Question

Express each of the following as a fraction in simplest form:
A. $ 25\% $
B. $ 625\% $
C. $ 33\dfrac{1}{2}\% $
D. $ 66\dfrac{2}{3}\% $

Answer 1

Hint: Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from a certain size whereas percentage is the number or ratio expressed as a fraction of a hundred. Know the difference between the fraction and the percentage and apply accordingly. We will find the fraction in the simplest form one by one.

Complete step-by-step answer:
A. $ 25\% $
Convert the given percentage in the form of fraction. Percentage is based on hundredth of the number.
  $ 25\% = \dfrac{{25}}{{100}} $
Convert the above fraction in the simplest form. Find the multiples of the terms in the numerator and the denominator.
 $ 25\% = \dfrac{{25}}{{25 \times 4}} $
Common multiple from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow 25\% = \dfrac{1}{4} $
So, the correct answer is “$\dfrac{1}{4} $”.

B. $ 625\% $
Convert the given percentage in the form of fraction. Percentage is based on hundredth of the number.
  $ 625\% = \dfrac{{625}}{{100}} $
Convert the above fraction in the simplest form. Find the multiples of the terms in the numerator and the denominator.
 $ 625\% = \dfrac{{25 \times 25}}{{25 \times 4}} $
Common multiple from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow 625\% = \dfrac{{25}}{4} $
So, the correct answer is “$\dfrac{25}{4} $”.

C. $ 33\dfrac{1}{2}\% $
Convert the given integer in the form of fraction.
 $ 33\dfrac{1}{2}\% = \dfrac{{67}}{2}\% $
Convert the given percentage in the form of fraction. Percentage is based on hundredth of the number.
 $ \dfrac{{67}}{2}\% = \dfrac{{67}}{{2 \times 100}} $
Simplify the above expression –
 $ \Rightarrow \dfrac{{67}}{2}\% = \dfrac{{67}}{{200}} $
There are no common multiples are possible so, resultant answer is $ \dfrac{{67}}{2}\% = \dfrac{{67}}{{200}} $
So, the correct answer is “$\dfrac{67}{200} $”.

D. $ 66\dfrac{2}{3}\% $
Convert the given integer in the form of fraction.
 $ 66\dfrac{2}{3}\% = \dfrac{{200}}{3}\% $
Convert the given percentage in the form of fraction. Percentage is based on hundredth of the number.
 $ \dfrac{{200}}{3}\% = \dfrac{{200}}{{3 \times 100}} $
Find the factors in the above expression-
 $ \dfrac{{200}}{3}\% = \dfrac{{2 \times 100}}{{3 \times 100}} $
Common multiple from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow \dfrac{{200}}{3}\% = \dfrac{2}{3} $
So, the correct answer is “$\dfrac{2}{3} $”.

Note: Be very good in multiples and simplification of the numbers. Always remember that the common multiples from the numerator and the denominator cancel each other. Multiples of the numbers are infinite; there is no end for the multiples of any number. Always remember that the first twenty multiples of the numbers till $ 20 $ at least.