Year 8: Finding values based on ratios

Ratios are used to compare two or more quantities. They're often written as fractions or using a colon (:).

Understanding ratios

A ratio compares two quantities of the same type. For example, a 2:3 ratio means for every 2 of something, there are 3 of the same thing.

Finding a missing value

You can use ratios to find a missing value if you know the other values. Here's how:

Using proportions

The most common way is using proportions. A proportion looks like this:
$a/b=c/d$
Where:
a and b are the known quantities.
c and d are the unknown quantities.

To find a missing value, you can cross-multiply and solve for the unknown variable. For example:

If a:$b=3$:4, and $a=12$, what is b?

Set up the proportion:
$12/3=x/4$
Cross-multiply:
$12\times 4=3\times x$
$48=3x$
Divide both sides by 3:
$x=16$

So, $b=16$.

Examples

Try these:
1. If 2:$5=x$:10, find x.
2. If a:$b=1$:2, and $b=8$, find a.