Question

A \[37\dfrac{1}{2}\% \] is equal to what fraction?

Answer 1

Hint: In maths, % sign is known as percentage. So, % means per cent or per hundred. To express a mixed percentage number as a fraction, begin by removing the percent sign, then put 100 in the denominator's place and reduce the fraction to the lowest terms. By solving this, we will get the final output.

Complete step-by-step answer:
We know that a percentage is the value given out of 100. It is denoted by % and so, \[\% = \dfrac{1}{{100}}\] .
Given that,
\[37\dfrac{1}{2}\% \]
\[ = 37.5\% \]
We will remove the % sign, we will get,
\[ = \dfrac{{37.5}}{{100}}\]
To make the numerator a whole number we need to remove the decimal point by multiplying by 10, and hence also divide by 10, we get,
\[ = \dfrac{{375}}{{100}} \times \dfrac{{10}}{{10}}\]
On simplify this, we will get,
\[ = \dfrac{{375}}{{1000}}\]
Taking HCF we get 125 and so simplify this, we will get,
\[ = \dfrac{{375 \div 125}}{{1000 \div 125}}\]
\[ = \dfrac{3}{8}\]

Another Method:
\[37\dfrac{1}{2}\% \]
\[ = \dfrac{{75}}{2}\% \]
Write \[\dfrac{1}{{100}}\] in place of % sign, we will get,
\[ = \dfrac{{\dfrac{{75}}{2}}}{{100}}\]
\[ = \dfrac{{75}}{{2 \times 100}}\]
On simplifying this, we will get,
\[ = \dfrac{3}{{2 \times 4}}\]
\[ = \dfrac{3}{8}\]

To check the answer:
\[\dfrac{3}{8}\]
Multiply by 100, we will get,
\[ = \dfrac{3}{8} \times 100\]
On simplifying this, we will get,
\[ = \dfrac{3}{2} \times 25\]
\[ = \dfrac{{75}}{2}\]
\[ = 37\dfrac{1}{2}\% \]
Hence, \[37\dfrac{1}{2}\% = \dfrac{3}{8}\] .
So, the correct answer is “$\dfrac{3}{8}$”.

Note: A fraction represents a part of the whole number. It consists of a numerator and denominator where numerator represents the number of equal parts and denominator represents the total amount that makes up a whole. In fact, fractions were used to compare the whole numbers with one another. A percentage is a fraction: per cent means the denominator is one hundred (100). It’s handy to remember all the decimal conversions for fractions of 8 - which was very useful when stocks traded in 1/8ths of a dollar per share.