Solve 1-5/6+7/12-9/20+11/30-frac{13}{42}+frac{15}{56}-frac{17}{72}+frac{19}{90}-frac{21}{110}

$$1 - \frac { 5 } { 6 } + \frac { 7 } { 12 } - \frac { 9 } { 20 } + \frac { 11 } { 30 } - \frac { 13 } { 42 } + \frac { 15 } { 56 } - \frac { 17 } { 72 } + \frac { 19 } { 90 } - \frac { 21 } { 110 }$$

Evaluate

$$\frac{9}{22}\approx 0.409090909$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$\frac{6}{6}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

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

$$\frac{6-5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Subtract 5 from 6 to get 1.

$$\frac{1}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 6 and 12 is 12. Convert \frac{1}{6} and \frac{7}{12} to fractions with denominator 12.

$$\frac{2}{12}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{2}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{2+7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Add 2 and 7 to get 9.

$$\frac{9}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{4}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 4 and 20 is 20. Convert \frac{3}{4} and \frac{9}{20} to fractions with denominator 20.

$$\frac{15}{20}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{15}{20} and \frac{9}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Subtract 9 from 15 to get 6.

$$\frac{6}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{3}{10}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 10 and 30 is 30. Convert \frac{3}{10} and \frac{11}{30} to fractions with denominator 30.

$$\frac{9}{30}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{9}{30} and \frac{11}{30} have the same denominator, add them by adding their numerators.

$$\frac{9+11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Add 9 and 11 to get 20.

$$\frac{20}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{20}{30} to lowest terms by extracting and canceling out 10.

$$\frac{2}{3}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 3 and 42 is 42. Convert \frac{2}{3} and \frac{13}{42} to fractions with denominator 42.

$$\frac{28}{42}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{28}{42} and \frac{13}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Subtract 13 from 28 to get 15.

$$\frac{15}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{15}{42} to lowest terms by extracting and canceling out 3.

$$\frac{5}{14}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 14 and 56 is 56. Convert \frac{5}{14} and \frac{15}{56} to fractions with denominator 56.

$$\frac{20}{56}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{20}{56} and \frac{15}{56} have the same denominator, add them by adding their numerators.

$$\frac{20+15}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Add 20 and 15 to get 35.

$$\frac{35}{56}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{35}{56} to lowest terms by extracting and canceling out 7.

$$\frac{5}{8}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 8 and 72 is 72. Convert \frac{5}{8} and \frac{17}{72} to fractions with denominator 72.

$$\frac{45}{72}-\frac{17}{72}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{45}{72} and \frac{17}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-17}{72}+\frac{19}{90}-\frac{21}{110}$$

Subtract 17 from 45 to get 28.

$$\frac{28}{72}+\frac{19}{90}-\frac{21}{110}$$

Reduce the fraction \frac{28}{72} to lowest terms by extracting and canceling out 4.

$$\frac{7}{18}+\frac{19}{90}-\frac{21}{110}$$

Least common multiple of 18 and 90 is 90. Convert \frac{7}{18} and \frac{19}{90} to fractions with denominator 90.

$$\frac{35}{90}+\frac{19}{90}-\frac{21}{110}$$

Since \frac{35}{90} and \frac{19}{90} have the same denominator, add them by adding their numerators.

$$\frac{35+19}{90}-\frac{21}{110}$$

Add 35 and 19 to get 54.

$$\frac{54}{90}-\frac{21}{110}$$

Reduce the fraction \frac{54}{90} to lowest terms by extracting and canceling out 18.

$$\frac{3}{5}-\frac{21}{110}$$

Least common multiple of 5 and 110 is 110. Convert \frac{3}{5} and \frac{21}{110} to fractions with denominator 110.

$$\frac{66}{110}-\frac{21}{110}$$

Since \frac{66}{110} and \frac{21}{110} have the same denominator, subtract them by subtracting their numerators.

$$\frac{66-21}{110}$$

Subtract 21 from 66 to get 45.

$$\frac{45}{110}$$

Reduce the fraction \frac{45}{110} to lowest terms by extracting and canceling out 5.

$$\frac{9}{22}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 11} = 0.4090909090909091$$