Question

Fill the following blanks: $\frac{15}{18}=\frac{\left[\right]}{6}=\frac{10}{\left[\right]}=\frac{\left[\right]}{30}$. Are these equivalent ratios?

Answer 1

Find the missing values:

Given: $\frac{15}{18}=\frac{\left[\right]}{6}=\frac{10}{\left[\right]}=\frac{\left[\right]}{30}$

$\frac{15}{18}=\frac{5\times 3}{6\times 3}$

$\Rightarrow \frac{15}{18}=\frac{5}{6}$ ….[1]

$\frac{5}{6}=\frac{5\times 2}{6\times 2}$ ( By multiplying both numerator and denominator by $2$ )

$\Rightarrow \frac{5}{6}=\frac{10}{12}$ …[2]

$\frac{5}{6}=\frac{5\times 5}{6\times 5}$ ( By multiplying both numerator and denominator by $5$ )

$\Rightarrow \frac{5}{6}=\frac{25}{30}$ …[3]

By comparing [1], [2] and [3], we can say that, $\frac{15}{18}=\frac{5}{6}=\frac{10}{12}=\frac{25}{30}$

Hence, $\frac{\mathbf{15}}{\mathbf{18}}\mathbf{=}\frac{\mathbf{5}}{\mathbf{6}}\mathbf{=}\frac{\mathbf{10}}{\mathbf{12}}\mathbf{=}\frac{\mathbf{25}}{\mathbf{30}}$.

Yes, they are equivalent ratios.