Question

Find $5$ fractions equivalent to $\dfrac{5}{8}$.

Answer 1

Hint: We first try to describe the relation between the denominator and the numerator to find the simplified form. We use the multiplication by any integer with both the denominator and the numerator of the simplified form to find the equivalent fractions.

Complete step by step answer:
We need to find the equivalent fractions of the proper fraction $\dfrac{5}{8}$.Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.For any fraction $\dfrac{p}{q}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}}$.

For our given fraction $\dfrac{5}{8}$, the G.C.D of the denominator and the numerator is 1.Therefore, the simplest form of $\dfrac{5}{8}$ is itself. Now to find the equivalent fractions we multiply the denominator and the numerator with the same natural number.

Now we multiply with the integers 2, 3, 4, 5, 6 with both the denominator and the numerator of the simplified fraction $\dfrac{5}{8}$ to find the other equivalent fractions.The forms will be $\dfrac{5\times 2}{8\times 2}=\dfrac{10}{16}$, $\dfrac{5\times 3}{8\times 3}=\dfrac{15}{24}$, $\dfrac{5\times 4}{8\times 4}=\dfrac{20}{32}$, $\dfrac{5\times 5}{8\times 5}=\dfrac{25}{40}$, $\dfrac{5\times 6}{8\times 6}=\dfrac{30}{48}$.

Therefore, the equivalent fractions of $\dfrac{5}{8}$ are $\dfrac{10}{16},\dfrac{15}{24},\dfrac{20}{32},\dfrac{25}{40},\dfrac{30}{48}$.

Note: The process is similar for both proper and improper fractions. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case. Also, we can only apply the process on the proper fraction part of a mixed fraction.