Solve -1/3+5/-frac{1{3}-7/6}=

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

Evaluate

$$-\frac{28}{9}\approx -3.111111111$$

Solution Steps

Convert 5 to fraction \frac{15}{3}.

$$\frac{-\frac{1}{3}+\frac{15}{3}}{-\frac{1}{3}-\frac{7}{6}}$$

Since -\frac{1}{3} and \frac{15}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-1+15}{3}}{-\frac{1}{3}-\frac{7}{6}}$$

Add -1 and 15 to get 14.

$$\frac{\frac{14}{3}}{-\frac{1}{3}-\frac{7}{6}}$$

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

$$\frac{\frac{14}{3}}{-\frac{2}{6}-\frac{7}{6}}$$

Since -\frac{2}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14}{3}}{\frac{-2-7}{6}}$$

Subtract 7 from -2 to get -9.

$$\frac{\frac{14}{3}}{\frac{-9}{6}}$$

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

$$\frac{\frac{14}{3}}{-\frac{3}{2}}$$

Divide \frac{14}{3} by -\frac{3}{2} by multiplying \frac{14}{3} by the reciprocal of -\frac{3}{2}.

$$\frac{14}{3}\left(-\frac{2}{3}\right)$$

Multiply \frac{14}{3} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\left(-2\right)}{3\times 3}$$

Do the multiplications in the fraction \frac{14\left(-2\right)}{3\times 3}.

$$\frac{-28}{9}$$

Fraction \frac{-28}{9} can be rewritten as -\frac{28}{9} by extracting the negative sign.

$$-\frac{28}{9}$$

Factor

$$-\frac{28}{9} = -3\frac{1}{9} = -3.111111111111111$$