Sharing an amount into a ratio

Ratio is all about sharing amounts into different sizes or proportions.  It will appear somewhere on your GCSE maths exam.  Study the example question below then test yourself.

Example Question

a)  Write the ratio 240:360 in its simplest form.

b)  Share 240 in the ratio 5:3.

c)  Chris and Dave shared their lottery winning in the ratio 2:3.  Dave received 360.  How much did Chris receive?

a)  To simplify a ratio we divide each part of the ratio by common factors until we cannot simplify any further.

24:36    (divide both sides by 10)
12:18     (divide by 2)                   
6:9      (divide by 2)                 
2:3      (divide by 3)                 

We cannot simplify any further so the ratio is in its simplest form.

To solve a ratio question when we are given the total amount follow these three steps:

Step 1:    Add together the ratio parts:
                5 + 3 = 8 parts

Step 2:    Divide your total amount by the number of parts:
                240 8 = 30 per part

Step 3:    Multiply your answer by your ratio parts:
                3 x 30 and 5 x 30
                90 and 150

When we are not given the total amount the method is different.  It's very important that you can spot the two different types of questions!

The money is split in the ratio 2:3 as Dave received 360 so:

2 : 3      
? : 360  

We need to find the missing number.  To do this divide the amount we do know by its corresponding ratio part.
So 360 3 = 120.  Finally multiply the other ratio part by 120 to get: 2 x 120 = 240.

So Chris receives 240.

Test Yourself!

a)  Write the ratio 120:200 in its simplest form.
b)  Hannah and Sarah share 140 in the ratio 2:5.  How much does Hannah receive?
c)  Sam and Bob shared their pocket money in the ratio 3:4.  Sam received 4.50.
How much did Bob receive?

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