Question

What are equivalent fractions to $\dfrac{5}{9}$ ?

Answer 1

Hint: We are asked to find the equivalent fractions to the given fraction which is $\dfrac{5}{9}$ . We can find the equivalent fractions by multiplying both numerator and denominator with the same numbers such that the value of the fractions remains unaltered.

Complete step by step solution:
In the question, we have been asked to find the equivalent fractions of $\dfrac{5}{9}$. We can use the fact that the value of a fraction does not change as long as we multiply the same number to both the numerator and denominator. Hence, we can find the equivalent fractions by multiplying integers starting from 1,2,3 and so on.
First, let us multiply 1, we end up with the same fraction, next let us multiply 2 to both the numerator and the denominator, we get,
$\dfrac{5\times 2}{9\times 2}=\dfrac{10}{18}$
Hence, $\dfrac{10}{18}$ is one of the equivalent fractions of $\dfrac{5}{9}$.
Next, let us multiply 3 to both numerator and denominator. We get,
$\dfrac{5\times 3}{9\times 3}=\dfrac{15}{27}$
Hence, $\dfrac{15}{27}$ is one of the equivalent fractions of $\dfrac{5}{9}$.
Next, let us multiply 4 to both numerator and denominator. We get,
$\dfrac{5\times 4}{9\times 4}=\dfrac{20}{36}$
Hence, $\dfrac{20}{36}$ is one of the equivalent fractions of $\dfrac{5}{9}$.
Like this we can keep on finding equivalent fractions by multiplying same numbers to both numerator and denominator.

Note: When we multiply numbers to both the numerator and denominator to find equivalent fractions, we can only multiply positive and negative numbers and we cannot multiply 0. The reason being, once we do this, we end up with a $\dfrac{0}{0}$ form which is considered as an indeterminate form. Hence one must remember to multiply only positive and negative numbers to find equivalent fractions.