Solve -21/3+5/8/(5-frac{1{2})(2/5-1)}

$$\frac { - 2 \frac { 1 } { 3 } + \frac { 5 } { 8 } } { ( 5 - \frac { 1 } { 2 } ) ( \frac { 2 } { 5 } - 1 ) }$$

Evaluate

$$\frac{205}{324}\approx 0.632716049$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{-\frac{6+1}{3}+\frac{5}{8}}{\left(5-\frac{1}{2}\right)\left(\frac{2}{5}-1\right)}$$

Add 6 and 1 to get 7.

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

Least common multiple of 3 and 8 is 24. Convert -\frac{7}{3} and \frac{5}{8} to fractions with denominator 24.

$$\frac{-\frac{56}{24}+\frac{15}{24}}{\left(5-\frac{1}{2}\right)\left(\frac{2}{5}-1\right)}$$

Since -\frac{56}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-56+15}{24}}{\left(5-\frac{1}{2}\right)\left(\frac{2}{5}-1\right)}$$

Add -56 and 15 to get -41.

$$\frac{-\frac{41}{24}}{\left(5-\frac{1}{2}\right)\left(\frac{2}{5}-1\right)}$$

Convert 5 to fraction \frac{10}{2}.

$$\frac{-\frac{41}{24}}{\left(\frac{10}{2}-\frac{1}{2}\right)\left(\frac{2}{5}-1\right)}$$

Since \frac{10}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{41}{24}}{\frac{10-1}{2}\left(\frac{2}{5}-1\right)}$$

Subtract 1 from 10 to get 9.

$$\frac{-\frac{41}{24}}{\frac{9}{2}\left(\frac{2}{5}-1\right)}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{-\frac{41}{24}}{\frac{9}{2}\left(\frac{2}{5}-\frac{5}{5}\right)}$$

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

$$\frac{-\frac{41}{24}}{\frac{9}{2}\times \frac{2-5}{5}}$$

Subtract 5 from 2 to get -3.

$$\frac{-\frac{41}{24}}{\frac{9}{2}\left(-\frac{3}{5}\right)}$$

Multiply \frac{9}{2} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{41}{24}}{\frac{9\left(-3\right)}{2\times 5}}$$

Do the multiplications in the fraction \frac{9\left(-3\right)}{2\times 5}.

$$\frac{-\frac{41}{24}}{\frac{-27}{10}}$$

Fraction \frac{-27}{10} can be rewritten as -\frac{27}{10} by extracting the negative sign.

$$\frac{-\frac{41}{24}}{-\frac{27}{10}}$$

Divide -\frac{41}{24} by -\frac{27}{10} by multiplying -\frac{41}{24} by the reciprocal of -\frac{27}{10}.

$$-\frac{41}{24}\left(-\frac{10}{27}\right)$$

Multiply -\frac{41}{24} times -\frac{10}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-41\left(-10\right)}{24\times 27}$$

Do the multiplications in the fraction \frac{-41\left(-10\right)}{24\times 27}.

$$\frac{410}{648}$$

Reduce the fraction \frac{410}{648} to lowest terms by extracting and canceling out 2.

$$\frac{205}{324}$$

Factor

$$\frac{5 \cdot 41}{2 ^ {2} \cdot 3 ^ {4}} = 0.6327160493827161$$