# Simplify a Ratio to the Form 1:n or m:1

In this worksheet, students will create and simplify ratios in the form 1:n or m:1 where the values of m and n can be decimals, converting values into the same units where required.

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 may have had a lot of practice in simplifying fractions and ratios into their simplest possible form by finding and applying the Highest Common Factor (HCF).

One of the things that you may have heard is that you cannot have decimals in the simplified versions of ratios.

There is, however, one important 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 (m:1).

This approach frequently means that you will have a decimal representing n or m.

In this situation alone, using a decimal in a ratio is allowed.

Let's look at this in action with some examples now.

e.g. Write 5:8 in the form 1:n.

As we are looking for 1:n, this means that the first number in our ratio must be 1 and the second can be a decimal or whatever we require.

Let's begin with our starting ratio:

5:8

In order to convert the first number to 1, we have to divide by 5 (as 5 ÷ 5 = 1).

So we need to do the same thing to the second number in the ratio:

5:8 ÷ 5 = 1 : 1.6

e.g. Write 25:10 in the form m:1.

As we are looking for m:1, this means that the second number in our ratio must be 1 and the first can be a decimal or whatever we require.

In order to convert the second number to 1, we have to divide by 10 (as 10 ÷ 10 = 1).

25:10 ÷ 10 = 2.5 : 1

In this activity, we will create and simplify ratios in the form 1:n or m:1 where the values of m and n can be decimals, converting values into the same units where required.

Type a number into the first space and a word into the second space to complete the sentence below.

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

Is the statement above true or false

True

False

Simplify the ratio 5:4 into the form 1:n.

True

False

Simplify 28:10 into the form m:1.

True

False

The ratios on the left below have been cancelled into the form m:1.

Match each uncancelled ratio with its correct simplified version.

## Column B

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

The ratios on the left below have been cancelled into the form 1:n.

Match each uncancelled ratio with its correct simplified version.

## Column B

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

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

## Column B

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

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

## Column B

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

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

Please note, where required, decimals have been rounded to two decimal places.

7:10

1.43 : 1

1 : 1.43

0.7 : 1

1 : 0.7

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

7:10

1.43 : 1

1 : 1.43

0.7 : 1

1 : 0.7

• Question 1

Type a number into the first space and a word into the second space to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
The hardest thing to recall here is the exception to our usual rule - in this case only, one of the numbers in our ratio can be a decimal. To express a ratio in the form 1:n, we need to convert the first number into 1, then complete the same operation on the other side, which may result in the creation of a decimal.
• Question 2

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

Is the statement above true or false

CORRECT ANSWER
False
EDDIE SAYS
This was a bit of a trick question! We can only use decimals in ratios on two occasions - when we are expressing a ratio in the form 1:n, but also in the form m:1. If you can commit these situations to memory, then you will never use a decimal in a ratio in the wrong circumstances.
• Question 3

Simplify the ratio 5:4 into the form 1:n.

CORRECT ANSWER
EDDIE SAYS
As we are looking for 1:n, this means that the first number in our ratio must be 1 and the second can be a decimal (or whatever we require). Let's begin with our starting ratio: 5:4 In order to convert the first number to 1, we have to divide by 5 (as 5 ÷ 5 = 1). So we need to do the same thing to the second number in the ratio: 5:4 ÷ 5 = 1 : 0.8
• Question 4

Simplify 28:10 into the form m:1.

CORRECT ANSWER
EDDIE SAYS
As we are looking for m:1, this means that the second number in our ratio must be 1 this time. Let's begin with our starting ratio: 28:10 In order to convert the second number to 1, we have to divide by 10 (as 10 ÷ 10 = 1). So we need to do the same thing to the second number in the ratio: 28:10 ÷ 10 = 2.8 : 1
• Question 5

The ratios on the left below have been cancelled into the form m:1.

Match each uncancelled ratio with its correct simplified version.

CORRECT ANSWER

## Column B

10:5
2:1
5:10
0.5 : 1
4:10
0.4 : 1
32:5
6.4 : 1
EDDIE SAYS
As we are looking for m:1, this means that the second number in our ratio must be 1 in all these cases. Let's work through each starting ratio, one at a time. 10:5 > ÷ 5 = 2:1 5:10 > ÷ 10 = 0.5 : 1 4:10 > ÷ 10 = 0.4 : 1 32:5 > ÷ 5 = 6.4 : 1 Remember that our second number does not have to be a decimal, it is simply allowed to be if required.
• Question 6

The ratios on the left below have been cancelled into the form 1:n.

Match each uncancelled ratio with its correct simplified version.

CORRECT ANSWER

## Column B

10:5
1 : 0.5
5:10
1:2
4:10
1 : 2.5
32:5
1 : 0.15625
EDDIE SAYS
As we are looking for 1:n, this means that the first number in our ratio must be 1 in all these cases. Let's work through each starting ratio, one at a time. 10:5 > ÷ 10 = 1 : 0.5 5:10 > ÷ 5 = 1:2 4:10 > ÷ 4 = 1 : 2.5 32:5 > ÷ 32 = 1 : 0.15625 Can you see how the same ratios are converted into totally different amounts, depending on whether we are asked to apply 1:n or m:1?
• Question 7

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

CORRECT ANSWER
EDDIE SAYS
As we are looking for 1:n, this means that the first number in our ratio must be 1. The difficulty here is that we must find our starting ratio, using amounts which are expressed in different units (£ and p). So, to start with, we need to convert them into the same format. There are 100 p in £1, which leads us to the starting ratio (when we remove our units as they are now the same) of: 100:70 In order to convert the first number to 1, we have to divide by 100 (as 100 ÷ 100 = 1). So we need to do the same thing to the second number in the ratio: 100:70 ÷ 100 = 1 : 0.7
• Question 8

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

CORRECT ANSWER
EDDIE SAYS
As we are looking for m:1, this means that the second number in our ratio must be 1. Again, our units are different here, so we need to get them into the same format. There are 1000 m in 1 km, which leads us to the starting ratio (when we remove our units as they are now the same) of: 1000:950 1000:950 ÷ 1000 = 1 : 0.95
• Question 9

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

Please note, where required, decimals have been rounded to two decimal places.

CORRECT ANSWER
7:10
1 : 1.43
0.7 : 1
EDDIE SAYS
It's important to notice here that the question doesn't specifically ask for 1:n or m:1, but rather a 'simplified version' in general. To test each option, we need to find the divisor and check it if works in both elements. e.g. For 7:10, we need to consider what 28:40 could have been divided by to reach this. The relationship between 28 and 7 would be '÷ 4'. Let's check that works in the other number: 40 ÷ 2 = 10 So the ratio 7:10 is an equivalent ratio to 28:40. How about using 1:n or m:1? If we use 1:n, then we need to convert our first number in the ratio to 1. To do this we divide by 28, which leads us to 1: 1.43 (to 2 decimal places). Can you find the equivalent ratio for m:1 independently? Did you spot that the three equivalent ratios present within these options?
• Question 10

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

CORRECT ANSWER
EDDIE SAYS
This one may look confusing, but it is really just tying everything together. All this means is that the number in the middle has to be 1. To achieve this, we need to divide all parts of the ratio by 35: 28:35:42 ÷ 35 = 0.8 : 1 : 1.2 You can now create and simplify ratios in the form 1:n or m:1 where the values of m and n can be decimals, converting values into the same units where required. If you are feeling on a roll, why not try another activity to practise the concept of ratio more?
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