Solve 5/6+(-2/3)+1/3-(-2/3divfrac{3}{2})=

$$\frac { 5 } { 6 } + ( \frac { - 2 } { 3 } ) + \frac { 1 } { 3 } - ( \frac { - 2 } { 3 } \div \frac { 3 } { 2 } ) =$$

Evaluate

$$\frac{17}{18}\approx 0.944444444$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{5}{6}-\frac{2}{3}+\frac{1}{3}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{2}{3} to fractions with denominator 6.

$$\frac{5}{6}-\frac{4}{6}+\frac{1}{3}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-4}{6}+\frac{1}{3}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Subtract 4 from 5 to get 1.

$$\frac{1}{6}+\frac{1}{3}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{1}{6}+\frac{2}{6}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Since \frac{1}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{6}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Add 1 and 2 to get 3.

$$\frac{3}{6}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\frac{\frac{-2}{3}}{\frac{3}{2}}$$

Divide \frac{-2}{3} by \frac{3}{2} by multiplying \frac{-2}{3} by the reciprocal of \frac{3}{2}.

$$\frac{1}{2}-\frac{-2\times 2}{3\times 3}$$

Multiply -2 and 2 to get -4.

$$\frac{1}{2}-\frac{-4}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{1}{2}-\frac{-4}{9}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{1}{2}-\left(-\frac{4}{9}\right)$$

The opposite of -\frac{4}{9} is \frac{4}{9}.

$$\frac{1}{2}+\frac{4}{9}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{8}{18}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+8}{18}$$

Add 9 and 8 to get 17.

$$\frac{17}{18}$$

Factor

$$\frac{17}{2 \cdot 3 ^ {2}} = 0.9444444444444444$$