RATIOS AND PROPORTIONS
A Ratio Is a Comparison
Many students get extremely nervous when they are asked to work with ratios. But there’s no need to be
nervous. A ratio is a comparison between the quantities of ingredients you have in a mixture, be it a class
full of people or a bowl of cake batter. Ratios can be written to look like fractions’don’t get them
confused.
The ratio of x to y can be expressed in the following three ways:
1.
- the ratio of x to y
- x: y
Part, Part, Whole
Ratios are a lot like fractions. In fact, anything you can do to a fraction (convert it to a decimal or
percentage, reduce it, and so on), you can do to a ratio. The difference is that a fraction gives you a part
(the top number) over a whole (the bottom number), while a ratio typically gives you two parts (boys to
girls, CDs to cassettes, sugar to flour), and it is your job to come up with the whole. For example, if there
is one cup of sugar for every two cups of flour in a recipe, that’s three cups of stuff. The ratio of sugar to
flour is 1:2. Add the parts to get the whole.
Ratios vs. Fractions
Keep in mind that a ratio
compares part of
something to another part.
A fraction compares
part of something to the
whole thing.
Ratio:
Fraction: Ratio to Real
If a class contains 3 students and the ratio of boys to girls in that class is 2:1, how many boys and how
many girls are there in the class? Of course: There are 2 boys and 1 girl.
Now, suppose a class contains 24 students and the ratio of boys to girls is still 2:1. How many boys and
how many girls are there in the class? This is a little harder, but the answer is easy to find if you think
about it. There are 16 boys and 8 girls.