Question

Solve

-3/5 times 5/16 times 7/12 times -16/3 times -5/7

Answer 1

To solve the expression

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

we first simplify the multiplication of the fractions. Let's break it down step by step.

1. **Combine the products:**

\[
= (-1) \times \frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times (-1) \times \frac{16}{3} \times (-1) \times \frac{5}{7}
\]

You have three negative signs, which means the product remains negative. Thus, we can write:

\[
= - \left( \frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{3} \times \frac{5}{7} \right)
\]

2. **Multiply the numerators and the denominators:**

The numerator is:

\[
3 \times 5 \times 7 \times 16 \times 5
\]

The denominator is:

\[
5 \times 16 \times 12 \times 3 \times 7
\]

So we write this as:

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

3. **Cancel common factors:**

- The 3 cancels with the 3 in the denominator.
- The 5 cancels with one of the 5s in the denominator.
- The 7 cancels with the 7 in the denominator.
- The 16 cancels with the 16 in the denominator.

This reduces our fraction to:

\[
= - \frac{5}{12}
\]

Thus, the final result is:

\[
\boxed{-\frac{5}{12}}
\]