Question : Simplify the following expression.
25 ÷ 5 of 12 × 2 − 9 ÷ 27 of 3 × 5 − 14 ÷ 28 × 4
Option 1: $-\frac{41}{91}$
Option 2: $-\frac{31}{9}$
Option 3: 18
Option 4: $-\frac{31}{18}$
Correct Answer: $-\frac{31}{18}$
Solution :
Given: 25 ÷ 5 of 12 × 2 − 9 ÷ 27 of 3 × 5 − 14 ÷ 28 × 4
= 25 ÷ (5 × 12) × 2 − 9 ÷ (27 × 3) × 5 − 14 ÷ 28 × 4
= $\frac{25}{60}\times 2 - \frac{9}{81}\times 5-\frac{14}{28}\times4$
= $\frac{5}{12}\times 2 - \frac{1}{9}\times 5-\frac{1}{2}\times4$
= $\frac{5}{6}- \frac{5}{9}-2$
= $\frac{15-10-36}{18}$
= $-\frac{31}{18}$
Hence, the correct answer is $-\frac{31}{18}$.
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