Solve 3/7div(-21/7)*(-64)div31/5*5/8

$$\frac { 3 } { 7 } \div ( - 2 \frac { 1 } { 7 } ) \times ( - 64 ) \div 3 \frac { 1 } { 5 } \times \frac { 5 } { 8 }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{\frac{\frac{3}{7}}{-\frac{14+1}{7}}\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Add 14 and 1 to get 15.

$$\frac{\frac{\frac{3}{7}}{-\frac{15}{7}}\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Divide \frac{3}{7} by -\frac{15}{7} by multiplying \frac{3}{7} by the reciprocal of -\frac{15}{7}.

$$\frac{\frac{3}{7}\left(-\frac{7}{15}\right)\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Multiply \frac{3}{7} times -\frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\left(-7\right)}{7\times 15}\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Do the multiplications in the fraction \frac{3\left(-7\right)}{7\times 15}.

$$\frac{\frac{-21}{105}\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Reduce the fraction \frac{-21}{105} to lowest terms by extracting and canceling out 21.

$$\frac{-\frac{1}{5}\left(-64\right)}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Express -\frac{1}{5}\left(-64\right) as a single fraction.

$$\frac{\frac{-\left(-64\right)}{5}}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Multiply -1 and -64 to get 64.

$$\frac{\frac{64}{5}}{\frac{3\times 5+1}{5}}\times \frac{5}{8}$$

Multiply 3 and 5 to get 15.

$$\frac{\frac{64}{5}}{\frac{15+1}{5}}\times \frac{5}{8}$$

Add 15 and 1 to get 16.

$$\frac{\frac{64}{5}}{\frac{16}{5}}\times \frac{5}{8}$$

Divide \frac{64}{5} by \frac{16}{5} by multiplying \frac{64}{5} by the reciprocal of \frac{16}{5}.

$$\frac{64}{5}\times \frac{5}{16}\times \frac{5}{8}$$

Multiply \frac{64}{5} times \frac{5}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 5}{5\times 16}\times \frac{5}{8}$$

Cancel out 5 in both numerator and denominator.

$$\frac{64}{16}\times \frac{5}{8}$$

Divide 64 by 16 to get 4.

$$4\times \frac{5}{8}$$

Express 4\times \frac{5}{8} as a single fraction.

$$\frac{4\times 5}{8}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{8}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$