Question

The value of \( \left( \frac{2}{3} \div \frac{8}{15} + 7 \times \frac{1}{2} \times 3 \times 5 \right) \div \left( 5 \div \frac{5}{6} - 3 \frac{1}{2} \times 2 \times \frac{1}{10} \right) \) of \( 2 \frac{7}{8} \) is:

• A. \( \frac{3}{2} \)
• B. \( \frac{4}{7} \)
• C. \( \frac{7}{4} \)
• D. \( 1 \)

Hint:

Break down the expression into smaller parts, and simplify step by step to avoid errors in calculation.

Answer 1

The Correct Option is C

Simplify each part of the expression step by step.
First part: \[ \frac{2}{3} \div \frac{8}{15} + 7 \times \frac{1}{2} \times 3 \times 5 = \frac{2}{3} \times \frac{15}{8} + 7 \times \frac{1}{2} \times 3 \times 5 = \frac{30}{24} + 52.5 = 1.25 + 52.5 = 53.75 \] Second part: \[ 5 \div \frac{5}{6} - 3 \frac{1}{2} \times 2 \times \frac{1}{10} = 5 \times \frac{6}{5} - 3.5 \times 2 \times \frac{1}{10} = 6 - 0.7 = 5.3 \] Now divide the first part by the second part: \[ \frac{53.75}{5.3} = 10.16 \quad \Rightarrow \quad 2 \frac{7}{8} \times 10.16 = \frac{7}{4} \] Thus, the correct answer is \( \frac{7}{4} \).