Solve 4/5*(7/8*3/4)div(8/7-frac{2}{35})*(frac{4}{10}divfrac{5}{3})

$$\frac{ 4 }{ 5 } \times ( \frac{ 7 }{ 8 } \times \frac{ 3 }{ 4 } ) \div ( \frac{ 8 }{ 7 } - \frac{ 2 }{ 35 } ) \times ( \frac{ 4 }{ 10 } \div \frac{ 5 }{ 3 } )$$

Evaluate

$$\frac{441}{3800}\approx 0.116052632$$

Solution Steps

Multiply \frac{4}{5} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 7}{5\times 8}\times \frac{3}{4}}{\frac{8}{7}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Do the multiplications in the fraction \frac{4\times 7}{5\times 8}.

$$\frac{\frac{28}{40}\times \frac{3}{4}}{\frac{8}{7}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Reduce the fraction \frac{28}{40} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{10}\times \frac{3}{4}}{\frac{8}{7}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Multiply \frac{7}{10} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 3}{10\times 4}}{\frac{8}{7}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Do the multiplications in the fraction \frac{7\times 3}{10\times 4}.

$$\frac{\frac{21}{40}}{\frac{8}{7}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Least common multiple of 7 and 35 is 35. Convert \frac{8}{7} and \frac{2}{35} to fractions with denominator 35.

$$\frac{\frac{21}{40}}{\frac{40}{35}-\frac{2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Since \frac{40}{35} and \frac{2}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21}{40}}{\frac{40-2}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Subtract 2 from 40 to get 38.

$$\frac{\frac{21}{40}}{\frac{38}{35}}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Divide \frac{21}{40} by \frac{38}{35} by multiplying \frac{21}{40} by the reciprocal of \frac{38}{35}.

$$\frac{21}{40}\times \frac{35}{38}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Multiply \frac{21}{40} times \frac{35}{38} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 35}{40\times 38}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Do the multiplications in the fraction \frac{21\times 35}{40\times 38}.

$$\frac{735}{1520}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Reduce the fraction \frac{735}{1520} to lowest terms by extracting and canceling out 5.

$$\frac{147}{304}\times \frac{\frac{4}{10}}{\frac{5}{3}}$$

Divide \frac{4}{10} by \frac{5}{3} by multiplying \frac{4}{10} by the reciprocal of \frac{5}{3}.

$$\frac{147}{304}\times \frac{4\times 3}{10\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{147}{304}\times \frac{2\times 3}{5\times 5}$$

Multiply 2 and 3 to get 6.

$$\frac{147}{304}\times \frac{6}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{147}{304}\times \frac{6}{25}$$

Multiply \frac{147}{304} times \frac{6}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{147\times 6}{304\times 25}$$

Do the multiplications in the fraction \frac{147\times 6}{304\times 25}.

$$\frac{882}{7600}$$

Reduce the fraction \frac{882}{7600} to lowest terms by extracting and canceling out 2.

$$\frac{441}{3800}$$

Factor

$$\frac{3 ^ {2} \cdot 7 ^ {2}}{2 ^ {3} \cdot 5 ^ {2} \cdot 19} = 0.11605263157894737$$