Academic Skills Advice
Summary
Ratio
Expressing ratios
A ratio is a way of comparing 2 or more quantities and should always be:
in the same units
in the correct order
cancelled down/simplified (always do the same to each side).
Example:

Write 50cm to 8m as a ratio:
Same units:
50cm to 800cm
As a ratio:
50:800
Cancel down:
1:16
(both sides will ÷ by 50)
Sharing Quantities in a Given Ratio
To do this:
find the total number of parts needed
Divide by the total number of parts to find the size of 1 part
Multiply each number in the ratio by the value of 1 part.
Example:

Split £280 in the ratio 5:3
Total number of parts needed:
Divide the money into 8 equal parts:
The original ratio is 5:3
5 x 35 = £175.
5+3 = 8
280÷8=£35 (each part is worth £35)
3 x 35 = £105.
The 2 amounts of money are: £175 and £105 (check these add to the original £280)
Sometimes you could be given one part of the money instead of the full amount.
Example:

Delia, Ed & Fatima share prize money in the ratio 3:4:5 (D:E:F). If Delia receives
£210 how much do the others receive and how much was the total prize money?
Delia received 3 parts which is equal to £210
£210 ÷ 3 = £70
(So each part = £70)
The original ratio is 3:4:5
5 x 70 = £350.
3 x 70 = £210.
4 x 70 = £280.
Therefore: D=£210, E=£280 and F=£350. Total prize money = £840.
© H Jackson 2010 / ACADEMIC SKILLS
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