Question

What is a fraction that is equivalent to $\dfrac{3}{8}$?

Answer 1

Hint: In the above question, we have been given a fractional number whose equivalent fraction is to be determined. For this, we have to multiply the numerator and denominator of the given fraction by a whole number. The whole numbers are a set of all non-zero positive integers. Therefore, we can choose the whole number to be two and multiply the numerator, equal to three, and the denominator, equal to eight, of the given fraction by two to obtain an equivalent fraction.

Complete step-by-step solution:
The fractional number given to us in the above question is equal to $\dfrac{3}{8}$. According to the question, we need to obtain a fraction equivalent to the given fraction. An equivalent fraction is the one which, on reducing to the lowest term, gets reduced to the original fraction. Therefore, for obtaining the equivalent fraction, we have to multiply the numerator and the denominator of the given fraction by the same whole number. Since we know that the whole numbers are a set of the non-zero positive integers, we can choose the number as two. Therefore, on multiplying the numerator and the denominator of the given fraction by two, we get
\[\begin{align}
  & \Rightarrow \dfrac{3\times 2}{8\times 2} \\
 & \Rightarrow \dfrac{6}{16} \\
\end{align}\]
Hence, we have found the fraction equivalent to the given fraction as \[\dfrac{6}{16}\].

Note: By multiplying the numerator and the denominator of the given fraction by the same whole number, we are essentially multiplying it by one. That’s why it is called the equivalent fraction. We can generalize the set of equivalent fractions as $\dfrac{3n}{8n}$, where n is any whole number.