Question

Monika answered $\dfrac{3}{4}$ of the questions on her quiz correctly. What percent of the questions did she answer correctly?
$A)25\%$
$B)34\%$
$C)50\%$
$D)75\%$

Answer 1

Hint: To solve this question we need to know the concept of percentage. This question asks us to change the fraction into percentage, which means this fraction will be represented as the fraction of $100$.

Complete step by step solution:
The question asks us to find the percentage of correct answers, when the answers marked correctly is $\dfrac{3}{4}$ of the questions given. To solve, the fraction $\dfrac{3}{4}$ needs to be converted into the fraction of $100$, which means percentage form. So solving this, the first step will be ,
The fraction will be multiplied by $100$, to find the value in percentage
$\Rightarrow \dfrac{3}{4}\times 100$
Multiply the terms in the numerator and the terms in the denominator,
$\Rightarrow \dfrac{3\times 100}{4}$
On multiplying we get
$\Rightarrow \dfrac{300}{4}$
The fraction need to be reduced in its lowest term, thus on reducing we get
$\Rightarrow 75$
 After the calculation of fraction in percentage we have got the value as$75$ but since the fraction which we have converted in percentage means the fraction of hundred therefore sign of percentage will be used ,$\%$ hence indicating the value to be in percentage.
$\therefore $ The percent of the question Monika answered correctly is Option $D)75\%$ when the answer marked correctly by her is $\dfrac{3}{4}$ of the question.

So, the correct answer is “Option D”.

Note: A number with a percentage sign means that the number is a fraction of 100. So here $75\%$ when written in fraction will be written as
$\Rightarrow \dfrac{75}{100}$
Now we will bring the fraction to it’s lowest form. We see that the common factor for both the numerator and the denominator is $25$. So on dividing the number by the common factor (same number) of both numerator and denominator which is $25$, we get:
$\Rightarrow \dfrac{3}{4}$
So, the fraction we get after converting the percentage to fraction is \[\dfrac{3}{4}\]. This mean the answer we obtained is correct.