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

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

Evaluate

$$\frac{8}{9}\approx 0.888888889$$

Solution Steps

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

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

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

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

Subtract 3 from 5 to get 2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

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

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

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

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

Subtract 1 from 6 to get 5.

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

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

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

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

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

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

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

Convert 1 to fraction \frac{9}{9}.

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

Since \frac{9}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 9 to get 8.

$$\frac{8}{9}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2}} = 0.8888888888888888$$