Question

Use the properties and rules for multiplying and dividing too solve.
(-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7)

Answer 1

To solve the expression \((-3) \div \left(\frac{3}{4}\right) \times \left(\frac{2}{7}\right) \times \left(-\frac{5}{16}\right) \div \left(\frac{5}{7}\right)\), let's break it down step-by-step.

1. First, we start with the division and multiplication. Recall that dividing by a fraction is the same as multiplying by its reciprocal.

2. We rewrite the expression:
\[
-3 \div \left(\frac{3}{4}\right) = -3 \times \left(\frac{4}{3}\right)
\]

3. Now the expression becomes:
\[
-3 \times \left(\frac{4}{3}\right) \times \left(\frac{2}{7}\right) \times \left(-\frac{5}{16}\right) \div \left(\frac{5}{7}\right)
\]

4. Next, we address the division by \(\frac{5}{7}\):
\[
\div \left(\frac{5}{7}\right) = \times \left(\frac{7}{5}\right)
\]

5. Now, substituting this back, we get:
\[
-3 \times \left(\frac{4}{3}\right) \times \left(\frac{2}{7}\right) \times \left(-\frac{5}{16}\right) \times \left(\frac{7}{5}\right)
\]

6. We can now simplify the expression step-by-step. First, we eliminate the \(-3\) and \(\frac{4}{3}\):
\[
(-3) \times \left(\frac{4}{3}\right) = -\frac{12}{3} = -4
\]

7. Now replacing:
\[
-4 \times \left(\frac{2}{7}\right) \times \left(-\frac{5}{16}\right) \times \left(\frac{7}{5}\right)
\]

8. Next, we can multiply \(-4\) with \(\left(-\frac{5}{16}\right)\):
\[
-4 \times -\frac{5}{16} = \frac{20}{16} = \frac{5}{4}
\]

9. Now we multiply:
\[
\frac{5}{4} \times \frac{2}{7} = \frac{10}{28} = \frac{5}{14}
\]

10. Finally, we multiply by \(\frac{7}{5}\):
\[
\frac{5}{14} \times \frac{7}{5} = \frac{35}{70} = \frac{1}{2}
\]

So the final answer is:
\[
\boxed{\frac{1}{2}}
\]