Question

What is $55\%$ as a fraction?

Answer 1

Hint: We need to find the value $55\%\;$ as a fraction. Firstly, we divide the given fraction by the number hundred. Then, we simplify the derived expression to express the given percentage in the form of the fraction.

Complete step by step answer:
Fractions, in mathematics, are used to represent the portion or the part of the entire or whole thing. They are generally represented as follows,
$\Rightarrow \dfrac{a}{b}$
Here,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
For Example:
$\Rightarrow \dfrac{1}{2},\dfrac{2}{5}$
A percentage is a value expressed as a fraction of a hundred or $\dfrac{1}{100}$ . It is denoted by the symbol ’$\%\;$’. The value expressed as a percentage does not have any dimension or unit of measurement.
For Example:
$\Rightarrow 2\%,3\%$
Now,
Let us understand how to solve the given question with an example.
Example:
Express $5\%\;$ as the fraction.
The word percent means ‘per hundred’.
Dividing the given percentage with hundred, we get,
$\Rightarrow 5\times \dfrac{1}{100}$
Multiplying the values, we get,
$\Rightarrow \dfrac{5}{100}$
Expressing the above as the product of factors, we get,
$\Rightarrow \dfrac{5}{5\times 20}$
Cancelling the common factors, we get,
$\Rightarrow \dfrac{1}{20}$
$\therefore 5\%=\dfrac{1}{20}$
According to our question,
$\Rightarrow 55\%$
Dividing the above expression with hundred, we get,
$\Rightarrow \dfrac{55}{100}$
Expressing the above as the product of factors, we get,
$\Rightarrow \dfrac{5\times 11}{5\times 20}$
Cancelling the common factors from the above expression, we get,
$\Rightarrow \dfrac{11}{20}$
$\therefore 55\%=\dfrac{11}{20}$

$\therefore$ The percentage $55\%\;$ is expressed in the form of a fraction as $\dfrac{11}{20}$

Note: The common mistakes made in percentages is we usually perform addition and subtraction of the percentage and the numbers in problems considering ‘$\%\;$’ as the units of measurement just like kg, g. Any percentage can be expressed as a fraction by simply dividing the value of percentage by 100.