Solve 19/14-6/7+3/4-5/14-(frac{2}{7}+frac{11}{28})

$$\frac { 19 } { 14 } - \frac { 6 } { 7 } + \frac { 3 } { 4 } - \frac { 5 } { 14 } - ( \frac { 2 } { 7 } + \frac { 11 } { 28 } )$$

Evaluate

$$\frac{3}{14}\approx 0.214285714$$

Solution Steps

Least common multiple of 14 and 7 is 14. Convert \frac{19}{14} and \frac{6}{7} to fractions with denominator 14.

$$\frac{19}{14}-\frac{12}{14}+\frac{3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Since \frac{19}{14} and \frac{12}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-12}{14}+\frac{3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Subtract 12 from 19 to get 7.

$$\frac{7}{14}+\frac{3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{1}{2}+\frac{3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Add 2 and 3 to get 5.

$$\frac{5}{4}-\frac{5}{14}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Least common multiple of 4 and 14 is 28. Convert \frac{5}{4} and \frac{5}{14} to fractions with denominator 28.

$$\frac{35}{28}-\frac{10}{28}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Since \frac{35}{28} and \frac{10}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-10}{28}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Subtract 10 from 35 to get 25.

$$\frac{25}{28}-\left(\frac{2}{7}+\frac{11}{28}\right)$$

Least common multiple of 7 and 28 is 28. Convert \frac{2}{7} and \frac{11}{28} to fractions with denominator 28.

$$\frac{25}{28}-\left(\frac{8}{28}+\frac{11}{28}\right)$$

Since \frac{8}{28} and \frac{11}{28} have the same denominator, add them by adding their numerators.

$$\frac{25}{28}-\frac{8+11}{28}$$

Add 8 and 11 to get 19.

$$\frac{25}{28}-\frac{19}{28}$$

Since \frac{25}{28} and \frac{19}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-19}{28}$$

Subtract 19 from 25 to get 6.

$$\frac{6}{28}$$

Reduce the fraction \frac{6}{28} to lowest terms by extracting and canceling out 2.

$$\frac{3}{14}$$

Factor

$$\frac{3}{2 \cdot 7} = 0.21428571428571427$$