Solve (6/8-10/24+14/48-18/80+frac{22}{120}

$$( \frac { 6 } { 8 } - \frac { 10 } { 24 } + \frac { 14 } { 48 } - \frac { 18 } { 80 } + \frac { 22 } { 120 }$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\frac{10}{24}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}-\frac{5}{12}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{5}{12} to fractions with denominator 12.

$$\frac{9}{12}-\frac{5}{12}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Since \frac{9}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-5}{12}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Subtract 5 from 9 to get 4.

$$\frac{4}{12}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}+\frac{14}{48}-\frac{18}{80}+\frac{22}{120}$$

Reduce the fraction \frac{14}{48} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}+\frac{7}{24}-\frac{18}{80}+\frac{22}{120}$$

Least common multiple of 3 and 24 is 24. Convert \frac{1}{3} and \frac{7}{24} to fractions with denominator 24.

$$\frac{8}{24}+\frac{7}{24}-\frac{18}{80}+\frac{22}{120}$$

Since \frac{8}{24} and \frac{7}{24} have the same denominator, add them by adding their numerators.

$$\frac{8+7}{24}-\frac{18}{80}+\frac{22}{120}$$

Add 8 and 7 to get 15.

$$\frac{15}{24}-\frac{18}{80}+\frac{22}{120}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{5}{8}-\frac{18}{80}+\frac{22}{120}$$

Reduce the fraction \frac{18}{80} to lowest terms by extracting and canceling out 2.

$$\frac{5}{8}-\frac{9}{40}+\frac{22}{120}$$

Least common multiple of 8 and 40 is 40. Convert \frac{5}{8} and \frac{9}{40} to fractions with denominator 40.

$$\frac{25}{40}-\frac{9}{40}+\frac{22}{120}$$

Since \frac{25}{40} and \frac{9}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-9}{40}+\frac{22}{120}$$

Subtract 9 from 25 to get 16.

$$\frac{16}{40}+\frac{22}{120}$$

Reduce the fraction \frac{16}{40} to lowest terms by extracting and canceling out 8.

$$\frac{2}{5}+\frac{22}{120}$$

Reduce the fraction \frac{22}{120} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}+\frac{11}{60}$$

Least common multiple of 5 and 60 is 60. Convert \frac{2}{5} and \frac{11}{60} to fractions with denominator 60.

$$\frac{24}{60}+\frac{11}{60}$$

Since \frac{24}{60} and \frac{11}{60} have the same denominator, add them by adding their numerators.

$$\frac{24+11}{60}$$

Add 24 and 11 to get 35.

$$\frac{35}{60}$$

Reduce the fraction \frac{35}{60} to lowest terms by extracting and canceling out 5.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$