Question

3/4 times [7/5 divided by (14/15-11/15)-5]

Answer 1

To solve the expression \( \frac{3}{4} \times \left[ \frac{7}{5} \div \left( \frac{14}{15} - \frac{11}{15} \right) - 5 \right] \), we will follow the order of operations.

1. **Calculate the subtraction in the parentheses:**
\[
\frac{14}{15} - \frac{11}{15} = \frac{14 - 11}{15} = \frac{3}{15} = \frac{1}{5}
\]

2. **Now replace this back into the expression:**
\[
\frac{3}{4} \times \left[ \frac{7}{5} \div \frac{1}{5} - 5 \right]
\]

3. **Divide \( \frac{7}{5} \) by \( \frac{1}{5} \):**
\[
\frac{7}{5} \div \frac{1}{5} = \frac{7}{5} \times 5 = 7
\]

4. **Now replace this back into the expression:**
\[
\frac{3}{4} \times \left[ 7 - 5 \right]
\]

5. **Calculate the subtraction:**
\[
7 - 5 = 2
\]

6. **Now replace this back into the expression:**
\[
\frac{3}{4} \times 2
\]

7. **Multiply \( \frac{3}{4} \) by \( 2 \):**
\[
\frac{3}{4} \times 2 = \frac{3 \times 2}{4} = \frac{6}{4} = \frac{3}{2}
\]

Thus, the final answer is:
\[
\frac{3}{2}
\]