Solve {1/6+(-3/4)*2/3}div{1/3-(-1frac{1}{6})}

$$\{ \frac { 1 } { 6 } + ( - \frac { 3 } { 4 } ) \times \frac { 2 } { 3 } \} \div \{ \frac { 1 } { 3 } - ( - 1 \frac { 1 } { 6 } ) \}$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

Multiply -\frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{6}+\frac{-3\times 2}{4\times 3}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

Do the multiplications in the fraction \frac{-3\times 2}{4\times 3}.

$$\frac{\frac{1}{6}+\frac{-6}{12}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{1}{6}-\frac{1}{2}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

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

$$\frac{\frac{1}{6}-\frac{3}{6}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

Since \frac{1}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-3}{6}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

Subtract 3 from 1 to get -2.

$$\frac{\frac{-2}{6}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

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

$$\frac{-\frac{1}{3}}{\frac{1}{3}-\left(-\frac{1\times 6+1}{6}\right)}$$

Multiply 1 and 6 to get 6.

$$\frac{-\frac{1}{3}}{\frac{1}{3}-\left(-\frac{6+1}{6}\right)}$$

Add 6 and 1 to get 7.

$$\frac{-\frac{1}{3}}{\frac{1}{3}-\left(-\frac{7}{6}\right)}$$

The opposite of -\frac{7}{6} is \frac{7}{6}.

$$\frac{-\frac{1}{3}}{\frac{1}{3}+\frac{7}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{7}{6} to fractions with denominator 6.

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

Since \frac{2}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

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

Add 2 and 7 to get 9.

$$\frac{-\frac{1}{3}}{\frac{9}{6}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

Divide -\frac{1}{3} by \frac{3}{2} by multiplying -\frac{1}{3} by the reciprocal of \frac{3}{2}.

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

Multiply -\frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Fraction \frac{-2}{9} can be rewritten as -\frac{2}{9} by extracting the negative sign.

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

Factor

$$-\frac{2}{9} = -0.2222222222222222$$