Ratios Explained: Simplifying and Sharing in a Ratio
What a ratio says, how to simplify one, how a ratio relates to fractions of the total, and the parts method for sharing an amount in a given ratio.
A recipe uses cups of flour for every cups of milk. The ratio of flour to milk is written and read "two to three". Double the recipe and you use cups to , but the ratio, the relationship, stays the same.
Flour to milk is : two equal parts against three.
Simplifying ratios
Ratios simplify just like fractions: divide every part by a common factor. becomes when you divide both by .
Make the units match before simplifying. cm to m is , which is , not .
Ratios and fractions
A ratio compares part with part. A fraction compares part with whole. In a class with boys and girls in the ratio , there are parts in total, so of the class are boys and are girls.
In a ratio , the first quantity is of the total.
does not mean the first is of the total. It means the first is of the second.
Sharing in a ratio
To share an amount in a ratio, count the total number of parts, find what one part is worth, then build each share.
Two people, one getting 2 parts for every 3 the other gets.
Orange squash is mixed with water in the ratio . How much squash is in a ml drink?
- 1
There are parts.
When you know one share
Sometimes you know one quantity rather than the total. Use it to find the value of one part, then carry on as before.
Red and blue counters are in the ratio . There are red counters. How many are blue?
- 1
Red is parts.
Common questions
- Is a ratio the same as a fraction?
Not quite. A ratio compares two parts with each other. The fractions of the total are and , because there are parts altogether.
- Does the order of a ratio matter?
Yes. Flour to milk is not the same as milk to flour, which is . Keep the order the words give.
The Ratios lesson has worked examples and unlimited practice that adapts to you.