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

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

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert -\frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

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

Since -\frac{2}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

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

Add -2 and 5 to get 3.

$$\frac{\frac{3}{6}}{\frac{3}{7}}$$

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

$$\frac{\frac{1}{2}}{\frac{3}{7}}$$

Divide \frac{1}{2} by \frac{3}{7} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{7}.

$$\frac{1}{2}\times \frac{7}{3}$$

Multiply \frac{1}{2} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{2\times 3}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 3}.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$