Solve (16/25*35/8div16/9)div(frac{3/5-4)}{(frac{7}{3}-2)frac{9}{8}(frac{3}{4}*6*frac{8}{9}*frac{14}{25}*frac{2}{21})}

$$\frac { ( \frac { 16 } { 25 } \times \frac { 35 } { 8 } \div \frac { 16 } { 9 } ) \div ( \frac { 3 } { 5 } - 4 ) } { ( \frac { 7 } { 3 } - 2 ) \frac { 9 } { 8 } ( \frac { 3 } { 4 } \cdot 6 \cdot \frac { 8 } { 9 } \cdot \frac { 14 } { 25 } \cdot \frac { 2 } { 21 } ) }$$

Evaluate

$$-\frac{1575}{272}\approx -5.790441176$$

Solution Steps

Multiply \frac{16}{25} times \frac{35}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{\frac{16\times 35}{25\times 8}}{\frac{16}{9}}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{16\times 35}{25\times 8}.

$$\frac{\frac{\frac{\frac{560}{200}}{\frac{16}{9}}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{560}{200} to lowest terms by extracting and canceling out 40.

$$\frac{\frac{\frac{\frac{14}{5}}{\frac{16}{9}}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Divide \frac{14}{5} by \frac{16}{9} by multiplying \frac{14}{5} by the reciprocal of \frac{16}{9}.

$$\frac{\frac{\frac{14}{5}\times \frac{9}{16}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{14}{5} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{14\times 9}{5\times 16}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{14\times 9}{5\times 16}.

$$\frac{\frac{\frac{126}{80}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{126}{80} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{63}{40}}{\frac{3}{5}-4}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{\frac{\frac{63}{40}}{\frac{3}{5}-\frac{20}{5}}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Since \frac{3}{5} and \frac{20}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{63}{40}}{\frac{3-20}{5}}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Subtract 20 from 3 to get -17.

$$\frac{\frac{\frac{63}{40}}{-\frac{17}{5}}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Divide \frac{63}{40} by -\frac{17}{5} by multiplying \frac{63}{40} by the reciprocal of -\frac{17}{5}.

$$\frac{\frac{63}{40}\left(-\frac{5}{17}\right)}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{63}{40} times -\frac{5}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{63\left(-5\right)}{40\times 17}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{63\left(-5\right)}{40\times 17}.

$$\frac{\frac{-315}{680}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{-315}{680} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{63}{136}}{\left(\frac{7}{3}-2\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{-\frac{63}{136}}{\left(\frac{7}{3}-\frac{6}{3}\right)\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Since \frac{7}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{63}{136}}{\frac{7-6}{3}\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Subtract 6 from 7 to get 1.

$$\frac{-\frac{63}{136}}{\frac{1}{3}\times \frac{9}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{1}{3} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{63}{136}}{\frac{1\times 9}{3\times 8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 8}.

$$\frac{-\frac{63}{136}}{\frac{9}{24}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{9}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{63}{136}}{\frac{3}{8}\times \frac{3}{4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{3}{8} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{63}{136}}{\frac{3\times 3}{8\times 4}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{3\times 3}{8\times 4}.

$$\frac{-\frac{63}{136}}{\frac{9}{32}\times 6\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Express \frac{9}{32}\times 6 as a single fraction.

$$\frac{-\frac{63}{136}}{\frac{9\times 6}{32}\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply 9 and 6 to get 54.

$$\frac{-\frac{63}{136}}{\frac{54}{32}\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{54}{32} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{63}{136}}{\frac{27}{16}\times \frac{8}{9}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{27}{16} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{63}{136}}{\frac{27\times 8}{16\times 9}\times \frac{14}{25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{27\times 8}{16\times 9}.

$$\frac{-\frac{63}{136}}{\frac{216}{144}\times \frac{14}{25}\times \frac{2}{21}}$$

Reduce the fraction \frac{216}{144} to lowest terms by extracting and canceling out 72.

$$\frac{-\frac{63}{136}}{\frac{3}{2}\times \frac{14}{25}\times \frac{2}{21}}$$

Multiply \frac{3}{2} times \frac{14}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{63}{136}}{\frac{3\times 14}{2\times 25}\times \frac{2}{21}}$$

Do the multiplications in the fraction \frac{3\times 14}{2\times 25}.

$$\frac{-\frac{63}{136}}{\frac{42}{50}\times \frac{2}{21}}$$

Reduce the fraction \frac{42}{50} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{63}{136}}{\frac{21}{25}\times \frac{2}{21}}$$

Multiply \frac{21}{25} times \frac{2}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{63}{136}}{\frac{21\times 2}{25\times 21}}$$

Cancel out 21 in both numerator and denominator.

$$\frac{-\frac{63}{136}}{\frac{2}{25}}$$

Divide -\frac{63}{136} by \frac{2}{25} by multiplying -\frac{63}{136} by the reciprocal of \frac{2}{25}.

$$-\frac{63}{136}\times \frac{25}{2}$$

Multiply -\frac{63}{136} times \frac{25}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-63\times 25}{136\times 2}$$

Do the multiplications in the fraction \frac{-63\times 25}{136\times 2}.

$$\frac{-1575}{272}$$

Fraction \frac{-1575}{272} can be rewritten as -\frac{1575}{272} by extracting the negative sign.

$$-\frac{1575}{272}$$

Factor

$$-\frac{1575}{272} = -5\frac{215}{272} = -5.790441176470588$$