Question

If \( A : B : C = 2 : 3 : 4 \), then find the value of \( \frac{A}{B} \div \frac{B}{C} \div \frac{C}{A} \):

• A. \( 24 : 8 : 9 \)
• B. \( 9 : 24 : 8 \)
• C. \( 8 : 9 : 24 \)
• D. \( 9 : 8 : 24 \)

Hint:

When dealing with ratios, ensure to handle division by inverting and multiplying for simpler calculations.

Answer 1

The Correct Option is C

We are given that \( A : B : C = 2 : 3 : 4 \), i.e., \[ \frac{A}{B} = \frac{2}{3}, \quad \frac{B}{C} = \frac{3}{4}, \quad \frac{C}{A} = \frac{4}{2} = 2. \] We need to solve for the value of \( \frac{A}{B} \div \frac{B}{C} \div \frac{C}{A} \). Step 1: Express the terms: \[ \frac{A}{B} = \frac{2}{3}, \quad \frac{B}{C} = \frac{3}{4}, \quad \frac{C}{A} = 2. \]

Step 2: Apply the division rule for fractions (dividing by a fraction is equivalent to multiplying by its reciprocal): \[ \frac{A}{B} \div \frac{B}{C} \div \frac{C}{A} = \frac{2}{3} \div \frac{3}{4} \div 2. \]

Step 3: Simplify step-by-step: \[ \frac{2}{3} \div \frac{3}{4} = \frac{2}{3} \times \frac{4}{3} = \frac{8}{9}. \] Now, divide by 2: \[ \frac{8}{9} \div 2 = \frac{8}{9} \times \frac{1}{2} = \frac{8}{18} = \frac{4}{9}. \] So, the value of the expression is \( 8 : 9 : 24 \).