Question

Write the next two equivalent fractions to each of the following fractions:
(a) $\dfrac{2}{3}$
(b) $\dfrac{5}{7}$
(c) $\dfrac{6}{11}$

Answer 1

Hint: Equivalent fractions are the fractions that have different numerator and denominator but are equal to the same value after simplification. We will get the first equivalent fraction such that the numerator will be the very next multiple of the numerator of the given fraction and the denominator will be the very next multiple of the denominator of the given fraction. Similarly, we have to write the next equivalent fraction by considering the next multiple of the numerator and denominator of the given fraction.

Complete step-by-step solution:
We have to find the next two equivalent fractions to the given fractions, Let us recollect what equivalent fractions are. Equivalent fractions are the fractions that have different numerator and denominator but are equal to the same value after simplification.
Now, let us consider each of the given fractions.
(a) Let us find the next two equivalent fractions of $\dfrac{2}{3}$ . We can write the first equivalent fraction such that the numerator will be the very next multiple of the numerator of $\dfrac{2}{3}$ and the denominator will be the very next multiple of the denominator of $\dfrac{2}{3}$ . We know that the multiples of 2 are 2, 4, 6, 8… and that of 3 are 3, 6, 9, 12, … .Therefore, we can write the first equivalent fraction as $\dfrac{4}{6}$ . Similarly, we have to write the next equivalent fraction by considering the next multiple of the numerator and denominator of $\dfrac{2}{3}$ .
Therefore, the next two equivalent fractions of $\dfrac{2}{3}$ are $\dfrac{4}{6},\dfrac{6}{9}$.
(b) Now, we have to find the next two equivalent fractions of $\dfrac{5}{7}$ . We know that the multiples of 5 are 5, 10, 15, … and that of 7 are 7, 14, 21, … .Therefore, the next two equivalent fractions of $\dfrac{5}{7}$ are $\dfrac{10}{14},\dfrac{15}{21}$ .
(c) Let us find the next two equivalent fractions of $\dfrac{6}{11}$ . We know that the multiples of 6 are 6, 12, 18, … and that of 11 are 11, 22, 33, … . Therefore, the next two equivalent fractions of $\dfrac{6}{11}$ are $\dfrac{12}{22},\dfrac{18}{33}$ .

Note: Students have a chance of making a mistake by writing the second equivalent fraction by considering the multiples of the numerator and denominator of the first equivalent fraction. We can verify the result by simplifying the equivalent fraction. For example, let us consider the equivalent fractions of $\dfrac{2}{3}$ . If we simplify the fraction $\dfrac{4}{6}$ by cancelling the common factor 2, we will get $\dfrac{2}{3}$ . Similarly, if we cancel $\dfrac{6}{9}$ by 3, we will get $\dfrac{2}{3}$ .