Question

Select all ratios equivalent to 4:5.20:2524:3025:20

Answer 1

SOLUTION

Equivalent ratios are ratios that have the same proportion to each other when put in simplest form. They are sometimes refers to as equivalent fraction.

Given the ratio

$\begin{gathered} 4\colon5 \\ \text{change to fraction, we have } \\ \frac{4}{5} \end{gathered}$

To obtain the equivalence of the fraction above, we multiply the numertor and denominator by the same number.

hence

$\begin{gathered} \frac{4}{5}=\frac{4\times2}{5\times2}=\frac{8}{10} \\ \\ \frac{4}{5}=\frac{4\times3}{5\times3}=\frac{12}{15} \\ \\ \frac{4}{5}=\frac{4\times4}{5\times4}=\frac{16}{20} \end{gathered}$

Then, multiplying both by 5, we have the equivalent fraction

$\begin{gathered} \frac{4}{5}=\frac{4\times5}{5\times5}=\frac{20}{25} \\ \end{gathered}$

convert the fraction to ratio, we have

$\frac{20}{25}=20\colon25$

Therefore

Answer: The equivalent ratio to 4 : 5 is 20 : 25