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

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

Evaluate

$$-\frac{x}{9}$$

Solution Steps

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

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

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

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

Subtract 3 from 5 to get 2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

$$-\frac{1}{3}x\left(\frac{6}{15}-\frac{1}{15}\right)$$

Since \frac{6}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x\times \frac{6-1}{15}$$

Subtract 1 from 6 to get 5.

$$-\frac{1}{3}x\times \frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{3}x\times \frac{1}{3}$$

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

$$\frac{-1}{3\times 3}x$$

Do the multiplications in the fraction \frac{-1}{3\times 3}.

$$\frac{-1}{9}x$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$-\frac{1}{9}x$$

Expand

$$-\frac{x}{9}$$

Solution Steps

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

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

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

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

Subtract 3 from 5 to get 2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

$$-\frac{1}{3}x\left(\frac{6}{15}-\frac{1}{15}\right)$$

Since \frac{6}{15} and \frac{1}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}x\times \frac{6-1}{15}$$

Subtract 1 from 6 to get 5.

$$-\frac{1}{3}x\times \frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{3}x\times \frac{1}{3}$$

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

$$\frac{-1}{3\times 3}x$$

Do the multiplications in the fraction \frac{-1}{3\times 3}.

$$\frac{-1}{9}x$$

Fraction \frac{-1}{9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$-\frac{1}{9}x$$