Solve left(9/9-8/frac{7{90}}+2/1right)*7/3+frac{24}{5}*left(frac{5}{8}-frac{2}{8}right)

$$\left( \frac{ \frac{ 9 }{ 9 } -8 }{ \frac{ 7 }{ 90 } } + \frac{ 2 }{ 1 } \right) \times \frac{ 7 }{ 3 } + \frac{ 24 }{ 5 } \times \left( \frac{ 5 }{ 8 } - \frac{ 2 }{ 8 } \right)$$

Evaluate

$$-\frac{3053}{15}\approx -203.533333333$$

Solution Steps

Divide 9 by 9 to get 1.

$$\left(\frac{1-8}{\frac{7}{90}}+\frac{2}{1}\right)\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Subtract 8 from 1 to get -7.

$$\left(\frac{-7}{\frac{7}{90}}+\frac{2}{1}\right)\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Divide -7 by \frac{7}{90} by multiplying -7 by the reciprocal of \frac{7}{90}.

$$\left(-7\times \frac{90}{7}+\frac{2}{1}\right)\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Multiply -7 times \frac{90}{7}.

$$\left(-90+\frac{2}{1}\right)\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Anything divided by one gives itself.

$$\left(-90+2\right)\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Add -90 and 2 to get -88.

$$-88\times \frac{7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Express -88\times \frac{7}{3} as a single fraction.

$$\frac{-88\times 7}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Multiply -88 and 7 to get -616.

$$\frac{-616}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Fraction \frac{-616}{3} can be rewritten as -\frac{616}{3} by extracting the negative sign.

$$-\frac{616}{3}+\frac{24}{5}\left(\frac{5}{8}-\frac{2}{8}\right)$$

Since \frac{5}{8} and \frac{2}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{616}{3}+\frac{24}{5}\times \frac{5-2}{8}$$

Subtract 2 from 5 to get 3.

$$-\frac{616}{3}+\frac{24}{5}\times \frac{3}{8}$$

Multiply \frac{24}{5} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{616}{3}+\frac{24\times 3}{5\times 8}$$

Do the multiplications in the fraction \frac{24\times 3}{5\times 8}.

$$-\frac{616}{3}+\frac{72}{40}$$

Reduce the fraction \frac{72}{40} to lowest terms by extracting and canceling out 8.

$$-\frac{616}{3}+\frac{9}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{616}{3} and \frac{9}{5} to fractions with denominator 15.

$$-\frac{3080}{15}+\frac{27}{15}$$

Since -\frac{3080}{15} and \frac{27}{15} have the same denominator, add them by adding their numerators.

$$\frac{-3080+27}{15}$$

Add -3080 and 27 to get -3053.

$$-\frac{3053}{15}$$

Factor

$$-\frac{3053}{15} = -203\frac{8}{15} = -203.53333333333333$$