 # Reduce a Ratio to its Simplest Form

In this worksheet, student practise simplifying a ratio. 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

A ratio is a method in maths that is used to compare two (or more) quantities.

So, for example, if I had 3 red balls and 9 blue balls, the ratio of red to blue balls would be 3:9

One thing that is vital in ratio is remembering that the order is important.

Cancelling a ratio

When you are trying to cancel a ratio, the rules are the same as if you were trying to cancel a fraction. You need to find the Highest Common Factor (HCF) and then divide by that.

Example 1: Cancel 9:3 to its simplest form.

The Highest Common Factor of 9 and 3 is 3, so we divide both sides by 3

3:1

Example 2: Simplify 25:85 as  far as possible.

The HCG of 25 and 85 is 5, so we divide both by 5.

5:17

Example 3: Write £2 to 30p as a ratio in its simplest form.

The key thing to notice here is that the units aren't the same so we have to change this.

Remember as well that the order for the ratio must be the same as in the question

£2 : 30 p

200 p : 30 p

Now we can cancel down, we can also get rid of the units now they are the same. The HCF here is 10, so we divide by 10.

20: 3

When we are cancelling a ratio, we divide both parts by the...

When we write a ratio, the order is important.

True or False.

True

False

Simplify 10:8 as far as possible.

Cancel 25:15 to its simplest form

I am trying to cancel the ratio 48:120

For each of the numbers given, state if it is either the highest common factor, a common factor or not a common factor.

Match the uncancelled ratio with their simplified form.

## Column B

25:25
1:3
7:21
9:10
48:120
5:3
9:10
2:5

What is £2.50 to 20 p as a ratio in its simplest form.

Write 4 hours to 24 minutes as a ratio in its simplest form.

Which of these ratios are simplified versions of...

28:40

14:20

7:10

7:20

Simplify 28:35:42 as far as possible.

• Question 1

When we are cancelling a ratio, we divide both parts by the...

EDDIE SAYS
It's those same three words we see every time we are cancelling anything. HCF: Highest Common Factor
• Question 2

When we write a ratio, the order is important.

True or False.

True
EDDIE SAYS
Absolutely true. 1:3 is NOT the same as 3:1
• Question 3

Simplify 10:8 as far as possible.

5:4
EDDIE SAYS
We need to find the HCF here which is 2. This means we need to divide both sides by 2.
• Question 4

Cancel 25:15 to its simplest form

5:3
EDDIE SAYS
We need to find the HCF here which is 5. This means we need to divide both sides by 5.
• Question 5

I am trying to cancel the ratio 48:120

For each of the numbers given, state if it is either the highest common factor, a common factor or not a common factor.

EDDIE SAYS
The only numbers here that aren't common factors are 5 and 48. Out of the rest of them, the biggest number you can divide both by is 24
• Question 6

Match the uncancelled ratio with their simplified form.

## Column B

25:25
5:3
7:21
1:3
48:120
2:5
9:10
9:10
EDDIE SAYS
Remember that you are always looking for the HCF. There are some as well that can't be simplified. 9/10, for example, has a HCF of 1 which means it cannot be reduced.
• Question 7

What is £2.50 to 20 p as a ratio in its simplest form.

25:2
EDDIE SAYS
For this question, we need to write both the numbers in the same units. £2.50 = 250 p We can now write the ratio as 250:20 and cancel down.
• Question 8

Write 4 hours to 24 minutes as a ratio in its simplest form.

10:1
EDDIE SAYS
As before, we need to convert the 4 hrs into minutes (240 minutes) Remember that order is important. The 4 hrs comes first in the question so it must come first in the ratio 4 hrs: 24 minutes 240 mins: 20 mins
• Question 9

Which of these ratios are simplified versions of...

28:40

14:20
7:10
EDDIE SAYS
It's important to notice here that the question doesn't ask for the simplest but 'a simplified version'. For this question, there are two common factors (2 and 4) so you could divide by either.
• Question 10

Simplify 28:35:42 as far as possible.

4:5:6
EDDIE SAYS
Does it matter that there are 3 numbers here? Not at all Just find the HCF (7) of all three and divide by that.
---- OR ----

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