Solve 11/6+31/12+51/20+71/30+9frac{1}{42}+11frac{1}{56}

$$1 \frac { 1 } { 6 } + 3 \frac { 1 } { 12 } + 5 \frac { 1 } { 20 } + 7 \frac { 1 } { 30 } + 9 \frac { 1 } { 42 } + 11 \frac { 1 } { 56 }$$

Evaluate

$$\frac{291}{8}=36.375$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\frac{6+1}{6}+\frac{3\times 12+1}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 6 and 1 to get 7.

$$\frac{7}{6}+\frac{3\times 12+1}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Multiply 3 and 12 to get 36.

$$\frac{7}{6}+\frac{36+1}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 36 and 1 to get 37.

$$\frac{7}{6}+\frac{37}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Least common multiple of 6 and 12 is 12. Convert \frac{7}{6} and \frac{37}{12} to fractions with denominator 12.

$$\frac{14}{12}+\frac{37}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Since \frac{14}{12} and \frac{37}{12} have the same denominator, add them by adding their numerators.

$$\frac{14+37}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 14 and 37 to get 51.

$$\frac{51}{12}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Reduce the fraction \frac{51}{12} to lowest terms by extracting and canceling out 3.

$$\frac{17}{4}+\frac{5\times 20+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Multiply 5 and 20 to get 100.

$$\frac{17}{4}+\frac{100+1}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 100 and 1 to get 101.

$$\frac{17}{4}+\frac{101}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Least common multiple of 4 and 20 is 20. Convert \frac{17}{4} and \frac{101}{20} to fractions with denominator 20.

$$\frac{85}{20}+\frac{101}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Since \frac{85}{20} and \frac{101}{20} have the same denominator, add them by adding their numerators.

$$\frac{85+101}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 85 and 101 to get 186.

$$\frac{186}{20}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Reduce the fraction \frac{186}{20} to lowest terms by extracting and canceling out 2.

$$\frac{93}{10}+\frac{7\times 30+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Multiply 7 and 30 to get 210.

$$\frac{93}{10}+\frac{210+1}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 210 and 1 to get 211.

$$\frac{93}{10}+\frac{211}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Least common multiple of 10 and 30 is 30. Convert \frac{93}{10} and \frac{211}{30} to fractions with denominator 30.

$$\frac{279}{30}+\frac{211}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Since \frac{279}{30} and \frac{211}{30} have the same denominator, add them by adding their numerators.

$$\frac{279+211}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Add 279 and 211 to get 490.

$$\frac{490}{30}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Reduce the fraction \frac{490}{30} to lowest terms by extracting and canceling out 10.

$$\frac{49}{3}+\frac{9\times 42+1}{42}+\frac{11\times 56+1}{56}$$

Multiply 9 and 42 to get 378.

$$\frac{49}{3}+\frac{378+1}{42}+\frac{11\times 56+1}{56}$$

Add 378 and 1 to get 379.

$$\frac{49}{3}+\frac{379}{42}+\frac{11\times 56+1}{56}$$

Least common multiple of 3 and 42 is 42. Convert \frac{49}{3} and \frac{379}{42} to fractions with denominator 42.

$$\frac{686}{42}+\frac{379}{42}+\frac{11\times 56+1}{56}$$

Since \frac{686}{42} and \frac{379}{42} have the same denominator, add them by adding their numerators.

$$\frac{686+379}{42}+\frac{11\times 56+1}{56}$$

Add 686 and 379 to get 1065.

$$\frac{1065}{42}+\frac{11\times 56+1}{56}$$

Reduce the fraction \frac{1065}{42} to lowest terms by extracting and canceling out 3.

$$\frac{355}{14}+\frac{11\times 56+1}{56}$$

Multiply 11 and 56 to get 616.

$$\frac{355}{14}+\frac{616+1}{56}$$

Add 616 and 1 to get 617.

$$\frac{355}{14}+\frac{617}{56}$$

Least common multiple of 14 and 56 is 56. Convert \frac{355}{14} and \frac{617}{56} to fractions with denominator 56.

$$\frac{1420}{56}+\frac{617}{56}$$

Since \frac{1420}{56} and \frac{617}{56} have the same denominator, add them by adding their numerators.

$$\frac{1420+617}{56}$$

Add 1420 and 617 to get 2037.

$$\frac{2037}{56}$$

Reduce the fraction \frac{2037}{56} to lowest terms by extracting and canceling out 7.

$$\frac{291}{8}$$

Factor

$$\frac{3 \cdot 97}{2 ^ {3}} = 36\frac{3}{8} = 36.375$$