Question

Identify the equivalent ratios among the following:

$1:4,3:9,1:3,4:12,2:6$

Answer 1

Identifying the equivalent ratios:

A ratio is similar to a fraction. So, if we divide or multiply the numerator and the denominator by the same number, we get an equivalent ratio.

Here, the given ratios are $1:4,3:9,1:3,4:12,2:6$.

So, we convert all the given ratios to their lowest form.

$$\begin{gathered} 1:4=1:4 \\ 3:9=\frac{3}{9}=\frac{3÷3}{9÷3}=\frac{1}{3}=1:3 \\ 1:3=1:3 \\ 4:12=\frac{4}{12}=\frac{4÷4}{12÷4}=\frac{1}{3}=1:3 \\ 2:6=\frac{2}{6}=\frac{2÷2}{6÷2}=\frac{1}{3}=1:3 \end{gathered}$$

Clearly, the ratios that have the same lowest form are $3:9,1:3,4:12,2:6$ i.e. these represent the same ratio.

Thus, the equivalent ratios are $3:9,1:3,4:12,2:6$.