Solve -1/2[2/3-1/2(1/3-frac{1}{5})]=

$$- \frac { 1 } { 2 } [ \frac { 2 } { 3 } - \frac { 1 } { 2 } ( \frac { 1 } { 3 } - \frac { 1 } { 5 } ) ] =$$

Evaluate

$$-\frac{3}{10}=-0.3$$

Solution Steps

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

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

Since \frac{5}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\left(\frac{2}{3}-\frac{1}{2}\times \frac{5-3}{15}\right)$$

Subtract 3 from 5 to get 2.

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

Multiply \frac{1}{2} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

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

$$-\frac{1}{2}\left(\frac{10}{15}-\frac{1}{15}\right)$$

Since \frac{10}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}\times \frac{10-1}{15}$$

Subtract 1 from 10 to get 9.

$$-\frac{1}{2}\times \frac{9}{15}$$

Reduce the fraction \frac{9}{15} to lowest terms by extracting and canceling out 3.

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

Multiply -\frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-3}{2\times 5}.

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

Fraction \frac{-3}{10} can be rewritten as -\frac{3}{10} by extracting the negative sign.

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

Factor

$$-\frac{3}{10} = -0.3$$