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# Find three equivalent fraction for the fraction $\dfrac{{18}}{{24}}$

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Hint: If a fraction having a different numerator and denominator has the same value as the given fraction then these fractions are known as the Equivalent Fractions of a fraction. To find the value of the equivalent fractions we multiply the numerator and denominator of the given fraction by the same number. But first we have to find the simplest form of the given fraction by dividing the numerator and denominator of the fraction by the Greatest Common Factor (G.C.F.) of both numerator and denominator.

Complete step-by-step answer:
Given:
The given fraction is $\dfrac{{18}}{{24}}$ .
The numerator of the fraction is $18$ and the denominator of the fraction is $24$ .
The greatest common factor of 18 and 24 is calculated by –
$18 = 2 \times 3 \times 3\\ 24 = 2 \times 2 \times 2 \times 3$
So,
$GCF(18,24) = 2\times 3$
$GCF(18,24) = 6$
Since the value of the greatest common factor $GCF \ne 1$ , we can further divide the numerator and denominator and get one of the equivalent fractions.
So, by dividing the numerator and denominator with 6 we get,
$\dfrac{{\left( {\dfrac{{18}}{6}} \right)}}{{\left( {\dfrac{{24}}{6}} \right)}} = \dfrac{3}{4}$
So, $\dfrac{3}{4}$ is the first equivalent fraction of the given fraction.
Now we use this value of the fraction to find the two other equivalent fractions.
Multiplying the numerator and denominator of the fraction $\dfrac{3}{4}$ by 2 we get,
$\dfrac{{3 \times 2}}{{4 \times 2}} = \dfrac{6}{8}$
So, $\dfrac{6}{8}$ is the second equivalent fraction of the given fraction.
And, similarly,
Multiplying the numerator and denominator of the fraction $\dfrac{3}{4}$ by 4 we get,
$\dfrac{{3 \times 4}}{{4 \times 4}} = \dfrac{{12}}{{16}}$
So, $\dfrac{{12}}{{16}}$ is the third equivalent fraction of the given fraction.
Therefore, the three equivalent fractions of the fraction $\dfrac{{18}}{{24}}$ are
$\dfrac{3}{4}$ , $\dfrac{6}{8}$ and $\dfrac{{12}}{{16}}$ .
So, the correct answer is “$\dfrac{3}{4}$ , $\dfrac{6}{8}$ and $\dfrac{{12}}{{16}}$”.

Note: It should be noted that the decimal value of the fraction remains the same because we are multiplying the same number with the numerator and denominator of the fraction. So, we can obtain as many equivalent fractions as we want by multiplying the same number to the numerator and denominator of a fraction.