Solve 1/7+2/3+6/7

$$\frac { 1 } { 7 } + \frac { 2 } { 3 } + \frac { 6 } { 7 }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{1}{7} and \frac{2}{3} to fractions with denominator 21.

$$\frac{3}{21}+\frac{14}{21}+\frac{6}{7}$$

Since \frac{3}{21} and \frac{14}{21} have the same denominator, add them by adding their numerators.

$$\frac{3+14}{21}+\frac{6}{7}$$

Add 3 and 14 to get 17.

$$\frac{17}{21}+\frac{6}{7}$$

Least common multiple of 21 and 7 is 21. Convert \frac{17}{21} and \frac{6}{7} to fractions with denominator 21.

$$\frac{17}{21}+\frac{18}{21}$$

Since \frac{17}{21} and \frac{18}{21} have the same denominator, add them by adding their numerators.

$$\frac{17+18}{21}$$

Add 17 and 18 to get 35.

$$\frac{35}{21}$$

Reduce the fraction \frac{35}{21} to lowest terms by extracting and canceling out 7.

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

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$