Solve (5/9+3/2+11/18)-(11/6-frac{1}{3}-frac{1}{18})+(frac{1}{6}+frac{3}{4}+frac{7}{12})

$$( \frac { 5 } { 9 } + \frac { 3 } { 2 } + \frac { 11 } { 18 } ) - ( \frac { 11 } { 6 } - \frac { 1 } { 3 } - \frac { 1 } { 18 } ) + ( \frac { 1 } { 6 } + \frac { 3 } { 4 } + \frac { 7 } { 12 } )$$

Evaluate

$$\frac{49}{18}\approx 2.722222222$$

Solution Steps

Least common multiple of 9 and 2 is 18. Convert \frac{5}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{10}{18}+\frac{27}{18}+\frac{11}{18}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{10}{18} and \frac{27}{18} have the same denominator, add them by adding their numerators.

$$\frac{10+27}{18}+\frac{11}{18}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Add 10 and 27 to get 37.

$$\frac{37}{18}+\frac{11}{18}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{37}{18} and \frac{11}{18} have the same denominator, add them by adding their numerators.

$$\frac{37+11}{18}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Add 37 and 11 to get 48.

$$\frac{48}{18}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Reduce the fraction \frac{48}{18} to lowest terms by extracting and canceling out 6.

$$\frac{8}{3}-\left(\frac{11}{6}-\frac{1}{3}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Least common multiple of 6 and 3 is 6. Convert \frac{11}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{8}{3}-\left(\frac{11}{6}-\frac{2}{6}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{11}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}-\left(\frac{11-2}{6}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Subtract 2 from 11 to get 9.

$$\frac{8}{3}-\left(\frac{9}{6}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{8}{3}-\left(\frac{3}{2}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Least common multiple of 2 and 18 is 18. Convert \frac{3}{2} and \frac{1}{18} to fractions with denominator 18.

$$\frac{8}{3}-\left(\frac{27}{18}-\frac{1}{18}\right)+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{27}{18} and \frac{1}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8}{3}-\frac{27-1}{18}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Subtract 1 from 27 to get 26.

$$\frac{8}{3}-\frac{26}{18}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Reduce the fraction \frac{26}{18} to lowest terms by extracting and canceling out 2.

$$\frac{8}{3}-\frac{13}{9}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Least common multiple of 3 and 9 is 9. Convert \frac{8}{3} and \frac{13}{9} to fractions with denominator 9.

$$\frac{24}{9}-\frac{13}{9}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{24}{9} and \frac{13}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-13}{9}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Subtract 13 from 24 to get 11.

$$\frac{11}{9}+\frac{1}{6}+\frac{3}{4}+\frac{7}{12}$$

Least common multiple of 9 and 6 is 18. Convert \frac{11}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{22}{18}+\frac{3}{18}+\frac{3}{4}+\frac{7}{12}$$

Since \frac{22}{18} and \frac{3}{18} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{18}+\frac{3}{4}+\frac{7}{12}$$

Add 22 and 3 to get 25.

$$\frac{25}{18}+\frac{3}{4}+\frac{7}{12}$$

Least common multiple of 18 and 4 is 36. Convert \frac{25}{18} and \frac{3}{4} to fractions with denominator 36.

$$\frac{50}{36}+\frac{27}{36}+\frac{7}{12}$$

Since \frac{50}{36} and \frac{27}{36} have the same denominator, add them by adding their numerators.

$$\frac{50+27}{36}+\frac{7}{12}$$

Add 50 and 27 to get 77.

$$\frac{77}{36}+\frac{7}{12}$$

Least common multiple of 36 and 12 is 36. Convert \frac{77}{36} and \frac{7}{12} to fractions with denominator 36.

$$\frac{77}{36}+\frac{21}{36}$$

Since \frac{77}{36} and \frac{21}{36} have the same denominator, add them by adding their numerators.

$$\frac{77+21}{36}$$

Add 77 and 21 to get 98.

$$\frac{98}{36}$$

Reduce the fraction \frac{98}{36} to lowest terms by extracting and canceling out 2.

$$\frac{49}{18}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 3 ^ {2}} = 2\frac{13}{18} = 2.7222222222222223$$