 # Use Multiplicative Relationships

In this worksheet, students practise finding the multiplicative relationship between two items as either a ratio or a fraction. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Calculations with Ratio

Difficulty level:   ### QUESTION 1 of 10

There are a number of times when you can write the relationship as a multiple.

For example, you could say, 'this bottle holds three times as much as that one'. This is a multiplicative relationship.

One of the skills you have to master is how to write this as either a ratio or a fraction.

Example 1: One jug of water is three times larger than another. Write the relationship as a ration.

We know that all ratios are written as the form a:b where a and b are whole numbers.

We can write this relationship as 1:3 or 3:1 (the question doesn't say which one is the bigger one so we can use either order)

Example 2: I have two pieces of wood. Piece A is 60 cm and piece B is 80 cm long.

a) Write the lengths of A: B as a ratio in its simplest form,

We start by writing them as they are - 60 : 80

We can then cancel these down to their simplest form by dividing by 20 - 3:4

b) Find the length of B as a fraction of A.

In this, we are finding B as a fraction of A, so B must go on the top of the fraction and A on the bottom.

This gives a fraction of 80/60. This can then be canceled down (again, divide by 20) to get 4/3

When we have a real life situation involving quantities, we can ...

Bag A contains 15 marbles and Bag B contains 10 marbles.

Write the relationship as a ratio in its simplest form.

(Don't put any spaces in your ratios, the system will mark it incorrect)

Bag A contains 15 marbles and Bag B contains 10 marbles.

Write the ratio A: B in its simplest form

(Don't put any spaces in your ratios, the system will mark it incorrect)

Match the situation with the ratio

## Column B

3 times the size
1:4
4 times the size
1:3
half the size
2:1
one tenth the size
10:1

It takes me 20 minutes to walk to the shop. If it takes James 15 minutes, what fraction of my time does James take?

Two cans of fizzy drink contain 250 ml and 400 ml.

What fraction of the smaller one does the larger one contain?

Match the situation with the fraction.

## Column B

6 minutes as a fraction of 10 minutes
1/2
6 minutes as a fraction of 20 minutes
1/12
100 ml as a fraction of 200 ml
3/10
2 hours as a fraction of 2 day
3/5

Two pieces of wood are in the ratio of 3:5. If the smaller one is 60 cm long, how long is the larger one?

I take 4/5 of the time as my friend Richard to finish a race.

If Richard takes 1 hour to finish, how many minutes do I take?

Three milk cartons are in the ratio of 2:3:5.

If the medium size one contains 450 ml, how much is in the smaller and larger ones?

 Contains (ml) Smaller Larger
• Question 1

When we have a real life situation involving quantities, we can ...

EDDIE SAYS
There's only two ways to write a multiplicative relationship. They have to be either a fraction or a ratio.
• Question 2

Bag A contains 15 marbles and Bag B contains 10 marbles.

Write the relationship as a ratio in its simplest form.

(Don't put any spaces in your ratios, the system will mark it incorrect)

3:2
2:3
EDDIE SAYS
If we write the two numbers as a ratio, we get... 15:10 We can then cancel this down to 3:2 The question doesn\'t say which has to come first so we can write either way.
• Question 3

Bag A contains 15 marbles and Bag B contains 10 marbles.

Write the ratio A: B in its simplest form

(Don't put any spaces in your ratios, the system will mark it incorrect)

3:2
EDDIE SAYS
If we write the two numbers as a ratio, we get... 15:10 We can then cancel this down to 3:2 Because the question says we want the ratio A: B, the order does matter in this case.
• Question 4

Match the situation with the ratio

## Column B

3 times the size
1:3
4 times the size
1:4
half the size
2:1
one tenth the size
10:1
EDDIE SAYS
This is all about key words, Twice means the second one is x 2 the first. half means the second on is half the first But we cant have 1:0.5 so we have to double each side to get 2:1
• Question 5

It takes me 20 minutes to walk to the shop. If it takes James 15 minutes, what fraction of my time does James take?

3/4
EDDIE SAYS
The trick here is to take note of the words 'fraction of my time'. This means my time has to go on the bottom and the other needs to go on the top. This gives 15/20 which cancels to ...
• Question 6

Two cans of fizzy drink contain 250 ml and 400 ml.

What fraction of the smaller one does the larger one contain?

8/5
EDDIE SAYS
Once again, we need to look at the phrase 'fraction of the smaller one'. This means the 250 goes on the bottom and the 400 on the top. This gives 400/250 which cancels to ...
• Question 7

Match the situation with the fraction.

## Column B

6 minutes as a fraction of 10 min...
3/5
6 minutes as a fraction of 20 min...
3/10
100 ml as a fraction of 200 ml
1/2
2 hours as a fraction of 2 day
1/12
EDDIE SAYS
Nice and simple. Remember that 'fraction of' means that the thing afterwards is on the denominator. Write the fraction (remembering to make the units the same) and cancel
• Question 8

Two pieces of wood are in the ratio of 3:5. If the smaller one is 60 cm long, how long is the larger one?

100
100cm
100 cm
EDDIE SAYS
This is actually a hidden ratio question. If the smaller part is 60 cm, this is worth 3 parts. We can find that one part is worth 20 cm The longer section is 5 parts and each part is worth 20 cm...
• Question 9

I take 4/5 of the time as my friend Richard to finish a race.

If Richard takes 1 hour to finish, how many minutes do I take?

48
EDDIE SAYS
All this question is asking is for 4/5 of 1 hour. As 1 hour is 60 minutes, we are trying to find 4/5 of 60 minutes. Remember that for fractions of amounts, divide by the bottom, multiply by the top.
• Question 10

Three milk cartons are in the ratio of 2:3:5.

If the medium size one contains 450 ml, how much is in the smaller and larger ones?

 Contains (ml) Smaller Larger
EDDIE SAYS
Just another hidden ratio question here. The middle carton has 450 ml, this is worth 3 parts. From this, we can find 1 part.(150 ml) From the 1 part, we can work out how much 2 and 5 parts are worth.
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