Question

Write a rational number equivalent to $\dfrac{18}{29}$ having $87$ as a denominator.

Answer 1

Hint: We will start by first dividing the required denominator by the given denominator and then we will proceed further with multiplying the numerator and denominator both by the number obtained earlier, the resultant fraction would be our answer.

Complete step by step answer:
We know that a rational number is one that can be written as the ratio of two integers. For example the given number is a fraction of integers: $18$ and $29$ . Now we have to find the equivalent rational number to it, so basically an equivalent fraction can be defined as fractions with different numerators and denominators that represent the same value or are equal to the same value. For example, $\dfrac{2}{4}=\dfrac{3}{6}=\dfrac{1}{2}$ .
We have to find a rational number which is equivalent to the given fraction, that is: $\dfrac{18}{29}$, with $87$ as a denominator.
We will proceed by first dividing the denominator in which fraction is to be converted, that is $87$ by the denominator that is given means $29$. Therefore, $\dfrac{87}{29}=3$ .
We will multiply the given fraction that is $\dfrac{18}{29}$ by the quotient found in the above step: $3$. $\Rightarrow \dfrac{18}{29}=\dfrac{18\times 3}{29\times 3}=\dfrac{54}{87}$ . This fraction has the same value as $\dfrac{18}{29}$.

Therefore the answer is: \[\dfrac{54}{87}\] .

Note: Note that you must only multiply or divide in order to get an equivalent fraction, never add or subtract the values. Division is done only when the numerator and the denominator stay as whole numbers.