Solve (35/27*54/21*9/25*8/7)div(frac{14}{9}-frac{21}{15}+frac{7}{12}-frac{11}{8}-frac{3}{4})

$$( \frac { 35 } { 27 } \cdot \frac { 54 } { 21 } \cdot \frac { 9 } { 25 } \cdot \frac { 8 } { 7 } ) \div ( \frac { 14 } { 9 } - \frac { 21 } { 15 } + \frac { 7 } { 12 } - \frac { 11 } { 8 } - \frac { 3 } { 4 } )$$

Evaluate

$$-\frac{3456}{3493}\approx -0.989407386$$

Solution Steps

Reduce the fraction \frac{54}{21} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{35}{27}\times \frac{18}{7}\times \frac{9}{25}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Multiply \frac{35}{27} times \frac{18}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35\times 18}{27\times 7}\times \frac{9}{25}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Do the multiplications in the fraction \frac{35\times 18}{27\times 7}.

$$\frac{\frac{630}{189}\times \frac{9}{25}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Reduce the fraction \frac{630}{189} to lowest terms by extracting and canceling out 63.

$$\frac{\frac{10}{3}\times \frac{9}{25}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Multiply \frac{10}{3} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{10\times 9}{3\times 25}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Do the multiplications in the fraction \frac{10\times 9}{3\times 25}.

$$\frac{\frac{90}{75}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Reduce the fraction \frac{90}{75} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{6}{5}\times \frac{8}{7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Multiply \frac{6}{5} times \frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6\times 8}{5\times 7}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Do the multiplications in the fraction \frac{6\times 8}{5\times 7}.

$$\frac{\frac{48}{35}}{\frac{14}{9}-\frac{21}{15}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Reduce the fraction \frac{21}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{48}{35}}{\frac{14}{9}-\frac{7}{5}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Least common multiple of 9 and 5 is 45. Convert \frac{14}{9} and \frac{7}{5} to fractions with denominator 45.

$$\frac{\frac{48}{35}}{\frac{70}{45}-\frac{63}{45}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Since \frac{70}{45} and \frac{63}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48}{35}}{\frac{70-63}{45}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Subtract 63 from 70 to get 7.

$$\frac{\frac{48}{35}}{\frac{7}{45}+\frac{7}{12}-\frac{11}{8}-\frac{3}{4}}$$

Least common multiple of 45 and 12 is 180. Convert \frac{7}{45} and \frac{7}{12} to fractions with denominator 180.

$$\frac{\frac{48}{35}}{\frac{28}{180}+\frac{105}{180}-\frac{11}{8}-\frac{3}{4}}$$

Since \frac{28}{180} and \frac{105}{180} have the same denominator, add them by adding their numerators.

$$\frac{\frac{48}{35}}{\frac{28+105}{180}-\frac{11}{8}-\frac{3}{4}}$$

Add 28 and 105 to get 133.

$$\frac{\frac{48}{35}}{\frac{133}{180}-\frac{11}{8}-\frac{3}{4}}$$

Least common multiple of 180 and 8 is 360. Convert \frac{133}{180} and \frac{11}{8} to fractions with denominator 360.

$$\frac{\frac{48}{35}}{\frac{266}{360}-\frac{495}{360}-\frac{3}{4}}$$

Since \frac{266}{360} and \frac{495}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48}{35}}{\frac{266-495}{360}-\frac{3}{4}}$$

Subtract 495 from 266 to get -229.

$$\frac{\frac{48}{35}}{-\frac{229}{360}-\frac{3}{4}}$$

Least common multiple of 360 and 4 is 360. Convert -\frac{229}{360} and \frac{3}{4} to fractions with denominator 360.

$$\frac{\frac{48}{35}}{-\frac{229}{360}-\frac{270}{360}}$$

Since -\frac{229}{360} and \frac{270}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48}{35}}{\frac{-229-270}{360}}$$

Subtract 270 from -229 to get -499.

$$\frac{\frac{48}{35}}{-\frac{499}{360}}$$

Divide \frac{48}{35} by -\frac{499}{360} by multiplying \frac{48}{35} by the reciprocal of -\frac{499}{360}.

$$\frac{48}{35}\left(-\frac{360}{499}\right)$$

Multiply \frac{48}{35} times -\frac{360}{499} by multiplying numerator times numerator and denominator times denominator.

$$\frac{48\left(-360\right)}{35\times 499}$$

Do the multiplications in the fraction \frac{48\left(-360\right)}{35\times 499}.

$$\frac{-17280}{17465}$$

Reduce the fraction \frac{-17280}{17465} to lowest terms by extracting and canceling out 5.

$$-\frac{3456}{3493}$$

Factor

$$-\frac{3456}{3493} = -0.9894073862009733$$