Q11. - Algebra 1

Question

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

 

$\frac{8.4}{9.2},\frac{8.8}{9.6}$

Step-by-Step Solution

Answer

No, the pair of ratios $\frac{8.4}{9.2},\frac{8.8}{9.6}$ are not equivalent ratios because $\frac{8.4}{9.2}\ne \frac{8.8}{9.6}$.

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.

$$\begin{gathered} \frac{8.4}{9.2}=\frac{84}{92} \\ =\frac{3\times \cancel{4}\times 7}{23\times \cancel{4}} \\ =\frac{21}{23} \end{gathered}$$

And,

$$\begin{gathered} \frac{8.8}{9.6}=\frac{88}{96} \\ =\frac{\cancel{8}\times 11}{\cancel{8}\times 12} \\ \text{=}\frac{11}{12} \end{gathered}$$

Step-3. State the conclusion.

As, both the results are not equal, that is., $\frac{21}{23}\ne \frac{11}{12}$, therefore, no, the given ratios are not equivalent.