Question

How do you write $ 135\% $ as a fraction in simplest form?

Answer 1

Hint: The symbol "Percent" or "%" means "out of 100" or "per 100", To simplify a fraction divide the top and bottom i.e., numerator and denominator of the given fraction by the highest common factor. This means look for the biggest number then divide into both, if gives the simplest form of the fraction.

Complete step-by-step answer:
Percent means multiply $ \dfrac{1}{{100}} $ to the respective number the resultant will be in the form of fraction.
Given $ 135\% $ can be written as
 $ \Rightarrow \,\,135\% = \dfrac{{135}}{{100}} $
The resultant fraction is improper fraction i.e., the numerator is greater than or equal to the denominator of a fraction. In that case, you could convert it into a whole number or mixed number fraction.
Where 135 is the numerator and 100 is the denominator.
To simplify a fraction, we divide both the numerator and denominator by the same number. A common factor is a number that divides both the numerator and denominator without leaving any remainders. We divide the fractions till we get 1 as the common factor for both the numerator and denominator.
First, you find the factors of both numerator and denominator
Factors of 135 are 1, 3, 5, 9, 15, 27, 45, and 135
Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100
Here common factors of 135 and 100 are 1 and 5
The highest common factor HCF of 135 and 100 is 5
So, we divide the both numerator and denominator of the fraction by 5
Consider $ \dfrac{{135}}{{100}} $
Divide the both numerator and denominator by 5, we get
 $ \Rightarrow \,\,\dfrac{{27}}{{20}} $
We can’t simplify further because the two numbers which are in the numerator and denominator don't have a common factor.
Hence, the simplest form of $ 135\% = \,\,\dfrac{{135}}{{100}} $ is $ \,\dfrac{{27}}{{20}} $
So, the correct answer is “$ \,\dfrac{{27}}{{20}} $ ”.

Note: In the arithmetic we can convert the number from one form to another form, while converting the number we have to follow some rule of conversion. Here to convert the percentage into a fraction we have to multiply the given number by $ \dfrac{1}{{100}} $ . We can simplify further and hence we obtain a simplest form.