Solve (1/7+1/4+13/28):2/3

$$( \frac { 1 } { 7 } + \frac { 1 } { 4 } + \frac { 13 } { 28 } ) : \frac { 2 } { 3 }$$

Evaluate

$$\frac{9}{7}\approx 1.285714286$$

Solution Steps

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

$$\frac{\frac{4}{28}+\frac{7}{28}+\frac{13}{28}}{\frac{2}{3}}$$

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

$$\frac{\frac{4+7}{28}+\frac{13}{28}}{\frac{2}{3}}$$

Add 4 and 7 to get 11.

$$\frac{\frac{11}{28}+\frac{13}{28}}{\frac{2}{3}}$$

Since \frac{11}{28} and \frac{13}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{11+13}{28}}{\frac{2}{3}}$$

Add 11 and 13 to get 24.

$$\frac{\frac{24}{28}}{\frac{2}{3}}$$

Reduce the fraction \frac{24}{28} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{6}{7}}{\frac{2}{3}}$$

Divide \frac{6}{7} by \frac{2}{3} by multiplying \frac{6}{7} by the reciprocal of \frac{2}{3}.

$$\frac{6}{7}\times \frac{3}{2}$$

Multiply \frac{6}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 3}{7\times 2}$$

Do the multiplications in the fraction \frac{6\times 3}{7\times 2}.

$$\frac{18}{14}$$

Reduce the fraction \frac{18}{14} to lowest terms by extracting and canceling out 2.

$$\frac{9}{7}$$

Factor

$$\frac{3 ^ {2}}{7} = 1\frac{2}{7} = 1.2857142857142858$$