Solve (1/2+1/3)-{(1-1/3)[5/2-(2+frac{1}{3})(1-frac{1}{7})]}

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) - \{ ( 1 - \frac { 1 } { 3 } ) [ \frac { 5 } { 2 } - ( 2 + \frac { 1 } { 3 } ) ( 1 - \frac { 1 } { 7 } ) ] \}$$

Evaluate

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

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{2}{6}-\left(1-\frac{1}{3}\right)\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}-\left(1-\frac{1}{3}\right)\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Add 3 and 2 to get 5.

$$\frac{5}{6}-\left(1-\frac{1}{3}\right)\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{5}{6}-\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{3-1}{3}\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Subtract 1 from 3 to get 2.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\left(2+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\left(\frac{6}{3}+\frac{1}{3}\right)\left(1-\frac{1}{7}\right)\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{6+1}{3}\left(1-\frac{1}{7}\right)\right)$$

Add 6 and 1 to get 7.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{7}{3}\left(1-\frac{1}{7}\right)\right)$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{7}{3}\left(\frac{7}{7}-\frac{1}{7}\right)\right)$$

Since \frac{7}{7} and \frac{1}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{7}{3}\times \frac{7-1}{7}\right)$$

Subtract 1 from 7 to get 6.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{7}{3}\times \frac{6}{7}\right)$$

Multiply \frac{7}{3} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{7\times 6}{3\times 7}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{6}{3}\right)$$

Divide 6 by 3 to get 2.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-2\right)$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{5}{2}-\frac{4}{2}\right)$$

Since \frac{5}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{2}{3}\times \frac{5-4}{2}$$

Subtract 4 from 5 to get 1.

$$\frac{5}{6}-\frac{2}{3}\times \frac{1}{2}$$

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

$$\frac{5}{6}-\frac{2\times 1}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{6}-\frac{1}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{5}{6}-\frac{2}{6}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{6}$$

Subtract 2 from 5 to get 3.

$$\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Factor

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