 # Simplifying a ratio to the form 1:n or m:1

In this worksheet, students practise simplifying ratios to the form 1:n or m:1. 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

By now, you will have plenty of practice of simplifying fractions and ratios to their simplest form by finding the HCF.

One of the things that you will have been told is that you cannot have decimals in the simplified versions.

There is however one exception to this rule.

You could be asked to write a ratio in the form 1:n or m:1. All this means is that either the first number must be 1 (1:n) or the second must be 1 (1:m).

This frequently means you have a decimal for the other number. In this situation, that is fine.

Example 1: Write 5:8 in the form 1:n.

As we are looking for 1:n, this means the first number must be 1 and the second can be a decimal.

5:8

To make the first number 1, we have to divide by 5 (5 &div; 5 = 1)

So we divide both sides by 5

1 : 1.6

Example 2: Write 25:10 in the form m:1.

As we are looking for m:1, this means the second number must be 1 and the first can be a decimal.

25:10

To make the second number 1, we have to divide by 10 (10 &div; 10 = 1)

So we divide both sides by 10

2.5 : 1

Complete the following sentence...

True or False?

A number in a ratio can only be a decimal if it is put in the form 1:n.

True

False

Simplify 5:4 into the form 1:n

Simplify 28:10 into the form m:1

These ratios have been cancelled into the form m:1.

Match the uncalncelled ratio with the simplified ones.

## Column B

10:5
6.4:1
5:10
0.4:1
4:10
2:1
32:5
0.5:1

These ratios have been canceled into the form 1:n.

Match the uncancelled ratio with the simplified ones.

## Column B

10:5
1:0.5
5:10
1:2
4:10
1:0.15625
32:5
1:2.5

Write £1to 70 p as a ratio in the form 1:n

Write 950 m to 1 km as a ratio in the form m:1

Which of these could be correct simplifications of 28:40?

7:10

1.43:1

1:1.43

0.7:1

1:0.7

Simplify 28:35:42 into the form n:1:m

• Question 1

Complete the following sentence...

EDDIE SAYS
The hardest thing to get your head round here is that one of the numbers can be a decimal. Just remember, make the first number 1 and do the same operation to the other side.
• Question 2

True or False?

A number in a ratio can only be a decimal if it is put in the form 1:n.

False
EDDIE SAYS
Not quite. Remember it can be in the form 1:n but also m:1
• Question 3

Simplify 5:4 into the form 1:n

1:0.8
EDDIE SAYS
If we have to make the first number 1, we do this by dividing by 5. If we then do this on the other side of the ratio we get 4 ÷ 5
• Question 4

Simplify 28:10 into the form m:1

2.8:1
EDDIE SAYS
If we have to make the second number 1, we do this by dividing by 10. If we then do this on the other side of the ratio we get 28 ÷ 10
• Question 5

These ratios have been cancelled into the form m:1.

Match the uncalncelled ratio with the simplified ones.

## Column B

10:5
2:1
5:10
0.5:1
4:10
0.4:1
32:5
6.4:1
EDDIE SAYS
Remember the rules, as we are looking for m:1, we need to make the second number 1. To do this, we divide both sides by the same.
• Question 6

These ratios have been canceled into the form 1:n.

Match the uncancelled ratio with the simplified ones.

## Column B

10:5
1:0.5
5:10
1:2
4:10
1:2.5
32:5
1:0.15625
EDDIE SAYS
Remember the rules, as we are looking for 1:n, we need to make the first number 1. To do this, we divide both sides by the same.
• Question 7

Write £1to 70 p as a ratio in the form 1:n

1:0.7
EDDIE SAYS
Our first job here is to convert these into the same units, i'd go for pence (it's easier) This would give 100:70 To put it in the form 1:n, we need to divide both sides by 100
• Question 8

Write 950 m to 1 km as a ratio in the form m:1

0.95:1
EDDIE SAYS
Our first job here is to convert these into the same units, i'd go for metres This would give 950:1000 To put it in the form m:1, we need to divide both sides by 1000
• Question 9

Which of these could be correct simplifications of 28:40?

7:10
1:1.43
0.7:1
EDDIE SAYS
Im sure you spotted the first one was the simplified version of the ratio. Did you then notice that there is a correct one for 1:n and a correct one for m:1?
• Question 10

Simplify 28:35:42 into the form n:1:m

0.8:1:1.2
EDDIE SAYS
This is just tying everything together. All this means is that the number in the middle has to be 1. We can therefore just divide all 3 parts of 35
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