Question

The equivalent fraction of $\dfrac{2}{3}$ having the denominator 18 is
A. $\dfrac{2}{18}$
B. $\dfrac{18}{3}$
C. $\dfrac{12}{18}$
D. $\dfrac{18}{27}$

Answer 1

Hint: We need to find the equivalent fraction of $\dfrac{2}{3}$ having the denominator 18 .The equivalent fraction having the denominator 18 can be found out by multiplying and dividing the given fraction with the number 6. Then, we simplify the fraction to get the desired result.

Complete step-by-step answer:
We are given a fraction and are asked to find the equivalent fraction having the denominator 18 to the given fraction. We will be solving the given question using the concept of factors and multiples .
A fraction, in mathematics, represents a part of a whole thing. It consists of two parts namely,
numerator, denominator.
The number on the top is called the numerator.
The number on the bottom is called the denominator.
Let us understand the concept of the fraction with an example as follows,
Example:
$= \dfrac{a}{b}$
In the above fraction,
$a$ is the numerator of the fraction
$b$ is the denominator of the fraction
Two rational numbers are the same if their lowest forms are the same. Equivalent rational numbers have the same value but are represented in a different form.
 If $\dfrac{p}{q}$ is a fraction and $r$ is any non-zero integer. The equivalent fraction to $\dfrac{p}{q}$ can be found out as follows,
$= \dfrac{p\times r}{q\times r}$
According to the question, we need to find the equivalent fraction of $\dfrac{2}{3}$ having the denominator 18.
From factors and multiples, we know that
$= 3\times 6=18$
From the above,
The equivalent fraction of $\dfrac{2}{3}$ having the denominator 18 can be found out by multiplying the numerator and denominator of the fraction by 6.
Multiplying the numerator and denominator of a fraction $\dfrac{2}{3}$ by 6, we get,
$= \dfrac{2}{3}\times \dfrac{6}{6}$
Simplifying the above expression, we get,
$= \dfrac{12}{18}$
$\therefore$ The equivalent fraction of $\dfrac{2}{3}$ having the denominator 18 is $\dfrac{12}{18}$
Option C holds the correct answer for the given question.

So, the correct answer is “Option C”.

Note: The equivalent rational numbers to $\dfrac{2}{3}$ are correct only if they give $\dfrac{2}{3}$ on simplifying them to their lowest forms by canceling out the common factors.
$= \dfrac{12}{18}=\dfrac{2\times 6}{3\times 6}=\dfrac{2}{3}$
The fraction $\dfrac{12}{18}$ gives $\dfrac{2}{3}$ when simplified to their lowest forms.
Hence, $\dfrac{12}{18}$ is the equivalent fraction of $\dfrac{2}{3}$ .