Check whether the given pairs of fractions are equivalent:

(i) $\dfrac{3}{10}, \dfrac{12}{40}$

(ii) $\dfrac{5}{8}, \dfrac{30}{48}$

(iii) $\dfrac{4}{6}, \dfrac{30}{20}$

(iv) $\dfrac{7}{13}, \dfrac{5}{11}$

(i) $\dfrac{3}{10}, \dfrac{12}{40}$

By cross multiplication,

3 × 40 = 120 and 10 × 12 = 120

Here, the cross products are equal.

Hence, $\dfrac{3}{10}$ and $\dfrac{12}{40}$ are equivalent fractions.

(ii) $\dfrac{5}{8}, \dfrac{30}{48}$

By cross multiplication,

5 × 48 = 240 and 8 × 30 = 240

Here, the cross products are equal.

Hence, $\dfrac{5}{8}$ and $\dfrac{30}{48}$ are equivalent fractions.

(iii) $\dfrac{4}{6}, \dfrac{30}{20}$

By cross multiplication,

4 × 20 = 80 and 6 × 30 = 180

Here, the cross products are not equal.

Hence, $\dfrac{4}{6}$ and $\dfrac{30}{20}$ are not equivalent fractions.

(iv) $\dfrac{7}{13}, \dfrac{5}{11}$

By cross multiplication,

7 × 11 = 77 and 13 × 5 = 65

Here, the cross products are not equal.

Hence, $\dfrac{7}{13}$ and $\dfrac{5}{11}$ are not equivalent fractions.