Solve 19/21+3/7-(1/2+1/3)

$$\frac { 19 } { 21 } + \frac { 3 } { 7 } - ( \frac { 1 } { 2 } + \frac { 1 } { 3 } )$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Least common multiple of 21 and 7 is 21. Convert \frac{19}{21} and \frac{3}{7} to fractions with denominator 21.

$$\frac{19}{21}+\frac{9}{21}-\left(\frac{1}{2}+\frac{1}{3}\right)$$

Since \frac{19}{21} and \frac{9}{21} have the same denominator, add them by adding their numerators.

$$\frac{19+9}{21}-\left(\frac{1}{2}+\frac{1}{3}\right)$$

Add 19 and 9 to get 28.

$$\frac{28}{21}-\left(\frac{1}{2}+\frac{1}{3}\right)$$

Reduce the fraction \frac{28}{21} to lowest terms by extracting and canceling out 7.

$$\frac{4}{3}-\left(\frac{1}{2}+\frac{1}{3}\right)$$

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

$$\frac{4}{3}-\left(\frac{3}{6}+\frac{2}{6}\right)$$

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

$$\frac{4}{3}-\frac{3+2}{6}$$

Add 3 and 2 to get 5.

$$\frac{4}{3}-\frac{5}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{8}{6}-\frac{5}{6}$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-5}{6}$$

Subtract 5 from 8 to get 3.

$$\frac{3}{6}$$

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$