Solve 3*(1/2+1/3)-2*(2-1/3)=

$$3 \cdot ( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) - 2 \cdot ( 2 - \frac { 1 } { 3 } ) =$$

Evaluate

$$-\frac{5}{6}\approx -0.833333333$$

Solution Steps

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

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

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$3\times \frac{3+2}{6}-2\left(2-\frac{1}{3}\right)$$

Add 3 and 2 to get 5.

$$3\times \frac{5}{6}-2\left(2-\frac{1}{3}\right)$$

Express 3\times \frac{5}{6} as a single fraction.

$$\frac{3\times 5}{6}-2\left(2-\frac{1}{3}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{15}{6}-2\left(2-\frac{1}{3}\right)$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}-2\left(2-\frac{1}{3}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{5}{2}-2\left(\frac{6}{3}-\frac{1}{3}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}-2\times \frac{6-1}{3}$$

Subtract 1 from 6 to get 5.

$$\frac{5}{2}-2\times \frac{5}{3}$$

Express 2\times \frac{5}{3} as a single fraction.

$$\frac{5}{2}-\frac{2\times 5}{3}$$

Multiply 2 and 5 to get 10.

$$\frac{5}{2}-\frac{10}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{10}{3} to fractions with denominator 6.

$$\frac{15}{6}-\frac{20}{6}$$

Since \frac{15}{6} and \frac{20}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-20}{6}$$

Subtract 20 from 15 to get -5.

$$-\frac{5}{6}$$

Factor

$$-\frac{5}{6} = -0.8333333333333334$$