Solve {l}{2/3+2/5+11/30}{-2/5-frac{8}{15}}

$$\left. \begin{array} { l } { \frac { 2 } { 3 } + \frac { 2 } { 5 } + \frac { 11 } { 30 } } \\ { - \frac { 2 } { 5 } - \frac { 8 } { 15 } } \end{array} \right.$$

Evaluate

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

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{6}{15}+\frac{11}{30}-\frac{2}{5}-\frac{8}{15}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+6}{15}+\frac{11}{30}-\frac{2}{5}-\frac{8}{15}$$

Add 10 and 6 to get 16.

$$\frac{16}{15}+\frac{11}{30}-\frac{2}{5}-\frac{8}{15}$$

Least common multiple of 15 and 30 is 30. Convert \frac{16}{15} and \frac{11}{30} to fractions with denominator 30.

$$\frac{32}{30}+\frac{11}{30}-\frac{2}{5}-\frac{8}{15}$$

Since \frac{32}{30} and \frac{11}{30} have the same denominator, add them by adding their numerators.

$$\frac{32+11}{30}-\frac{2}{5}-\frac{8}{15}$$

Add 32 and 11 to get 43.

$$\frac{43}{30}-\frac{2}{5}-\frac{8}{15}$$

Least common multiple of 30 and 5 is 30. Convert \frac{43}{30} and \frac{2}{5} to fractions with denominator 30.

$$\frac{43}{30}-\frac{12}{30}-\frac{8}{15}$$

Since \frac{43}{30} and \frac{12}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43-12}{30}-\frac{8}{15}$$

Subtract 12 from 43 to get 31.

$$\frac{31}{30}-\frac{8}{15}$$

Least common multiple of 30 and 15 is 30. Convert \frac{31}{30} and \frac{8}{15} to fractions with denominator 30.

$$\frac{31}{30}-\frac{16}{30}$$

Since \frac{31}{30} and \frac{16}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-16}{30}$$

Subtract 16 from 31 to get 15.

$$\frac{15}{30}$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

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

Factor

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