Solve 1/6/frac{1{3}}+1/5/frac{1{2}}-frac{frac{1}{3}}{frac{1}{2}}

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

Evaluate

$$\frac{7}{30}\approx 0.233333333$$

Solution Steps

Divide \frac{1}{6} by \frac{1}{3} by multiplying \frac{1}{6} by the reciprocal of \frac{1}{3}.

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

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

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

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

$$\frac{1}{2}+\frac{\frac{1}{5}}{\frac{1}{2}}-\frac{\frac{1}{3}}{\frac{1}{2}}$$

Divide \frac{1}{5} by \frac{1}{2} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{2}.

$$\frac{1}{2}+\frac{1}{5}\times 2-\frac{\frac{1}{3}}{\frac{1}{2}}$$

Multiply \frac{1}{5} and 2 to get \frac{2}{5}.

$$\frac{1}{2}+\frac{2}{5}-\frac{\frac{1}{3}}{\frac{1}{2}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{5}{10}+\frac{4}{10}-\frac{\frac{1}{3}}{\frac{1}{2}}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{10}-\frac{\frac{1}{3}}{\frac{1}{2}}$$

Add 5 and 4 to get 9.

$$\frac{9}{10}-\frac{\frac{1}{3}}{\frac{1}{2}}$$

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

$$\frac{9}{10}-\frac{1}{3}\times 2$$

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

$$\frac{9}{10}-\frac{2}{3}$$

Least common multiple of 10 and 3 is 30. Convert \frac{9}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{27}{30}-\frac{20}{30}$$

Since \frac{27}{30} and \frac{20}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-20}{30}$$

Subtract 20 from 27 to get 7.

$$\frac{7}{30}$$

Factor

$$\frac{7}{2 \cdot 3 \cdot 5} = 0.23333333333333334$$