Question

How do you write ${\displaystyle \frac{26}{32}}$ as a percent?

Answer 1

Hint: We need to find the percentage of the fraction ${\displaystyle \frac{26}{32}}$. We multiply the fraction with 100 to find the percentage value. The fraction form is the value of the numerator with respect to the denominator value. We need to convert the denominator of the fraction to 100 and then take the numerator as the required solution of the problem.

Complete step-by-step solution:
The fraction is the respective ratio of two numbers. We find the value of the numerator with respect to the denominator of the fraction.
In case of percentage, we need to convert the denominator of the fraction into 100.
The numerator of the fraction with denominator being 100 will be the solution of the problem.
We now try to find the percentage value of the fraction. We multiply the fraction with 100.
Therefore, $${\displaystyle \frac{26}{32}}\times 100={\displaystyle \frac{2600}{32}}$$.
For our give fraction ${\displaystyle \frac{2600}{32}}$, the G.C.D of the denominator and the numerator is 8.
$\begin{array}{rl}& 2|\underset{―}{32,2600}\\ & 2|\underset{―}{16,1300}\\ & 2|\underset{―}{8,650}\\ & 1|\underset{―}{4,325}\end{array}$
The GCD becomes $2\times 2\times 2=8$.
Now we divide both the denominator and the numerator with 8 and get ${\displaystyle \frac{{}^{2600}/{}_8}{{}^{32}/{}_8}}={\displaystyle \frac{325}{4}}$.
The percentage value is ${\displaystyle \frac{325}{4}}=81.25$
The fraction is ${\displaystyle \frac{26}{32}}$ and its percentage value is $81.25$.

Note: The value of the fraction is actually the unitary value of 4 out of 100. Therefore, in percentage value we got 4 as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.