Solve 31/2+2/3+1/2

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

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

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

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{21}{6}+\frac{4}{6}+\frac{1}{2}$$

Since \frac{21}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{21+4}{6}+\frac{1}{2}$$

Add 21 and 4 to get 25.

$$\frac{25}{6}+\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{25}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{25}{6}+\frac{3}{6}$$

Since \frac{25}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{25+3}{6}$$

Add 25 and 3 to get 28.

$$\frac{28}{6}$$

Reduce the fraction \frac{28}{6} to lowest terms by extracting and canceling out 2.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$