Tutor’s Toolkit: Application of Number

Carrying Out Calculations

C7	Use proportion and calculate ratios where appropriate

Useful Web Links:

BBC Bitesize Revision: Maths: Ratio
http://www.bbc.co.uk/schools/gcsebitesize/maths/numberf/ratiorev1.shtml

BBC Skillswise: Numbers: Ratio and proportion
http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/

C7.1	Ratio notation

Scope: 

Students need to be able to:
•	Write correct ratio notation.
•	Simplify ratios.

What students need to know:

Write correct ratio notation.

•	A map scale is normally given in ratio notation. In Carrying Out Calculations, Section C6, a map scale was given as 1:25,000. This means that every 1cm on the map represents 25,000cm on the ground.

•	A paint colour mix could say that it needs two parts red for every three parts blue. We would say that the ratio of red to blue is 2:3. Notice that it is vital that we say what the ratio represents, so that you can see which way round it is. If we got the ratio wrong and said 3:2 it would be a reddy blue and not the bluey red we needed!

•	We can divide amounts up using ratio notation. An elderly relative divides their estate up so the one daughter gets more than the other. They could say how much each was getting by setting the ratio of the mount for the first daughter to the amount for the second daughter as 5:2. 

•	Ratio notation shows the same information as fractions, but in a slightly different way. A ratio of 1:1 shows that there are 2 parts in total and each part is the same. In other words  each.

•	In the case of the daughters and the will, the ratio was 5:2. That’s 7 parts in total. So the first daughter will get  and the second daughter will get  of the money.

Simplify ratios.

Just like fractions, ratios can be simplified.
A ratio of 8:4 is eight parts of one for every four parts of the other.

	That’s just the same as 2 parts of one to every one part of the other.
	8:4 = 8  4 : 4  4 = 2:1
	We can divide (or multiply) both parts of a ratio by the same number and it stays the same ratio. When there is no whole number which divides both parts exactly, the ratio is in its simplest form.

For example:
•	18:12 = 18  6 : 12  6 = 3:2
•	24:20:16 = 24  4 : 20  4 : 16  4 = 6:5:4

C7.2	Calculate proportions

Scope: 

Students need to be able to:
•	Make proportion calculations.

What students need to know:

Make proportion calculations

If I know how much a certain quantity of something costs, I can use that information to work out how much any other quantity of the same stuff costs. This works because the price and the quantity are in proportion – as one increases, the other increases by the same proportion.

(Notice that, in reality, prices are not always in proportion with quantities – there may be a discount for buying a lot, for example – so you need to be sure that the quantities are in proportion).

Proportion calculation works in the same way as conversions 
(For further information, refer to Carrying Out Calculations, Section C4) and scale drawings (refer to Carrying Out Calculations, Section C6)

Example Question:
7m of cloth cost £17.50. How much would 10m cost?

Solution:
The usual method is to work out how much a unit costs. In this case that would be 1 metre of the cloth.

£17.50  7 = £2.50.
So, 1 metre costs £2.50.
Now, 10 metres will cost 10  £2.50 = £25.00