Solve 2/3+3/4+5/6+1/2

$$\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 5 } { 6 } + \frac { 1 } { 2 }$$

Evaluate

$$\frac{11}{4}=2.75$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{9}{12}+\frac{5}{6}+\frac{1}{2}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{12}+\frac{5}{6}+\frac{1}{2}$$

Add 8 and 9 to get 17.

$$\frac{17}{12}+\frac{5}{6}+\frac{1}{2}$$

Least common multiple of 12 and 6 is 12. Convert \frac{17}{12} and \frac{5}{6} to fractions with denominator 12.

$$\frac{17}{12}+\frac{10}{12}+\frac{1}{2}$$

Since \frac{17}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{17+10}{12}+\frac{1}{2}$$

Add 17 and 10 to get 27.

$$\frac{27}{12}+\frac{1}{2}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\frac{9}{4}+\frac{1}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{9}{4}+\frac{2}{4}$$

Since \frac{9}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{4}$$

Add 9 and 2 to get 11.

$$\frac{11}{4}$$

Factor

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$