Convert the following fractions into equivalent like fractions:

(i) $\dfrac{7}{8}, \dfrac{5}{14}$

(ii) $\dfrac{5}{6}, \dfrac{7}{16}$

(iii) $\dfrac{3}{4}, \dfrac{5}{6}, \dfrac{7}{8}$

(i) $\dfrac{7}{8}, \dfrac{5}{14}$

L.C.M. of 8 and 14 is :

LCM of 8 and 14 = 2 x 2 x 2 x 7 = 56

$\Rightarrow \dfrac{7}{8} = \dfrac{7 \times 7}{8 \times 7} = \dfrac{49}{56} \\[1em] \Rightarrow \dfrac{5}{14} = \dfrac{5 \times 4}{14 \times 4} = \dfrac{20}{56}$

Hence, the equivalent like fractions are $\dfrac{49}{56}$ and $\dfrac{20}{56}$.

(ii) $\dfrac{5}{6}, \dfrac{7}{16}$

L.C.M. of 6 and 16 is :

LCM of 6 and 16 = 2 x 2 x 2 x 2 x 3 = 48.

$\Rightarrow \dfrac{5}{6} = \dfrac{5 \times 8}{6 \times 8} = \dfrac{40}{48} \\[1em] \Rightarrow \dfrac{7}{16} = \dfrac{7 \times 3}{16 \times 3} = \dfrac{21}{48}$

Hence, the equivalent like fractions are $\dfrac{40}{48}$ and $\dfrac{21}{48}$.

(iii) $\dfrac{3}{4}, \dfrac{5}{6}, \dfrac{7}{8}$

L.C.M. of 4, 6 and 8 is :

LCM of 4, 6 and 8 = 2 x 2 x 2 x 3 = 24.

$\Rightarrow \dfrac{3}{4} = \dfrac{3 \times 6}{4 \times 6} = \dfrac{18}{24} \\[1em] \Rightarrow \dfrac{5}{6} = \dfrac{5 \times 4}{6 \times 4} = \dfrac{20}{24} \\[1em] \Rightarrow \dfrac{7}{8} = \dfrac{7 \times 3}{8 \times 3} = \dfrac{21}{24}$

Hence, the equivalent like fractions are $\dfrac{18}{24}, \dfrac{20}{24}$ and $\dfrac{21}{24}$.