Solve 3/4*6/5div7/4div3/5

$$\frac { 3 } { 4 } \times \frac { 6 } { 5 } \div \frac { 7 } { 4 } \div \frac { 3 } { 5 }$$

Evaluate

$$\frac{6}{7}\approx 0.857142857$$

Solution Steps

Divide \frac{\frac{3}{4}\times \frac{6}{5}}{\frac{7}{4}} by \frac{3}{5} by multiplying \frac{\frac{3}{4}\times \frac{6}{5}}{\frac{7}{4}} by the reciprocal of \frac{3}{5}.

$$\frac{\frac{3}{4}\times \frac{6}{5}\times 5}{\frac{7}{4}\times 3}$$

Multiply \frac{3}{4} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 6}{4\times 5}\times 5}{\frac{7}{4}\times 3}$$

Do the multiplications in the fraction \frac{3\times 6}{4\times 5}.

$$\frac{\frac{18}{20}\times 5}{\frac{7}{4}\times 3}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{10}\times 5}{\frac{7}{4}\times 3}$$

Express \frac{9}{10}\times 5 as a single fraction.

$$\frac{\frac{9\times 5}{10}}{\frac{7}{4}\times 3}$$

Multiply 9 and 5 to get 45.

$$\frac{\frac{45}{10}}{\frac{7}{4}\times 3}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{2}}{\frac{7}{4}\times 3}$$

Express \frac{7}{4}\times 3 as a single fraction.

$$\frac{\frac{9}{2}}{\frac{7\times 3}{4}}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{9}{2}}{\frac{21}{4}}$$

Divide \frac{9}{2} by \frac{21}{4} by multiplying \frac{9}{2} by the reciprocal of \frac{21}{4}.

$$\frac{9}{2}\times \frac{4}{21}$$

Multiply \frac{9}{2} times \frac{4}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 4}{2\times 21}$$

Do the multiplications in the fraction \frac{9\times 4}{2\times 21}.

$$\frac{36}{42}$$

Reduce the fraction \frac{36}{42} to lowest terms by extracting and canceling out 6.

$$\frac{6}{7}$$

Factor

$$\frac{2 \cdot 3}{7} = 0.8571428571428571$$