Solve 3/2-(5/6-7/12)-(9/20-frac{11}{30})-(frac{13}{42}-frac{15}{56})-(frac{17}{72}-frac{19}{90})

$$\frac{ 3 }{ 2 } -( \frac{ 5 }{ 6 } - \frac{ 7 }{ 12 } )-( \frac{ 9 }{ 20 } - \frac{ 11 }{ 30 } )-( \frac{ 13 }{ 42 } - \frac{ 15 }{ 56 } )-( \frac{ 17 }{ 72 } - \frac{ 19 }{ 90 } )$$

Evaluate

$$\frac{11}{10}=1.1$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{7}{12} to fractions with denominator 12.

$$\frac{3}{2}-\left(\frac{10}{12}-\frac{7}{12}\right)-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{10}{12} and \frac{7}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{10-7}{12}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 7 from 10 to get 3.

$$\frac{3}{2}-\frac{3}{12}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

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

$$\frac{3}{2}-\frac{1}{4}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

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

$$\frac{6}{4}-\frac{1}{4}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{6}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{4}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 1 from 6 to get 5.

$$\frac{5}{4}-\left(\frac{9}{20}-\frac{11}{30}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Least common multiple of 20 and 30 is 60. Convert \frac{9}{20} and \frac{11}{30} to fractions with denominator 60.

$$\frac{5}{4}-\left(\frac{27}{60}-\frac{22}{60}\right)-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{27}{60} and \frac{22}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}-\frac{27-22}{60}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 22 from 27 to get 5.

$$\frac{5}{4}-\frac{5}{60}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

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

$$\frac{5}{4}-\frac{1}{12}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Least common multiple of 4 and 12 is 12. Convert \frac{5}{4} and \frac{1}{12} to fractions with denominator 12.

$$\frac{15}{12}-\frac{1}{12}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{15}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-1}{12}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 1 from 15 to get 14.

$$\frac{14}{12}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Reduce the fraction \frac{14}{12} to lowest terms by extracting and canceling out 2.

$$\frac{7}{6}-\left(\frac{13}{42}-\frac{15}{56}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Least common multiple of 42 and 56 is 168. Convert \frac{13}{42} and \frac{15}{56} to fractions with denominator 168.

$$\frac{7}{6}-\left(\frac{52}{168}-\frac{45}{168}\right)-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{52}{168} and \frac{45}{168} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}-\frac{52-45}{168}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 45 from 52 to get 7.

$$\frac{7}{6}-\frac{7}{168}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Reduce the fraction \frac{7}{168} to lowest terms by extracting and canceling out 7.

$$\frac{7}{6}-\frac{1}{24}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Least common multiple of 6 and 24 is 24. Convert \frac{7}{6} and \frac{1}{24} to fractions with denominator 24.

$$\frac{28}{24}-\frac{1}{24}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Since \frac{28}{24} and \frac{1}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-1}{24}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Subtract 1 from 28 to get 27.

$$\frac{27}{24}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$\frac{9}{8}-\left(\frac{17}{72}-\frac{19}{90}\right)$$

Least common multiple of 72 and 90 is 360. Convert \frac{17}{72} and \frac{19}{90} to fractions with denominator 360.

$$\frac{9}{8}-\left(\frac{85}{360}-\frac{76}{360}\right)$$

Since \frac{85}{360} and \frac{76}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{8}-\frac{85-76}{360}$$

Subtract 76 from 85 to get 9.

$$\frac{9}{8}-\frac{9}{360}$$

Reduce the fraction \frac{9}{360} to lowest terms by extracting and canceling out 9.

$$\frac{9}{8}-\frac{1}{40}$$

Least common multiple of 8 and 40 is 40. Convert \frac{9}{8} and \frac{1}{40} to fractions with denominator 40.

$$\frac{45}{40}-\frac{1}{40}$$

Since \frac{45}{40} and \frac{1}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-1}{40}$$

Subtract 1 from 45 to get 44.

$$\frac{44}{40}$$

Reduce the fraction \frac{44}{40} to lowest terms by extracting and canceling out 4.

$$\frac{11}{10}$$

Factor

$$\frac{11}{2 \cdot 5} = 1\frac{1}{10} = 1.1$$