Use the properties of operations and rules for multiplying and dividing to solve

Question

(-3) ÷ (3/4) × (-5/16) ÷ (5/7)

Answer 1

To solve the expression $(-3)÷\left(\frac{3}{4}\right)\times (-\frac{5}{16})÷\left(\frac{5}{7}\right)$, we will follow the order of operations and simplify step by step.

1. Rewrite the division as multiplication by the reciprocal: $$(-3)÷\left(\frac{3}{4}\right)=(-3)\times \left(\frac{4}{3}\right)$$ This results in: $$(-3)\times \left(\frac{4}{3}\right)=-\frac{12}{3}=-4.$$

2. Now substitute back into the expression: The expression now looks like: $$-4\times (-\frac{5}{16})÷\left(\frac{5}{7}\right).$$

3. Perform the multiplication: $$-4\times (-\frac{5}{16})=\frac{20}{16}=\frac{5}{4}.$$

4. Now rewrite the division: $$\frac{5}{4}÷\left(\frac{5}{7}\right)=\frac{5}{4}\times \left(\frac{7}{5}\right).$$

5. Perform the multiplication: $$\frac{5}{4}\times \left(\frac{7}{5}\right)=\frac{5\times 7}{4\times 5}=\frac{35}{20}.$$

6. Simplify the result: $$\frac{35}{20}=\frac{7}{4}.$$

The final result of the expression $(-3)÷\left(\frac{3}{4}\right)\times (-\frac{5}{16})÷\left(\frac{5}{7}\right)$ is: $$\frac{7}{4}.$$