Solve (1/6+1/5)div(2/7+1/2)

$$( \frac { 1 } { 6 } + \frac { 1 } { 5 } ) \div ( \frac { 2 } { 7 } + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{7}{15}\approx 0.466666667$$

Solution Steps

Least common multiple of 6 and 5 is 30. Convert \frac{1}{6} and \frac{1}{5} to fractions with denominator 30.

$$\frac{\frac{5}{30}+\frac{6}{30}}{\frac{2}{7}+\frac{1}{2}}$$

Since \frac{5}{30} and \frac{6}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+6}{30}}{\frac{2}{7}+\frac{1}{2}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{11}{30}}{\frac{2}{7}+\frac{1}{2}}$$

Least common multiple of 7 and 2 is 14. Convert \frac{2}{7} and \frac{1}{2} to fractions with denominator 14.

$$\frac{\frac{11}{30}}{\frac{4}{14}+\frac{7}{14}}$$

Since \frac{4}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11}{30}}{\frac{4+7}{14}}$$

Add 4 and 7 to get 11.

$$\frac{\frac{11}{30}}{\frac{11}{14}}$$

Divide \frac{11}{30} by \frac{11}{14} by multiplying \frac{11}{30} by the reciprocal of \frac{11}{14}.

$$\frac{11}{30}\times \frac{14}{11}$$

Multiply \frac{11}{30} times \frac{14}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 14}{30\times 11}$$

Cancel out 11 in both numerator and denominator.

$$\frac{14}{30}$$

Reduce the fraction \frac{14}{30} to lowest terms by extracting and canceling out 2.

$$\frac{7}{15}$$

Factor

$$\frac{7}{3 \cdot 5} = 0.4666666666666667$$