Question

How do you write $40\% $ as a fraction?

Answer 1

Hint: To convert the above question into a fraction, we need to remove the percentage sign by dividing the given number by 100 and then factorize the numerator and denominator to convert the fraction to its reduced form.

Complete step by step solution:
As we know that when we remove $\% $ sign 100 will come in denominator, as we can see below.
$40\% = \dfrac{{40}}{{100}}$
Now, we will do factors of 40 and 100 to get reduced fraction
$ = \dfrac{{2 \times 2 \times 2 \times 5}}{{5 \times 5 \times 2 \times 2}} \Rightarrow \dfrac{2}{5}$
As we observe that a pair of 2 and a 5 are common in numerator and denominator, so we will cancel them out and proceed with remaining factors.
$ = \dfrac{2}{5}$ (As we can see that our numerator and denominator both are prime numbers, which we can’t reduce further)
Hence, the fraction of $40\% $ is $\dfrac{2}{5}$ .

Note: We should remember that when the percentage sign removes then the number will get 100 at their denominator. We should also keep in mind that we should find out the reduced fraction which we can get after factorization.