Question

If $\dfrac{3}{4}$ is equivalent to $\dfrac{x}{20},$ then the value of $x$ is
$\left( a \right) 15$
$\left( b \right) 18$
$\left( c \right) 12$
$\left( d \right) $ None of these

Answer 1

Hint: We know that if two fractions are said to be equivalent, then either of them can be found by multiplying and dividing the same number with the other. So, we will compare the denominators and find the number with which the first fraction is divided so that we get the denominator of the second fraction.

Complete step-by-step answer:
Let us suppose that the fraction $\dfrac{3}{4}$ is equivalent to another fraction $\dfrac{x}{20}.$
We are asked to find the value of $x.$
We know that two fractions are said to be equivalent when either of the numerator is a multiple of the other and the denominator of the former is the multiple of the denominator of the latter.
In this question, we need to find the numerator of the second fraction when we have the denominator of the fraction and both the numerator and the denominator of the first fraction.
Let us consider the denominator of the fraction whose numerator we need to find. That is, $20.$
As we can see, the denominator of the first fraction is $4$ and $20$ is a multiple of $4.$
We have $4\times 5=20$ and so, we will get $\dfrac{20}{4}=5.$
From this, we can learn that the first fraction $\dfrac{3}{4}$ is divided with $5$ and we get the denominator of the second fraction.
So, now we need to multiply the numerator of the first fraction with $5$ to get the numerator of the second fraction. That is, $x.$
So, we will get $3\times 5=15.$
Therefore, the second fraction is $\dfrac{15}{20}$ and it is equivalent to $\dfrac{3}{4}.$
Hence $x=15.$
So, the correct answer is “Option A”.

Note: If we need to find an equivalent fraction of a given fraction, we only need to multiply and divide the fraction with the same number. Thus, we can find many fractions equivalent to the given fraction.