Solve 1/2+1(2/3)-6/12+12/3

$$\frac { 1 } { 2 } + 1 ( \frac { 2 } { 3 } ) - \frac { 6 } { 12 } + 1 \frac { 2 } { 3 }$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Multiply 1 and \frac{2}{3} to get \frac{2}{3}.

$$\frac{1}{2}+\frac{2}{3}-\frac{6}{12}+\frac{1\times 3+2}{3}$$

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

$$\frac{3}{6}+\frac{4}{6}-\frac{6}{12}+\frac{1\times 3+2}{3}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{6}-\frac{6}{12}+\frac{1\times 3+2}{3}$$

Add 3 and 4 to get 7.

$$\frac{7}{6}-\frac{6}{12}+\frac{1\times 3+2}{3}$$

Reduce the fraction \frac{6}{12} to lowest terms by extracting and canceling out 6.

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

Least common multiple of 6 and 2 is 6. Convert \frac{7}{6} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{7}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 7 to get 4.

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

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Since \frac{2}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 5 to get 7.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$