Solve left|-3/6+frac{2/9right|/-frac{-2{3}}}{1/2-frac{5}{6}}

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

Evaluate

$$-\frac{5}{4}=-1.25$$

Solution Steps

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

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

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

$$\frac{\frac{|-\frac{9}{18}+\frac{4}{18}|}{-\frac{-2}{3}}}{\frac{1}{2}-\frac{5}{6}}$$

Since -\frac{9}{18} and \frac{4}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{|\frac{-9+4}{18}|}{-\frac{-2}{3}}}{\frac{1}{2}-\frac{5}{6}}$$

Add -9 and 4 to get -5.

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

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{5}{18} is \frac{5}{18}.

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

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

$$\frac{\frac{\frac{5}{18}}{-\left(-\frac{2}{3}\right)}}{\frac{1}{2}-\frac{5}{6}}$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

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

Divide \frac{5}{18} by \frac{2}{3} by multiplying \frac{5}{18} by the reciprocal of \frac{2}{3}.

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

Multiply \frac{5}{18} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 3}{18\times 2}.

$$\frac{\frac{15}{36}}{\frac{1}{2}-\frac{5}{6}}$$

Reduce the fraction \frac{15}{36} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{5}{12}}{\frac{1}{2}-\frac{5}{6}}$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{\frac{5}{12}}{\frac{3}{6}-\frac{5}{6}}$$

Since \frac{3}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{12}}{\frac{3-5}{6}}$$

Subtract 5 from 3 to get -2.

$$\frac{\frac{5}{12}}{\frac{-2}{6}}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{5}{12}}{-\frac{1}{3}}$$

Divide \frac{5}{12} by -\frac{1}{3} by multiplying \frac{5}{12} by the reciprocal of -\frac{1}{3}.

$$\frac{5}{12}\left(-3\right)$$

Express \frac{5}{12}\left(-3\right) as a single fraction.

$$\frac{5\left(-3\right)}{12}$$

Multiply 5 and -3 to get -15.

$$\frac{-15}{12}$$

Reduce the fraction \frac{-15}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{4}$$

Factor

$$-\frac{5}{4} = -1\frac{1}{4} = -1.25$$