Question

Find the equivalent fraction of $$\dfrac{6}{11}$$ having:

(i) denominator 77

(ii) numerator 60

Answer 1

We know that equivalent fractions are fractions having different numerators and denominators, but have the same value.

(i) Equivalent fraction of $$\dfrac{6}{11}$$ having denominator as $$77$$:

Let $$\dfrac{6}{11} = \dfrac{x}{77}$$

We can see that, $$77 = (11 \times 7)$$

Since the denominator is obtained by multiplying the denominator of the original fraction by $$7$$, the numerator will be $$7$$ multiplied by the numerator of the original fraction.

$$\therefore \ x=6\times 7=42$$

Hence, $$\dfrac{42}{77}$$ is the equivalent fraction of $$\dfrac{6}{11}$$ having denominator $$77$$.

(ii) Equivalent fraction of $$\dfrac{6}{11}$$ having numerator as $$60$$:

Let $$\dfrac{6}{11} = \dfrac{60}{x}$$

We can see that, $$60 = (6 \times 10)$$

Since the numerator is obtained by multiplying the numerator of the original fraction by $$10$$, the denominator will be $$10$$ multiplied by the denominator of the original fraction.

$$\therefore \ x=11\times 10=110$$

Hence, $$\dfrac{60}{110}$$ is the equivalent fraction of $$\dfrac{6}{11}$$ having numerator $$60$$.