Solve 11/2+{1/4+(-2/3)}div{-5/8*(-frac{4}{9})}

$$1 \frac { 1 } { 2 } + \{ \frac { 1 } { 4 } + ( - \frac { 2 } { 3 } ) \} \div \{ - \frac { 5 } { 8 } \times ( - \frac { 4 } { 9 } ) \}$$

Evaluate

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Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}+\frac{\frac{1}{4}-\frac{2}{3}}{-\frac{5}{8}\left(-\frac{4}{9}\right)}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{\frac{1}{4}-\frac{2}{3}}{-\frac{5}{8}\left(-\frac{4}{9}\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{1}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{3}{2}+\frac{\frac{3}{12}-\frac{8}{12}}{-\frac{5}{8}\left(-\frac{4}{9}\right)}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}+\frac{\frac{3-8}{12}}{-\frac{5}{8}\left(-\frac{4}{9}\right)}$$

Subtract 8 from 3 to get -5.

$$\frac{3}{2}+\frac{-\frac{5}{12}}{-\frac{5}{8}\left(-\frac{4}{9}\right)}$$

Multiply -\frac{5}{8} times -\frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{-\frac{5}{12}}{\frac{-5\left(-4\right)}{8\times 9}}$$

Do the multiplications in the fraction \frac{-5\left(-4\right)}{8\times 9}.

$$\frac{3}{2}+\frac{-\frac{5}{12}}{\frac{20}{72}}$$

Reduce the fraction \frac{20}{72} to lowest terms by extracting and canceling out 4.

$$\frac{3}{2}+\frac{-\frac{5}{12}}{\frac{5}{18}}$$

Divide -\frac{5}{12} by \frac{5}{18} by multiplying -\frac{5}{12} by the reciprocal of \frac{5}{18}.

$$\frac{3}{2}-\frac{5}{12}\times \frac{18}{5}$$

Multiply -\frac{5}{12} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{-5\times 18}{12\times 5}$$

Do the multiplications in the fraction \frac{-5\times 18}{12\times 5}.

$$\frac{3}{2}+\frac{-90}{60}$$

Reduce the fraction \frac{-90}{60} to lowest terms by extracting and canceling out 30.

$$\frac{3}{2}-\frac{3}{2}$$

Subtract \frac{3}{2} from \frac{3}{2} to get 0.

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Factor

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