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

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

Evaluate

$$\frac{43}{62}\approx 0.693548387$$

Solution Steps

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

$$\frac{1}{2}+\frac{\frac{3}{12}-\frac{8}{12}}{-\frac{5}{8}\times \frac{3\times 9+4}{9}}$$

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

$$\frac{1}{2}+\frac{\frac{3-8}{12}}{-\frac{5}{8}\times \frac{3\times 9+4}{9}}$$

Subtract 8 from 3 to get -5.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{-\frac{5}{8}\times \frac{3\times 9+4}{9}}$$

Multiply 3 and 9 to get 27.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{-\frac{5}{8}\times \frac{27+4}{9}}$$

Add 27 and 4 to get 31.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{-\frac{5}{8}\times \frac{31}{9}}$$

Multiply -\frac{5}{8} times \frac{31}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{\frac{-5\times 31}{8\times 9}}$$

Do the multiplications in the fraction \frac{-5\times 31}{8\times 9}.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{\frac{-155}{72}}$$

Fraction \frac{-155}{72} can be rewritten as -\frac{155}{72} by extracting the negative sign.

$$\frac{1}{2}+\frac{-\frac{5}{12}}{-\frac{155}{72}}$$

Divide -\frac{5}{12} by -\frac{155}{72} by multiplying -\frac{5}{12} by the reciprocal of -\frac{155}{72}.

$$\frac{1}{2}-\frac{5}{12}\left(-\frac{72}{155}\right)$$

Multiply -\frac{5}{12} times -\frac{72}{155} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{-5\left(-72\right)}{12\times 155}$$

Do the multiplications in the fraction \frac{-5\left(-72\right)}{12\times 155}.

$$\frac{1}{2}+\frac{360}{1860}$$

Reduce the fraction \frac{360}{1860} to lowest terms by extracting and canceling out 60.

$$\frac{1}{2}+\frac{6}{31}$$

Least common multiple of 2 and 31 is 62. Convert \frac{1}{2} and \frac{6}{31} to fractions with denominator 62.

$$\frac{31}{62}+\frac{12}{62}$$

Since \frac{31}{62} and \frac{12}{62} have the same denominator, add them by adding their numerators.

$$\frac{31+12}{62}$$

Add 31 and 12 to get 43.

$$\frac{43}{62}$$

Factor

$$\frac{43}{2 \cdot 31} = 0.6935483870967742$$