# How do you solve 3:12 = x:16?

Jul 26, 2016

x = 4

#### Explanation:

We can express the ratios as fractions.

$\Rightarrow \frac{3}{12} = \frac{x}{16}$

Solve for x by $\textcolor{b l u e}{\text{cross-multiplication}}$

$\frac{\textcolor{red}{3}}{\textcolor{b l u e}{12}} = \frac{\textcolor{b l u e}{x}}{\textcolor{red}{16}}$

multiply the same colours across (X) the fraction.

$\Rightarrow \textcolor{b l u e}{12 x} = \textcolor{red}{3 \times 16} = \textcolor{red}{48}$

now we have to solve : 12x = 48

divide both sides by 12

$\frac{{\cancel{12}}^{1} x}{\cancel{12}} ^ 1 = {\cancel{48}}^{4} / {\cancel{12}}^{1} \Rightarrow x = 4$

That is 3:12 = 4:16 = 1:4 'in simplest form'