Solve (1/6+11/3)div(4-13/2)

$$( \frac { 1 } { 6 } + 1 \frac { 1 } { 3 } ) \div ( 4 - \frac { 13 } { 2 } )$$

Evaluate

$$-\frac{3}{5}=-0.6$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\frac{1}{6}+\frac{3+1}{3}}{4-\frac{13}{2}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{1}{6}+\frac{4}{3}}{4-\frac{13}{2}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{4}{3} to fractions with denominator 6.

$$\frac{\frac{1}{6}+\frac{8}{6}}{4-\frac{13}{2}}$$

Since \frac{1}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+8}{6}}{4-\frac{13}{2}}$$

Add 1 and 8 to get 9.

$$\frac{\frac{9}{6}}{4-\frac{13}{2}}$$

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

$$\frac{\frac{3}{2}}{4-\frac{13}{2}}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{\frac{3}{2}}{\frac{8}{2}-\frac{13}{2}}$$

Since \frac{8}{2} and \frac{13}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}}{\frac{8-13}{2}}$$

Subtract 13 from 8 to get -5.

$$\frac{\frac{3}{2}}{-\frac{5}{2}}$$

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

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

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

$$\frac{3\left(-2\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{3\left(-2\right)}{2\times 5}.

$$\frac{-6}{10}$$

Reduce the fraction \frac{-6}{10} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{3}{5} = -0.6$$