Solve (1/7+1/4)div11/14+5/6

$$( \frac { 1 } { 7 } + \frac { 1 } { 4 } ) \div \frac { 11 } { 14 } + \frac { 5 } { 6 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Least common multiple of 7 and 4 is 28. Convert \frac{1}{7} and \frac{1}{4} to fractions with denominator 28.

$$\frac{\frac{4}{28}+\frac{7}{28}}{\frac{11}{14}}+\frac{5}{6}$$

Since \frac{4}{28} and \frac{7}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+7}{28}}{\frac{11}{14}}+\frac{5}{6}$$

Add 4 and 7 to get 11.

$$\frac{\frac{11}{28}}{\frac{11}{14}}+\frac{5}{6}$$

Divide \frac{11}{28} by \frac{11}{14} by multiplying \frac{11}{28} by the reciprocal of \frac{11}{14}.

$$\frac{11}{28}\times \frac{14}{11}+\frac{5}{6}$$

Multiply \frac{11}{28} times \frac{14}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 14}{28\times 11}+\frac{5}{6}$$

Cancel out 11 in both numerator and denominator.

$$\frac{14}{28}+\frac{5}{6}$$

Reduce the fraction \frac{14}{28} to lowest terms by extracting and canceling out 14.

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

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{3}{6}+\frac{5}{6}$$

Since \frac{3}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{6}$$

Add 3 and 5 to get 8.

$$\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$