Solve 1/2-[2/7-3/4-(5/14+1)+(frac{1}{4}+frac{1}{7}-frac{3}{4})+2]

$$\frac { 1 } { 2 } - [ \frac { 2 } { 7 } - \frac { 3 } { 4 } - ( \frac { 5 } { 14 } + 1 ) + ( \frac { 1 } { 4 } + \frac { 1 } { 7 } - \frac { 3 } { 4 } ) + 2 ]$$

Evaluate

$$\frac{19}{28}\approx 0.678571429$$

Solution Steps

Least common multiple of 7 and 4 is 28. Convert \frac{2}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{1}{2}-\left(\frac{8}{28}-\frac{21}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Since \frac{8}{28} and \frac{21}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\left(\frac{8-21}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Subtract 21 from 8 to get -13.

$$\frac{1}{2}-\left(-\frac{13}{28}-\left(\frac{5}{14}+1\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Convert 1 to fraction \frac{14}{14}.

$$\frac{1}{2}-\left(-\frac{13}{28}-\left(\frac{5}{14}+\frac{14}{14}\right)+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Since \frac{5}{14} and \frac{14}{14} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{5+14}{14}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Add 5 and 14 to get 19.

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{19}{14}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Least common multiple of 28 and 14 is 28. Convert -\frac{13}{28} and \frac{19}{14} to fractions with denominator 28.

$$\frac{1}{2}-\left(-\frac{13}{28}-\frac{38}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Since -\frac{13}{28} and \frac{38}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\left(\frac{-13-38}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Subtract 38 from -13 to get -51.

$$\frac{1}{2}-\left(-\frac{51}{28}+\frac{1}{4}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Least common multiple of 28 and 4 is 28. Convert -\frac{51}{28} and \frac{1}{4} to fractions with denominator 28.

$$\frac{1}{2}-\left(-\frac{51}{28}+\frac{7}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Since -\frac{51}{28} and \frac{7}{28} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\left(\frac{-51+7}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Add -51 and 7 to get -44.

$$\frac{1}{2}-\left(\frac{-44}{28}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Reduce the fraction \frac{-44}{28} to lowest terms by extracting and canceling out 4.

$$\frac{1}{2}-\left(-\frac{11}{7}+\frac{1}{7}-\frac{3}{4}+2\right)$$

Since -\frac{11}{7} and \frac{1}{7} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\left(\frac{-11+1}{7}-\frac{3}{4}+2\right)$$

Add -11 and 1 to get -10.

$$\frac{1}{2}-\left(-\frac{10}{7}-\frac{3}{4}+2\right)$$

Least common multiple of 7 and 4 is 28. Convert -\frac{10}{7} and \frac{3}{4} to fractions with denominator 28.

$$\frac{1}{2}-\left(-\frac{40}{28}-\frac{21}{28}+2\right)$$

Since -\frac{40}{28} and \frac{21}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\left(\frac{-40-21}{28}+2\right)$$

Subtract 21 from -40 to get -61.

$$\frac{1}{2}-\left(-\frac{61}{28}+2\right)$$

Convert 2 to fraction \frac{56}{28}.

$$\frac{1}{2}-\left(-\frac{61}{28}+\frac{56}{28}\right)$$

Since -\frac{61}{28} and \frac{56}{28} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{-61+56}{28}$$

Add -61 and 56 to get -5.

$$\frac{1}{2}-\left(-\frac{5}{28}\right)$$

The opposite of -\frac{5}{28} is \frac{5}{28}.

$$\frac{1}{2}+\frac{5}{28}$$

Least common multiple of 2 and 28 is 28. Convert \frac{1}{2} and \frac{5}{28} to fractions with denominator 28.

$$\frac{14}{28}+\frac{5}{28}$$

Since \frac{14}{28} and \frac{5}{28} have the same denominator, add them by adding their numerators.

$$\frac{14+5}{28}$$

Add 14 and 5 to get 19.

$$\frac{19}{28}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 7} = 0.6785714285714286$$