Question

What is $\dfrac{3}{12}$ equivalent to?

Answer 1

Hint: First of all, we need to understand the meaning of equivalent numbers. The equivalent number of a fraction is another fraction which has the same fundamental value as the original fraction. The equivalent fraction of one fraction is obtained by either multiplying or dividing the numerator and denominator with the same number. We shall proceed using this fact to get our answer.

Complete step-by-step answer:
Let us first derive a general formula for calculating the equivalent fraction of a given fraction. Let us say there is an arbitrary fraction given by, $\dfrac{a}{b}$, and we need to calculate its equivalent fractions. For that purpose, we need to multiply the numerator and denominator of our fraction with the same number. Let us multiply our numerator and denominator with a random number ‘k’, such that our new fraction becomes, $\dfrac{ak}{bk}$ . Here, the new fraction is termed as an equivalent fraction to our original fraction.
Now, the fraction given to us in the problem is: $\dfrac{3}{12}$

Let us find some equivalent fractions of the given fraction by multiply the numerator and the denominator with the numbers: 5, 6, 8 and 9 respectively. On multiplying our fraction with these numbers, we get:
$\begin{align}
  & =\dfrac{3\times 5}{12\times 5}=\dfrac{15}{60} \\
 & =\dfrac{3\times 6}{12\times 6}=\dfrac{18}{72} \\
 & =\dfrac{3\times 7}{12\times 7}=\dfrac{21}{84} \\
 & =\dfrac{3\times 8}{12\times 8}=\dfrac{24}{96} \\
\end{align}$

Thus, we get some of the equivalent fractions of $\dfrac{3}{12}$ as $\dfrac{15}{60},\dfrac{18}{72},\dfrac{21}{84}\text{ and }\dfrac{24}{96}$.
Hence, some of the equivalent of $\dfrac{3}{12}$ comes out to be $\dfrac{15}{60},\dfrac{18}{72},\dfrac{21}{84}\text{ and }\dfrac{24}{96}$.

Note: In our problem, we have been asked to find the equivalent of the given fraction and not calculate the value of the given fraction. Also, any fraction can have infinite number of equivalent fractions as it could be multiplied and divided by infinite number of numbers.