what is (-3) divided by (3/4) times (2/7) times (-15/6) divided by (5/7)

Answer 1

Let's break down the expression step-by-step:

The expression is:

\[ \left(-3 \div \frac{3}{4}\right) \times \left(\frac{2}{7}\right) \times \left(-\frac{15}{6}\right) \div \left(\frac{5}{7}\right) \]

Step 1: Division of -3 by 3/4

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ -3 \div \frac{3}{4} = -3 \times \frac{4}{3} = -\frac{12}{3} = -4 \]

Step 2: Multiply by \( \frac{2}{7} \)

Now we multiply -4 by \( \frac{2}{7} \):

\[ -4 \times \frac{2}{7} = -\frac{8}{7} \]

Step 3: Multiply by \(-\frac{15}{6}\)

Now multiply by \(-\frac{15}{6}\):

\[ -\frac{8}{7} \times -\frac{15}{6} = \frac{8 \times 15}{7 \times 6} = \frac{120}{42} \]

Step 4: Simplify \(\frac{120}{42}\)

Now we simplify \(\frac{120}{42}\):

\[ \frac{120 \div 6}{42 \div 6} = \frac{20}{7} \]

Step 5: Divide by \(\frac{5}{7}\)

Finally, we need to divide by \(\frac{5}{7}\):

\[ \frac{20}{7} \div \frac{5}{7} = \frac{20}{7} \times \frac{7}{5} = \frac{20 \times 7}{7 \times 5} = \frac{20}{5} = 4 \]

Thus, the final result of the entire expression is:

\[ \boxed{4} \]