Question

# Find the three equivalent fractions for the fraction $\dfrac{3}{18}$.

Hint: First of all, it is necessary to recollect what equivalent fractions are. Then multiply the numerator and denominator of the given fraction by the same number to get the equivalent fraction of the given fraction.

Here we have to find the three equivalent fractions for the fraction $\dfrac{3}{18}$.
Before proceeding with this question, we must know what equivalent fractions are.

The equivalent fractions are a type of fractions that seem to be different (not having the same numbers) but they are equivalent, that is they have equal values.
The two equivalent fractions have equal values both in numerator and denominator after simplifications of the given fractions.

For example, $\dfrac{1}{4},\dfrac{2}{8},\dfrac{3}{12},\dfrac{4}{16}$ are all equivalent fraction because they all give $\dfrac{1}{4}$ after simplification.
We know that if we multiply or divide any number by 1, its value remains the same.

Also, we can write 1 in the form of a fraction as $\dfrac{1}{1}\text{ or }\dfrac{2}{2}\text{ or }\dfrac{3}{3}\text{ or }\dfrac{5}{5}\text{ or }\dfrac{n}{n}$ and here n can be any number. When we simplify any of these numbers we will get 1.

We know that if we multiply $1=\dfrac{n}{n}$ to any number or fraction value of that number or fraction will remain constant.
Now, here let us consider the fraction given in the question.
$F=\dfrac{3}{18}$
By multiplying 1 on both the sides, we get,
$F\times 1=\dfrac{3}{18}\times 1$
By substituting $1=\dfrac{n}{n}$ on the RHS of the above equation, we get,
$F=\dfrac{3}{18}\times \dfrac{n}{n}=\dfrac{3n}{18n}....\left( i \right)$
In the above fraction, by substituting the different values of n, we can find the equivalent fraction to $\dfrac{3}{18}$

Let us substitute n = 2 in equation (i), we get,
$F=\dfrac{3\times 2}{18\times 2}=\dfrac{6}{36}$
Let us substitute n = 10 in equation (i), we get,
$F=\dfrac{3\times 10}{18\times 10}=\dfrac{30}{180}$
Let us substitute n = 120 in equation (i), we get,
$F=\dfrac{3\times 120}{18\times 120}=\dfrac{360}{2160}$
So, we get 3 fractions equivalent to $\dfrac{3}{18}$ as,
$\dfrac{6}{36},\dfrac{30}{180}\text{ and }\dfrac{360}{2160}$

Here, we can see that the values of all the above fractions are equal and that is equal to 0.167.

Note:
Students must remember that equivalent fractions are those which are equal, that means if $\dfrac{a}{b}=\dfrac{c}{d}$, then $\dfrac{a}{b}$ and $\dfrac{c}{d}$ are an equivalent fraction. Also, students can cross-check the given fraction by simplifying it. For example, let us cross-check $\dfrac{360}{2160}$. We can write,
$\dfrac{360}{2160}=\dfrac{3\times 120}{18\times 120}$
By canceling the like terms, we get,
$\dfrac{360}{2160}=\dfrac{3}{18}$