Question

Check if the following pair is equivalent fractions? \[\dfrac{3}{8}\] and \[\dfrac{{15}}{{40}}\]

Answer 1

Hint: Here we are asked to find whether the given fractions are a pair of equivalent fractions. An equivalent fraction is a fraction obtained by multiplying or dividing it with the same number. So, from the given two fractions, if we multiply any one of the fractions by a number or divide by a number, we should get another fraction.

Complete step-by-step solution:
It is given that the fractions are \[\dfrac{3}{8}\] and \[\dfrac{{15}}{{40}}\] we aim to find whether these two fractions are equivalent are not.
We know that an equivalent fraction is a fraction that is obtained by multiplying or dividing it with the same number.
Now we have to check it by multiplying or dividing any one of the fractions by a number so that we will get the other fraction.
Consider the first given fraction \[\dfrac{3}{8}\]. In this fraction, the numerator is three, and the denominator is eight.
We aim to get the other fraction that is \[\dfrac{{15}}{{40}}\] by multiplying or dividing the fraction \[\dfrac{3}{8}\].
We can see that if we multiply the first fraction’s numerator and denominator by five, we will get fifteen and forty as a result. Thus, we will get the second fraction.
\[\dfrac{3}{8} \times \dfrac{5}{5} = \dfrac{{15}}{{40}}\]
Let us check whether the second fraction also yields the first fraction on multiplying or dividing.
The second fraction is \[\dfrac{{15}}{{40}}\]. If we divide the numerator and denominator of this fraction by five, we will get five and eight. Thus, we will get the first fraction.
\[\dfrac{{15}}{{40}} \div \dfrac{5}{5} = \dfrac{3}{8}\]
Thus, the given two fractions are equivalent.

Note: It is enough to check any one of the fractions by multiplying or dividing to get another. The multiplication of two fractions is done by multiplying the numerator and denominator separately. Also, the division is done in the same way.