Solve 1/6+2/3+5/7+7/6+frac{11}{8}=

$$\frac { 1 } { 6 } + \frac { 2 } { 3 } + \frac { 5 } { 7 } + \frac { 7 } { 6 } + \frac { 11 } { 8 } =$$

Evaluate

$$\frac{229}{56}\approx 4.089285714$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{2}{3} to fractions with denominator 6.

$$\frac{1}{6}+\frac{4}{6}+\frac{5}{7}+\frac{7}{6}+\frac{11}{8}$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{6}+\frac{5}{7}+\frac{7}{6}+\frac{11}{8}$$

Add 1 and 4 to get 5.

$$\frac{5}{6}+\frac{5}{7}+\frac{7}{6}+\frac{11}{8}$$

Least common multiple of 6 and 7 is 42. Convert \frac{5}{6} and \frac{5}{7} to fractions with denominator 42.

$$\frac{35}{42}+\frac{30}{42}+\frac{7}{6}+\frac{11}{8}$$

Since \frac{35}{42} and \frac{30}{42} have the same denominator, add them by adding their numerators.

$$\frac{35+30}{42}+\frac{7}{6}+\frac{11}{8}$$

Add 35 and 30 to get 65.

$$\frac{65}{42}+\frac{7}{6}+\frac{11}{8}$$

Least common multiple of 42 and 6 is 42. Convert \frac{65}{42} and \frac{7}{6} to fractions with denominator 42.

$$\frac{65}{42}+\frac{49}{42}+\frac{11}{8}$$

Since \frac{65}{42} and \frac{49}{42} have the same denominator, add them by adding their numerators.

$$\frac{65+49}{42}+\frac{11}{8}$$

Add 65 and 49 to get 114.

$$\frac{114}{42}+\frac{11}{8}$$

Reduce the fraction \frac{114}{42} to lowest terms by extracting and canceling out 6.

$$\frac{19}{7}+\frac{11}{8}$$

Least common multiple of 7 and 8 is 56. Convert \frac{19}{7} and \frac{11}{8} to fractions with denominator 56.

$$\frac{152}{56}+\frac{77}{56}$$

Since \frac{152}{56} and \frac{77}{56} have the same denominator, add them by adding their numerators.

$$\frac{152+77}{56}$$

Add 152 and 77 to get 229.

$$\frac{229}{56}$$

Factor

$$\frac{229}{2 ^ {3} \cdot 7} = 4\frac{5}{56} = 4.089285714285714$$