 # Reduce a Ratio to its Simplest Form

In this worksheet, students practise simplifying a ratio with 3 or more parts. 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,  9 blue balls and 10 green balls, the ratio of red to blue balls would be 3:9:10

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) of all the numbers and then divide by that.

Example 1: Cancel 9:3:6 to its simplest form.

The Highest Common Factor of 9,3 and 6 is 3, so we divide each part by 3

3:1:2

Example 2: Simplify 25:85:15 as  far as possible.

The HCG of 25, 85 and 15 is 5, so we divide each part by 5.

5:17:3

Example 3: Write £2 to 30p to 45p 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 : 45p

200 p : 30 p : 45p

Now we can cancel down, we can also get rid of the units now they are the same. The HCF here is 5, so we divide by 5.

40: 6: 9

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

When we write a ratio, the order is important.

True or False.

True

False

Simplify 10:8:2 as far as possible.

Cancel 30:20:10 to its simplest form

I am trying to cancel the ratio 25:35:42

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

15:20:5
4:10:1
7:21:28
3:4:1
48:120:12
1:3:4
9:10:11
9:10:11

What is 200 m, ,1 km, 750 m as a ratio in its simplest form.

Write 42 minutes : 70 minutes: 2 hours as a ratio in it's simplest form.

Which of these ratios are simplified versions of...

21 : 63 ; 42

1:3:2

7:21:14

3:9:6

Simplify 180 : 360 : 720 : 900 as far as possible.

• Question 1

When we are cancelling a ratio, we divide all 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 : 5 is NOT the same as 5 : 3 : 1
• Question 3

Simplify 10:8:2 as far as possible.

5:4:1
EDDIE SAYS
We need to find the HCF here which is 2. This means we need to divide by 2.
• Question 4

Cancel 30:20:10 to its simplest form

3:2:1
EDDIE SAYS
We need to find the HCF here which is 10. This means we need to divide by 10.
• Question 5

I am trying to cancel the ratio 25:35:42

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 of all three are 5 and 14. While they are common factors of 2 of the numbers, it needs to be a common factor of all 3. Out of the rest of them, the biggest number you can divide all of them by is 7
• Question 6

Match the uncancelled ratio with their simplified form.

## Column B

15:20:5
3:4:1
7:21:28
1:3:4
48:120:12
4:10:1
9:10:11
9:10:11
EDDIE SAYS
Remember that you are always looking for the HCF. There are some as well that can't be simplified. 9:10:11, for example, has a HCF of 1 which means it cannot be reduced.
• Question 7

What is 200 m, ,1 km, 750 m as a ratio in its simplest form.

4:20:15
EDDIE SAYS
For this question, we need to write both the numbers in the same units. 1km = 1000m We can now write the ratio as 200:1000:750 and cancel down.
• Question 8

Write 42 minutes : 70 minutes: 2 hours as a ratio in it's simplest form.

21:35:60
EDDIE SAYS
As before, we need to convert the 2 hrs into minutes (120 minutes) Remember that order is important. The 2 hrs comes flast in the question so it must come last in the ratio 42 minutes : 70 minutes: 2 hours 21 : 35 : 60
• Question 9

Which of these ratios are simplified versions of...

21 : 63 ; 42

1:3:2
7:21:14
3:9:6
EDDIE SAYS
It's important to notice here that the question doesn't ask for the simplest but 'a simplified version'. Did you notice they were all the valid?
• Question 10

Simplify 180 : 360 : 720 : 900 as far as possible.

1:2:4:5
EDDIE SAYS
Does it matter that there are 4 numbers here? Not at all Just find the HCF (180) of all four and divide by that.
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