Question

What is equivalent to $\dfrac{2}{5}$?

Answer 1

Hint: In the above problem, we are asked to find $\dfrac{2}{5}$ is equivalent to. For that we are going to multiply the numerator and the denominator by the same integer and then the result of that multiplication in the numerator and the denominator is equivalent to $\dfrac{2}{5}$. Also, you can multiply any integer to this fraction.

Complete step-by-step solution:
We have given $\dfrac{2}{5}$ and are asked to find what $\dfrac{2}{5}$ is equivalent to. So, to find the value which is equivalent to $\dfrac{2}{5}$, we are going to multiply the numerator and the denominator by some integer.
Let us take the integer 2 and multiplying the numerator and the denominator by this integer 2 we get,
$\dfrac{2\times 2}{5\times 2}=\dfrac{4}{10}$
Similarly, we can take other integer say 3 also and multiplying the numerator and the denominator by 3 we get,
$\dfrac{2\times 3}{5\times 3}=\dfrac{6}{15}$
Likewise, we can take any integer say “n” and multiplying the numerator and the denominator by n to the given fraction we get,
$\dfrac{2\times n}{5\times n}=\dfrac{2n}{5n}$
Hence, we have found that $\dfrac{2}{5}$ is equivalent to $\dfrac{2n}{5n}$.

Note: We can check the fractions equivalent to the given fraction which we have found in the above solution is correct or not by simplifying all the fractions and then verify whether the simplification of these fraction is giving us $\dfrac{2}{5}$ or not.
The first fraction which we have shown in the above solution is as follows:
$\dfrac{4}{10}$
Now, as you can see the numerator and the denominator of the above fraction will be divided by 2 and we get,
$\dfrac{2}{5}$
This is the same fraction which we have given in the above problem.
Similarly, we can check for the second fraction $\dfrac{6}{15}$. Now, in this fraction, the numerator and the denominator is divided by 3 and we get,
$\dfrac{2}{5}$
Again, we are getting the same fraction which is given in the above problem. Similarly, we can check for the last fraction also.