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 * 4 = 3 * 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.