Chapter 7.1, Problem 48HP

To determine

To write: The four ratios that are equivalent to $2:5$ .

Answer to Problem 48HP

The four ratios that are equivalent to $2:5$ are $\frac{4}{10},\frac{6}{15},\frac{8}{20},\frac{10}{25}$

Explanation of Solution

Consider the first proportion.

  $\begin{array}{c}\frac{2}{5}=\frac{2\cdot 3}{5\cdot 3}\\ =\frac{6}{15}\end{array}$

Consider the second proportion.

  $\begin{array}{c}\frac{2}{5}=\frac{2\cdot 4}{5\cdot 4}\\ =\frac{8}{20}\end{array}$

Consider the third proportion.

  $\begin{array}{c}\frac{2}{5}=\frac{2\cdot 5}{5\cdot 5}\\ =\frac{10}{25}\end{array}$

Consider the fourth proportion.

  $\begin{array}{c}\frac{2}{5}=\frac{2\cdot 2}{5\cdot 2}\\ =\frac{4}{10}\end{array}$

The four ratio are equivalent because it is of the general form $2k:5k$ .

Therefore, the four ratios that are equivalent to $2:5$ are $\frac{4}{10},\frac{6}{15},\frac{8}{20},\frac{10}{25}$