Question

Simplify each ratio.1) 12:202) 18:45

Answer 1

In order to simplify a ratio you need to divide each number by the same integer and the results of both divisions must be integers too. This happens when the number you use to divide is a multiple of both.

We have 12:20, which common multiples they have? I'm going to list them: 1, 2 and 4. The important thing here is to divide by the greatest common multiple:

`\begin{gathered} (12)/(4)=3 \\ (20)/(4)=5 \end{gathered}`

So the simplified ratio is 3:5

For 18 and 45 we have the multiples: 1, 3, 9. So we have to divide by 9:

`\begin{gathered} (18)/(9)=2 \\ (45)/(9)=5 \end{gathered}`

And the simplified ratio is 2:5