Solve 11/3-7/12+9/20-11/30+frac{13}{42}-frac{15}{56}+frac{17}{72}-frac{19}{90}

$$1 \frac{ 1 }{ 3 } - \frac{ 7 }{ 12 } + \frac{ 9 }{ 20 } - \frac{ 11 }{ 30 } + \frac{ 13 }{ 42 } - \frac{ 15 }{ 56 } + \frac{ 17 }{ 72 } - \frac{ 19 }{ 90 }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{3+1}{3}-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Add 3 and 1 to get 4.

$$\frac{4}{3}-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Least common multiple of 3 and 12 is 12. Convert \frac{4}{3} and \frac{7}{12} to fractions with denominator 12.

$$\frac{16}{12}-\frac{7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Since \frac{16}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-7}{12}+\frac{9}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Subtract 7 from 16 to get 9.

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

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

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

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

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

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

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

Add 15 and 9 to get 24.

$$\frac{24}{20}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Reduce the fraction \frac{24}{20} to lowest terms by extracting and canceling out 4.

$$\frac{6}{5}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Least common multiple of 5 and 30 is 30. Convert \frac{6}{5} and \frac{11}{30} to fractions with denominator 30.

$$\frac{36}{30}-\frac{11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Since \frac{36}{30} and \frac{11}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36-11}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Subtract 11 from 36 to get 25.

$$\frac{25}{30}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Reduce the fraction \frac{25}{30} to lowest terms by extracting and canceling out 5.

$$\frac{5}{6}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Least common multiple of 6 and 42 is 42. Convert \frac{5}{6} and \frac{13}{42} to fractions with denominator 42.

$$\frac{35}{42}+\frac{13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Since \frac{35}{42} and \frac{13}{42} have the same denominator, add them by adding their numerators.

$$\frac{35+13}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Add 35 and 13 to get 48.

$$\frac{48}{42}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Reduce the fraction \frac{48}{42} to lowest terms by extracting and canceling out 6.

$$\frac{8}{7}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Least common multiple of 7 and 56 is 56. Convert \frac{8}{7} and \frac{15}{56} to fractions with denominator 56.

$$\frac{64}{56}-\frac{15}{56}+\frac{17}{72}-\frac{19}{90}$$

Since \frac{64}{56} and \frac{15}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-15}{56}+\frac{17}{72}-\frac{19}{90}$$

Subtract 15 from 64 to get 49.

$$\frac{49}{56}+\frac{17}{72}-\frac{19}{90}$$

Reduce the fraction \frac{49}{56} to lowest terms by extracting and canceling out 7.

$$\frac{7}{8}+\frac{17}{72}-\frac{19}{90}$$

Least common multiple of 8 and 72 is 72. Convert \frac{7}{8} and \frac{17}{72} to fractions with denominator 72.

$$\frac{63}{72}+\frac{17}{72}-\frac{19}{90}$$

Since \frac{63}{72} and \frac{17}{72} have the same denominator, add them by adding their numerators.

$$\frac{63+17}{72}-\frac{19}{90}$$

Add 63 and 17 to get 80.

$$\frac{80}{72}-\frac{19}{90}$$

Reduce the fraction \frac{80}{72} to lowest terms by extracting and canceling out 8.

$$\frac{10}{9}-\frac{19}{90}$$

Least common multiple of 9 and 90 is 90. Convert \frac{10}{9} and \frac{19}{90} to fractions with denominator 90.

$$\frac{100}{90}-\frac{19}{90}$$

Since \frac{100}{90} and \frac{19}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100-19}{90}$$

Subtract 19 from 100 to get 81.

$$\frac{81}{90}$$

Reduce the fraction \frac{81}{90} to lowest terms by extracting and canceling out 9.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$