Ratio and Proportion

Concept:If $a$, $b$, $c$, and $d$ are in proportion, the ratio $a:b$ is equal to the ratio $c:d$.This implies $a \times d = b \times c$, which is the fundamental rule to find the fourth proportional $d$.Explanation:We are given $a = 60$, $b = 48$, and $c = 30$.We need to find $d$ such that $60:48 = 30:d$.Applying the cross-multiplication rule: $60 \times d = 48 \times 30$.This simplifies to $60d = 1440$.To solve for $d$, divide both sides of the equation by $60$: $d = \frac{1440}{60}$.Simplify the fraction by canceling common factors: $d = \frac{1440 \div 60}{60 \div 60} = \frac{24}{1}$.Alternatively, cancel before multiplying: $d = \frac{48 \times 30}{60} = 48 \times \frac{1}{2} = 24$.Therefore, the fourth proportional to $60$, $48$, and $30$ is $24$.Answer:$24$