Solve 7/11-5/7+1/7+2/3

$$\frac { 7 } { 11 } - \frac { 5 } { 7 } + \frac { 1 } { 7 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{169}{231}\approx 0.731601732$$

Solution Steps

Least common multiple of 11 and 7 is 77. Convert \frac{7}{11} and \frac{5}{7} to fractions with denominator 77.

$$\frac{49}{77}-\frac{55}{77}+\frac{1}{7}+\frac{2}{3}$$

Since \frac{49}{77} and \frac{55}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-55}{77}+\frac{1}{7}+\frac{2}{3}$$

Subtract 55 from 49 to get -6.

$$-\frac{6}{77}+\frac{1}{7}+\frac{2}{3}$$

Least common multiple of 77 and 7 is 77. Convert -\frac{6}{77} and \frac{1}{7} to fractions with denominator 77.

$$-\frac{6}{77}+\frac{11}{77}+\frac{2}{3}$$

Since -\frac{6}{77} and \frac{11}{77} have the same denominator, add them by adding their numerators.

$$\frac{-6+11}{77}+\frac{2}{3}$$

Add -6 and 11 to get 5.

$$\frac{5}{77}+\frac{2}{3}$$

Least common multiple of 77 and 3 is 231. Convert \frac{5}{77} and \frac{2}{3} to fractions with denominator 231.

$$\frac{15}{231}+\frac{154}{231}$$

Since \frac{15}{231} and \frac{154}{231} have the same denominator, add them by adding their numerators.

$$\frac{15+154}{231}$$

Add 15 and 154 to get 169.

$$\frac{169}{231}$$

Factor

$$\frac{13 ^ {2}}{3 \cdot 7 \cdot 11} = 0.7316017316017316$$