Solve 1+11/6+11/3+11/2+12/3+1frac{5}{6}+2+2frac{1}{6}+2frac{1}{3}+2frac{1}{2}+2frac{2}{3}+2frac{5}{6}+3+3frac{1}{6}

$$1 + 1 \frac { 1 } { 6 } + 1 \frac { 1 } { 3 } + 1 \frac { 1 } { 2 } + 1 \frac { 2 } { 3 } + 1 \frac { 5 } { 6 } + 2 + 2 \frac { 1 } { 6 } + 2 \frac { 1 } { 3 } + 2 \frac { 1 } { 2 } + 2 \frac { 2 } { 3 } + 2 \frac { 5 } { 6 } + 3 + 3 \frac { 1 } { 6 }$$

Evaluate

$$\frac{175}{6}\approx 29.166666667$$

Solution Steps

Multiply 1 and 6 to get 6.

$$1+\frac{6+1}{6}+\frac{1\times 3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 6 and 1 to get 7.

$$1+\frac{7}{6}+\frac{1\times 3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

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

$$\frac{6}{6}+\frac{7}{6}+\frac{1\times 3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{6}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{6+7}{6}+\frac{1\times 3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 6 and 7 to get 13.

$$\frac{13}{6}+\frac{1\times 3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 1 and 3 to get 3.

$$\frac{13}{6}+\frac{3+1}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 3 and 1 to get 4.

$$\frac{13}{6}+\frac{4}{3}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Least common multiple of 6 and 3 is 6. Convert \frac{13}{6} and \frac{4}{3} to fractions with denominator 6.

$$\frac{13}{6}+\frac{8}{6}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{13}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{13+8}{6}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 13 and 8 to get 21.

$$\frac{21}{6}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{2}+\frac{1\times 2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 1 and 2 to get 2.

$$\frac{7}{2}+\frac{2+1}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 2 and 1 to get 3.

$$\frac{7}{2}+\frac{3}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{7}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{7+3}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 7 and 3 to get 10.

$$\frac{10}{2}+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Divide 10 by 2 to get 5.

$$5+\frac{1\times 3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 1 and 3 to get 3.

$$5+\frac{3+2}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 3 and 2 to get 5.

$$5+\frac{5}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{15}{3}+\frac{5}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{15}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{15+5}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 15 and 5 to get 20.

$$\frac{20}{3}+\frac{1\times 6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 1 and 6 to get 6.

$$\frac{20}{3}+\frac{6+5}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 6 and 5 to get 11.

$$\frac{20}{3}+\frac{11}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Least common multiple of 3 and 6 is 6. Convert \frac{20}{3} and \frac{11}{6} to fractions with denominator 6.

$$\frac{40}{6}+\frac{11}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{40}{6} and \frac{11}{6} have the same denominator, add them by adding their numerators.

$$\frac{40+11}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 40 and 11 to get 51.

$$\frac{51}{6}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Reduce the fraction \frac{51}{6} to lowest terms by extracting and canceling out 3.

$$\frac{17}{2}+2+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{17}{2}+\frac{4}{2}+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{17}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{17+4}{2}+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 17 and 4 to get 21.

$$\frac{21}{2}+\frac{2\times 6+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{21}{2}+\frac{12+1}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 12 and 1 to get 13.

$$\frac{21}{2}+\frac{13}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Least common multiple of 2 and 6 is 6. Convert \frac{21}{2} and \frac{13}{6} to fractions with denominator 6.

$$\frac{63}{6}+\frac{13}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{63}{6} and \frac{13}{6} have the same denominator, add them by adding their numerators.

$$\frac{63+13}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 63 and 13 to get 76.

$$\frac{76}{6}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Reduce the fraction \frac{76}{6} to lowest terms by extracting and canceling out 2.

$$\frac{38}{3}+\frac{2\times 3+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 2 and 3 to get 6.

$$\frac{38}{3}+\frac{6+1}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 6 and 1 to get 7.

$$\frac{38}{3}+\frac{7}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{38}{3} and \frac{7}{3} have the same denominator, add them by adding their numerators.

$$\frac{38+7}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 38 and 7 to get 45.

$$\frac{45}{3}+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Divide 45 by 3 to get 15.

$$15+\frac{2\times 2+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 2 and 2 to get 4.

$$15+\frac{4+1}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 4 and 1 to get 5.

$$15+\frac{5}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Convert 15 to fraction \frac{30}{2}.

$$\frac{30}{2}+\frac{5}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{30}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{30+5}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 30 and 5 to get 35.

$$\frac{35}{2}+\frac{2\times 3+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 2 and 3 to get 6.

$$\frac{35}{2}+\frac{6+2}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 6 and 2 to get 8.

$$\frac{35}{2}+\frac{8}{3}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Least common multiple of 2 and 3 is 6. Convert \frac{35}{2} and \frac{8}{3} to fractions with denominator 6.

$$\frac{105}{6}+\frac{16}{6}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{105}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.

$$\frac{105+16}{6}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 105 and 16 to get 121.

$$\frac{121}{6}+\frac{2\times 6+5}{6}+3+\frac{3\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{121}{6}+\frac{12+5}{6}+3+\frac{3\times 6+1}{6}$$

Add 12 and 5 to get 17.

$$\frac{121}{6}+\frac{17}{6}+3+\frac{3\times 6+1}{6}$$

Since \frac{121}{6} and \frac{17}{6} have the same denominator, add them by adding their numerators.

$$\frac{121+17}{6}+3+\frac{3\times 6+1}{6}$$

Add 121 and 17 to get 138.

$$\frac{138}{6}+3+\frac{3\times 6+1}{6}$$

Divide 138 by 6 to get 23.

$$23+3+\frac{3\times 6+1}{6}$$

Add 23 and 3 to get 26.

$$26+\frac{3\times 6+1}{6}$$

Multiply 3 and 6 to get 18.

$$26+\frac{18+1}{6}$$

Add 18 and 1 to get 19.

$$26+\frac{19}{6}$$

Convert 26 to fraction \frac{156}{6}.

$$\frac{156}{6}+\frac{19}{6}$$

Since \frac{156}{6} and \frac{19}{6} have the same denominator, add them by adding their numerators.

$$\frac{156+19}{6}$$

Add 156 and 19 to get 175.

$$\frac{175}{6}$$

Factor

$$\frac{5 ^ {2} \cdot 7}{2 \cdot 3} = 29\frac{1}{6} = 29.166666666666668$$