Question

Find three equivalent ratios of $\dfrac{{12}}{{13}}$ .

Answer 1

Hint: To get a ratio equivalent to a given ratio use multiply or divide both the terms of the given ratio by the same non zero number. We will learn how to find the equivalent ratio of a given ratio by writing the ratio as a fraction and then compare by using multiplication and division.


Complete step by step solution:
$12:32 = \dfrac{{12}}{{32}}$
$\dfrac{{\left( {12 \times 2} \right)}}{{32 \times 2}}$ [Multiply numerator by 2 and denominator by 2]
$ \Rightarrow \dfrac{{24}}{{64}} = \dfrac{3}{8}$
Similarly we again, use need to write the given ratio $\dfrac{3}{8}$ as dfraction to get another equivalent ratio
$\dfrac{{3 \times 2}}{{8 \times 2}} = \dfrac{6}{{16}}$[Both multiply numerator and denominator by 2]
Similarly use again, we need to write the given ratio$\dfrac{6}{{16}}$ as fraction to get
$\dfrac{{6 \times 2}}{{16 \times 2}} = \dfrac{{12}}{{32}}$[Both multiple numerator and denominator by 2]
Similarly we again, we need to write the given ratio $\dfrac{{12}}{{32}}$ as fraction to get
$\dfrac{{12 \times 2}}{{32 \times 2}} = \dfrac{{24}}{{64}} = \dfrac{3}{8}$
$\dfrac{{3 \times 6}}{{8 \times 6}} = \dfrac{{18}}{{48}}$ [Multiply both numerator and denominator by 6]
$\therefore $ $12:32$ is the second equivalent ratio
$18:48$ is the third equivalent ratio
Therefore, the three equivalent ratios of $3:8$ are $6:16$ , $12:32$ and $18:48$.


Note: Students keep in mind that we will multiply the same number into numerator and denominator to convert into the equivalent fraction and ratio. To get an equivalent ratio to a given ratio by multiplying and dividing both.