Q12. - Algebra 1

Question

Determine whether each pair of ratios are equivalent ratios. Write yes or no. 

 

$\frac{4}{3},\frac{6}{8}$

Step-by-Step Solution

Answer

No, the pair of ratios $\frac{4}{3},\frac{6}{8}$ are not equivalent ratios because $\frac{4}{3}\ne \frac{6}{8}$.

Step-1. Define equivalent ratios.

Equivalent ratios are two ratios which have same relationship between the numbers.

Step-2. Simplify the ratios.

Simplify both the ratios by dividing them with the common factor, if there is any.

$\begin{array}{c}\frac{4}{3}=\frac{4\times 1}{3\times 1}\\ =\frac{4}{3}\end{array}$

And,

$\begin{array}{c}\frac{6}{8}=\frac{\cancel{2}\times 3}{\cancel{2}\times 4}\\ =\frac{3}{4}\end{array}$

Step-3. State the conclusion.

As, both the results are not equal, that is., $\frac{4}{3}\ne \frac{3}{4}$, therefore, no, the given ratios are not equivalent.