Solve 1/2-3/2(1/3+2/5+frac{1}{30})=

$$\frac { 1 } { 2 } - \frac { 3 } { 2 } ( \frac { 1 } { 3 } + \frac { 2 } { 5 } + \frac { 1 } { 30 } ) =$$

Evaluate

$$-\frac{13}{20}=-0.65$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{1}{2}-\frac{3}{2}\left(\frac{5}{15}+\frac{6}{15}+\frac{1}{30}\right)$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{3}{2}\left(\frac{5+6}{15}+\frac{1}{30}\right)$$

Add 5 and 6 to get 11.

$$\frac{1}{2}-\frac{3}{2}\left(\frac{11}{15}+\frac{1}{30}\right)$$

Least common multiple of 15 and 30 is 30. Convert \frac{11}{15} and \frac{1}{30} to fractions with denominator 30.

$$\frac{1}{2}-\frac{3}{2}\left(\frac{22}{30}+\frac{1}{30}\right)$$

Since \frac{22}{30} and \frac{1}{30} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{3}{2}\times \frac{22+1}{30}$$

Add 22 and 1 to get 23.

$$\frac{1}{2}-\frac{3}{2}\times \frac{23}{30}$$

Multiply \frac{3}{2} times \frac{23}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{3\times 23}{2\times 30}$$

Do the multiplications in the fraction \frac{3\times 23}{2\times 30}.

$$\frac{1}{2}-\frac{69}{60}$$

Reduce the fraction \frac{69}{60} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}-\frac{23}{20}$$

Least common multiple of 2 and 20 is 20. Convert \frac{1}{2} and \frac{23}{20} to fractions with denominator 20.

$$\frac{10}{20}-\frac{23}{20}$$

Since \frac{10}{20} and \frac{23}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-23}{20}$$

Subtract 23 from 10 to get -13.

$$-\frac{13}{20}$$

Factor

$$-\frac{13}{20} = -0.65$$