may want to have a calculator handy to use, so you can concentrate on practising these methods and not exhausting your mental maths brain!

Let's get started.

Calculate the new values of each number below once they have been increased by the percentage shown.

Give each answer to 2 decimal places

It's time to try finding a percentage decrease now.

Calculate the new values of each number below once they have been decreased by the percentage shown.

Give each answer to 2 decimal places

Match each increase or decrease sum below to its correct amount.

## Column B

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

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

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

Who now earns more?

Mike

Margot

They both earn the same 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 need to make? Oh no... your scarf has shrunk 31% in the wash!

Its original length was 120 cm.

What is its new length rounded to the nearest cm?  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 the most fuel left at the end of the rally?

Neil

Sarah

They both had the same amount A set of 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?

Neil

Sarah

They both had the same amount

A motor insurance company offers discounts on premiums for careful drivers.

Their rates of discount are shown in this table:

 Years of 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 of no claims.

His full premium, before discounts, is £550.

Mrs. Parker has one year of no claims.

Her full premium, before discounts, is £345.

Jimmy has three years of no claims.

His full premium, before discounts, is £690.

Paul has two years of no claims.

His full premium, before discounts, is £820.

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

Neil

Sarah

They both had the same amount Last year John's boss (who as you can see is a bit grumpy) gave John a 10% 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 10%.

John's boss says he's no worse off than he was before the rise, but John doesn't agree.

Who is correct John or his boss?

John

His boss

They're both right as it's exactly the same

• Question 1

Calculate the new values of each number below once they have been increased by the percentage shown.

Give each answer to 2 decimal places

EDDIE SAYS
Take these one at a time and calculate the multiplier needed to increase each value. Remember that as we are calculating an increase, we need to add our % on top of 100%. Here is what your working should look like: 320 × 1.11 = 355.20 102 × 1.17 = 119.34 48 × 1.03 = 49.44 82 × 1.23 = 100.86 92 × 1.61 = 148.12 290 × 1.07 = 310.30 Did you remember that any percentage less than 10 needs an extra 0? If you calculated 48 × 1.30, you would have increased by 30% not 3%.
• Question 2

It's time to try finding a percentage decrease now.

Calculate the new values of each number below once they have been decreased by the percentage shown.

Give each answer to 2 decimal places

EDDIE SAYS
Did you remember the extra step at the beginning here? It's so easy to miss this out. Before we decrease, we need to remember to subtract the percentage decrease from 100 to reach our multiplier. Decrease 72 by 6: 100 - 6 = 94 72 × 0.94 = 67.68 Decrease 82 by 13: 100 - 13 = 87 82 × 0.87= 71.34 Decrease 101 by 28: 100 - 28 = 72 101 × 0.72 = 72.72 Decrease 189 by 42: 100 - 42 = 58 189 × 0.58 = 109.62 Decrease 55 by 8: 100 - 8 = 92 55 × 0.92 = 50.60 Decrease 47 by 31: 100 - 31 = 69 47 × 0.69 = 32.43 Imagine you were selling your old mobile 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 each increase or decrease sum below to its correct amount.

## 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 we see increase and decrease questions together, it's easy to forget that extra step to apply when decreasing. If we are increasing a percentage by 46%, it is easiest to use the multiplier 1 (which means just take the whole amount) and increase by 46%, so using a multiplier of 1.46. When decreasing, think: "I'm decreasing, so I have to take something away". This should start you off on the right foot. So, to decrease by 24%, remember to take 24 away from 100 first. 100 - 24 = 76. Now, we don't want the whole amount this time, so our multiplier starts with 0 and we just use the percentage left e.g 76, so our multiplier needs to be 0.76. Your working should look something like this: 123 × 1.23 = 151.29 342 × 1.61 = 550.62 72 × 0.76 = 54.72 53 × 1.325 = 70.225 48 × 0.94 = 45.12 632 × 0.875 = 553 How did you get on with matching those questions and answers?
• Question 4

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

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

Who now earns more?

Margot
EDDIE SAYS
Hopefully you are now getting used to using multipliers. So much quicker than trying to work it out the long way isn't it? Let's work out both their wages and then compare. Mike's wage decrease can be calculated like this: 100 - 5 = 95 400 × 0.95 = 380 Margot's wage decrease can be calculated like this: 350 × 1.12 = 392 So who earns more?
• 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 need to make?

69
EDDIE SAYS
This is a good example of how a percentage question can presented in written format. Let's look for our keywords here: percentage and increase. This should direct us to the sum: 56 × 1.23 = 68.88 How many whole toffee apples do you need to make, as you cannot make part of one?
• Question 6 Oh no... your scarf has shrunk 31% in the wash!

Its original length was 120 cm.

What is its new length rounded to the nearest cm?

EDDIE SAYS
This is just another way of wording a decrease question - the key word was 'shrunk', which should lead us to calculate a percentage decrease. 100 - 31 = 69 120 × 0.69 = 82.8 Should 82.8 be rounded to up to 83 cm or down to 82 cm?
• 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 the most fuel left at the end of the rally?

Sarah
EDDIE SAYS
The words increase and decrease are not always used in questions. It is important to take your time and identify words that can help you. In this case, the word 'used' suggests that we need to calculate a percentage decrease. Let's calculate the remaining fuel for both Neil and Sarah, then compare who has more. Neil: 100 - 25 = 75% 8 × 0.75 = 6 gallons Sarah: 100 - 40 = 60 12 × 0.60 = 7.2 gallons So who has the most fuel left at the end of the race?
• Question 8 A set of 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?

EDDIE SAYS
This type of question could easily catch you out. Read it very carefully. The first reduction is straightforward to calculate like this: 100 - 13 = 87 850 × 0.87 = £739.50 Now this is where we need to be careful. The further reduction of 8% needs to be taken from the new price of £739.50, not the original price: 100 - 8 = 92 739.50 × 0.92= £680.34 Does that make sense?
• Question 9

A motor insurance company offers discounts on premiums for careful drivers.

Their rates of discount are shown in this table:

 Years of 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 of no claims.

His full premium, before discounts, is £550.

Mrs. Parker has one year of no claims.

Her full premium, before discounts, is £345.

Jimmy has three years of no claims.

His full premium, before discounts, is £690.

Paul has two years of no claims.

His full premium, before discounts, is £820.

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

EDDIE SAYS
Oh my goodness, this seems a lot of work, as there is so much information - let's take a deep breath! Read through carefully once. Once you have done this you can see it is not that difficult at all. We're just applying a percentage discount in four different sums. Be careful to pick out the correct information, as the questions don't necessarily follow the order of the table. 550 × 0.40 = £220 345 × 0.85 = £293.25 690 × 0.55 = £379.50 820 × 0.75 = £615 Just goes to show how much money you can save by being a careful driver!
• Question 10 Last year John's boss (who as you can see is a bit grumpy) gave John a 10% 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 10%.

John's boss says he's no worse off than he was before the rise, but John doesn't agree.

Who is correct John or his 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 we have to use our creativity. Hint: Keep your numbers simple to help you! Suppose John's earn £20,000, a 10% increase would be: 20000 × 1.10 = £22,000 Looking good John! A 10% decrease of £22,000 is: 22000 × 0.90 = £19,800 So John will end up with even less than he started with! He's been well and truly robbed there! Congratulations on completing this activity! Why not try another percentages activity while you are on a roll?
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