Question

Use the properties of operations and rules from multiplying and dividing to solve -3/5×5/16×7/12÷-3/16×-5/7

Answer 1

To solve the expression \(-\frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \div -\frac{3}{16} \times -\frac{5}{7}\), we can follow the order of operations and simplify step by step.

First, we can rearrange the expression using the multiplication and division properties:

\[
-\frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{-3} \times \frac{7}{-5}
\]

Now, note that when dividing by \(-\frac{3}{16}\) and also multiplying by \(-\frac{5}{7}\), we can write it as multiplying by their reciprocal.

Next, we can simplify the expression step by step:

1. **First simplify \(-\frac{3}{5} \times \frac{5}{16}\)**:
\[
-\frac{3}{5} \times \frac{5}{16} = -\frac{3 \times 5}{5 \times 16} = -\frac{3}{16} \quad \text{(the 5 cancels)}
\]

2. **Substituting into the expression**:
\[
-\frac{3}{16} \times \frac{7}{12} \times \frac{16}{-3} \times \frac{7}{-5}
\]

3. **Now simplifying \(-\frac{3}{16} \times \frac{16}{-3}\)**:
\[
-\frac{3}{16} \times \frac{16}{-3} = 1 \quad \text{(the -3 and 16 cancel)}
\]

4. **Now the expression becomes**:
\[
1 \times \frac{7}{12} \times \frac{7}{-5}
\]
\[
= \frac{7}{12} \times \frac{7}{-5}
\]

5. **Finally, multiply \(\frac{7}{12} \times \frac{7}{-5}\)**:
\[
= \frac{7 \times 7}{12 \times -5} = \frac{49}{-60} = -\frac{49}{60}
\]

Thus, the final result is:

\[
\boxed{-\frac{49}{60}}
\]