Question

Give four equivalent ratios of 12:15.

Answer 1

Hint: The given ratio is 12:15 which can be written in the form $\dfrac{12}{15}$. Now, we know that two ratios will be equivalent if a common factor is multiplied or divided both in the numerator and the denominator. Thus, we can multiply four common factors in the numerator and denominator to obtain the equivalent ratios.
Complete step-by-step answer:
The given ratio is $\dfrac{12}{15}$. Now, we know that we can obtain different equivalent ratios from the given ratio by multiplying a common factor in the numerator and in the denominator. We can choose the factors as we want.
Let us choose 2, 3, 5 and 8 as the common factors, multiplying them in the numerator and the denominator of the given ratio we obtain
$\text{Equivalent Ratio of }\dfrac{12}{15}=\dfrac{12\times 2}{15\times 2}=\dfrac{24}{30}$
Similarly, using 3, we obtain another equivalent ratio as
$\text{Equivalent Ratio of }\dfrac{12}{15}=\dfrac{12\times 3}{15\times 3}=\dfrac{36}{45}$
Using 5 we obtain the ratio as
$\text{Equivalent Ratio of }\dfrac{12}{15}=\dfrac{12\times 5}{15\times 5}=\dfrac{60}{75}$
And using 8 we obtain the ratio as
$\text{Equivalent Ratio of }\dfrac{12}{15}=\dfrac{12\times 8}{15\times 8}=\dfrac{96}{120}$
Thus, we obtain four equivalent ratios of $\dfrac{12}{15}$ to be $\dfrac{24}{34}$, $\dfrac{36}{45}$, $\dfrac{60}{75}$, $\dfrac{96}{120}$.
Note: In this question, we have taken four arbitrary values to multiply in the numerator and denominator to obtain the equivalent ratios. However, we could have used any other integers or fractions instead of 2, 3, 5 and 8 to obtain new equivalent fractions and all of them would have been valid answers to this question.