Solve (7/9-0,5-5/6):(2/3+1/6)=

$$( \frac { 7 } { 9 } - 0,5 - \frac { 5 } { 6 } ) : ( \frac { 2 } { 3 } + \frac { 1 } { 6 } ) =$$

Evaluate

$$-\frac{2}{3}\approx -0,666666667$$

Solution Steps

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{9}-\frac{1}{2}-\frac{5}{6}}{\frac{2}{3}+\frac{1}{6}}$$

Least common multiple of 9 and 2 is 18. Convert \frac{7}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{\frac{14}{18}-\frac{9}{18}-\frac{5}{6}}{\frac{2}{3}+\frac{1}{6}}$$

Since \frac{14}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-9}{18}-\frac{5}{6}}{\frac{2}{3}+\frac{1}{6}}$$

Subtract 9 from 14 to get 5.

$$\frac{\frac{5}{18}-\frac{5}{6}}{\frac{2}{3}+\frac{1}{6}}$$

Least common multiple of 18 and 6 is 18. Convert \frac{5}{18} and \frac{5}{6} to fractions with denominator 18.

$$\frac{\frac{5}{18}-\frac{15}{18}}{\frac{2}{3}+\frac{1}{6}}$$

Since \frac{5}{18} and \frac{15}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-15}{18}}{\frac{2}{3}+\frac{1}{6}}$$

Subtract 15 from 5 to get -10.

$$\frac{\frac{-10}{18}}{\frac{2}{3}+\frac{1}{6}}$$

Reduce the fraction \frac{-10}{18} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{5}{9}}{\frac{2}{3}+\frac{1}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{-\frac{5}{9}}{\frac{4}{6}+\frac{1}{6}}$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{5}{9}}{\frac{4+1}{6}}$$

Add 4 and 1 to get 5.

$$\frac{-\frac{5}{9}}{\frac{5}{6}}$$

Divide -\frac{5}{9} by \frac{5}{6} by multiplying -\frac{5}{9} by the reciprocal of \frac{5}{6}.

$$-\frac{5}{9}\times \frac{6}{5}$$

Multiply -\frac{5}{9} times \frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\times 6}{9\times 5}$$

Do the multiplications in the fraction \frac{-5\times 6}{9\times 5}.

$$\frac{-30}{45}$$

Reduce the fraction \frac{-30}{45} to lowest terms by extracting and canceling out 15.

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

Factor

$$-\frac{2}{3} = -0.6666666666666666$$