Solve 0.5+7/3-(-5/3+3/2)=

$$0.5 + \frac { 7 } { 3 } - ( - \frac { 5 } { 3 } + \frac { 3 } { 2 } ) =$$

Evaluate

$$3$$

Solution Steps

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+\frac{7}{3}-\left(-\frac{5}{3}+\frac{3}{2}\right)$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{7}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{14}{6}-\left(-\frac{5}{3}+\frac{3}{2}\right)$$

Since \frac{3}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+14}{6}-\left(-\frac{5}{3}+\frac{3}{2}\right)$$

Add 3 and 14 to get 17.

$$\frac{17}{6}-\left(-\frac{5}{3}+\frac{3}{2}\right)$$

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

$$\frac{17}{6}-\left(-\frac{10}{6}+\frac{9}{6}\right)$$

Since -\frac{10}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{17}{6}-\frac{-10+9}{6}$$

Add -10 and 9 to get -1.

$$\frac{17}{6}-\left(-\frac{1}{6}\right)$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$\frac{17}{6}+\frac{1}{6}$$

Since \frac{17}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{17+1}{6}$$

Add 17 and 1 to get 18.

$$\frac{18}{6}$$

Divide 18 by 6 to get 3.

$$3$$

Factor

$$3$$