Question

Find two equivalent fractions of $\dfrac{3}{5}$.

Answer 1

Hint:Equivalent fraction is meant by all fractions of the form $\dfrac{p}{q}$ where p and q are integers and gives the same decimal value. A simple way for finding equivalent fractions is to multiply and divide the numerator and denominator of the given fraction by a particular integer value. Then the newly obtained fraction after multiplication will be equivalent to the earlier one.

Complete step-by-step answer:
Let us find the nearest equivalent fraction by multiplying both the numerator and denominator by a smaller integer say 2. Then,
 $\dfrac{{3 \times 2}}{{5 \times 2}} = \dfrac{6}{{10}}$
Similarly if we multiply another integer on both numerator and denominator say by 3:
$\dfrac{{3 \times 3}}{{5 \times 3}} = \dfrac{9}{{15}}$
Now let us check the decimal value of all the three fractions $\dfrac{3}{5}$, $\dfrac{6}{{10}}$, $\dfrac{9}{{15}}$ which are all the same.
Decimal value of all the three fractions = 0.6

Two equivalent fractions for $\dfrac{3}{5}$ are $\dfrac{6}{{10}}$ and $\dfrac{9}{{15}}$.

Note:If $\dfrac{p}{q}$ is the given fraction, then we multiply a particular integer value ‘r’ on both numerator and denominator to obtain an equivalent fraction for $\dfrac{p}{q}$. Which will be : $\dfrac{{pr}}{{qr}}$. In here after cancellation of r we obtain the earlier fraction $\dfrac{p}{q}$.In a similar way of multiplying and dividing the given fraction by different integer values, we will obtain an infinite number of equivalent fractions. All those infinite number of fractions will have the same decimal value. As we have multiplied positive integers on both numerator and denominator, we could also multiply negative integers like -2, -3 etc and obtain the equivalent fractions.