Simplify $\dfrac{48}{72}$ and express it in lowest terms. Compare $\dfrac{5}{8}$ and $\dfrac{7}{12}$ using cross multiplication.

Given,

Fractions = $\dfrac{48}{72}$ and $\dfrac{5}{8}$, $\dfrac{7}{12}$.

Simplifying $\dfrac{48}{72}$:

HCF of 48 and 72 :

$\begin{array}{l|r} 2 & 72 \ \hline 2 & 36 \ \hline 2 & 18 \ \hline 3 & 9 \ \hline 3 & 3 \ \hline & 1 \end{array} \quad \text{ and } \quad \begin{array}{l|r} 2 & 48 \ \hline 2 & 24 \ \hline 2 & 12 \ \hline 2 & 6 \ \hline 3 & 3 \ \hline & 1 \end{array}$

⇒ 72 = 2³ × 3²

⇒ 48 = 2⁴ × 3

⇒ HCF = 2³ × 3 = 8 × 3 = 24

The HCF of 48 and 72 is 24.

$\dfrac{48}{72} = \dfrac{48 \div 24}{72 \div 24} = \dfrac{2}{3}$

Comparing $\dfrac{5}{8}$ and $\dfrac{7}{12}$ by cross multiplication:

Cross multiply: 5 × 12 = 60 and 7 × 8 = 56.

Since 60 > 56, we have $\dfrac{5}{8} \gt \dfrac{7}{12}$.