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# Ratio

"A ratio is a comparison between two like quantities in the same units."

Simplest form ratios

A ratio, such as a:b can be reduced similarly like fractions, using a lowest common denominator approach.

Eg.
2:4 is the same as
1:2

The example ratios 2:4 and 1:2 are also known as equivalent ratios because they really are the same. See also Proportion.

Finding a ratio between quantities

change into same units, then
put lower one on the left
find the simplest

Eg.
300mls and 1.5litres goes to
300mls and 1500 litres
300:1500
3:15
1:5

Dividing a quantity into ratios

If you are given a ratio and a total, you can work out the ratio amounts thus:
Divide the total by the parts to find 1 part
Times the ratio amount by 1 part.

Eg.
20m total, 2:3
2+3=5
20/5=4
4*2 is 8:4*3 is 12
8 metres, 12 metres.

If you are given a ratio and one part:
Divide value by the ratio amount, gives you multiplying factor
Times factor by other ratio amount, now you know value of both sides

Eg.
5:7, 5 parts is 20
20/5 is 4
7 times 4 is 28
28 + 20 is 48 total