Question

write three equivalent ratios for each. Explain how you found each ratio.d) 4/9 : 1 1/3

Answer 1

Answer:

4/3 : 4

4 : 12

16/3 : 16

Explanation:

First, we need to transform the mixed number 1 1/3 into a fraction using the following equation:

$\begin{gathered} A\frac{b}{c}=\frac{A\times c+b}{c} \\ 1\frac{1}{3}=\frac{1\times3+1}{3}=\frac{3+1}{3}=\frac{4}{3} \end{gathered}$

Therefore the ratio is now 4/9 : 4/3

So, to find equivalent ratios, we can multiply both numbers by a constant value, for example, 3, 9, and 12.

Then, the equivalent ratios are:

Multiplying by 3:

$\begin{gathered} \frac{4}{9}\times3\colon\frac{4}{3}\times3 \\ \frac{4\times3}{9}\colon\frac{4\times3}{3} \\ \frac{4}{3}\colon4 \end{gathered}$

Multiplying by 9:

$\begin{gathered} \frac{4}{9}\times9\colon\frac{4}{3}_{}\times9 \\ \frac{4\times9}{9}\colon\frac{4\times9}{3} \\ 4\colon12 \end{gathered}$

Multiplying by 12:

$\begin{gathered} \frac{4}{9}\times12\colon\frac{4}{3}\times12 \\ \frac{4\times12}{9}\colon\frac{4\times12}{3} \\ \frac{16}{3}\colon16 \end{gathered}$

Therefore, the tree equivalent ratios are:

4/3 : 4

4 : 12

16/3 : 16