Solve 1/2+3/4+2+1+4/3+2/5+frac{8}{3}+frac{2}{2}+frac{1}{1}+frac{5}{2}+frac{7}{11}

$$\frac{ 1 }{ 2 } + \frac{ 3 }{ 4 } +2+1+ \frac{ 4 }{ 3 } + \frac{ 2 }{ 5 } + \frac{ 8 }{ 3 } + \frac{ 2 }{ 2 } + \frac{ 1 }{ 1 } + \frac{ 5 }{ 2 } + \frac{ 7 }{ 11 }$$

Evaluate

$$\frac{3033}{220}\approx 13.786363636$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{1}{2}+\frac{3}{4}+2+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+\frac{1}{1}+\frac{5}{2}+\frac{7}{11}$$

Divide 1 by 1 to get 1.

$$\frac{1}{2}+\frac{3}{4}+2+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

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

$$\frac{2}{4}+\frac{3}{4}+2+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}+2+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 2 and 3 to get 5.

$$\frac{5}{4}+2+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{5}{4}+\frac{8}{4}+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{5}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+8}{4}+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 5 and 8 to get 13.

$$\frac{13}{4}+1+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{13}{4}+\frac{4}{4}+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{13}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\frac{13+4}{4}+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 13 and 4 to get 17.

$$\frac{17}{4}+\frac{4}{3}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Least common multiple of 4 and 3 is 12. Convert \frac{17}{4} and \frac{4}{3} to fractions with denominator 12.

$$\frac{51}{12}+\frac{16}{12}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{51}{12} and \frac{16}{12} have the same denominator, add them by adding their numerators.

$$\frac{51+16}{12}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 51 and 16 to get 67.

$$\frac{67}{12}+\frac{2}{5}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Least common multiple of 12 and 5 is 60. Convert \frac{67}{12} and \frac{2}{5} to fractions with denominator 60.

$$\frac{335}{60}+\frac{24}{60}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{335}{60} and \frac{24}{60} have the same denominator, add them by adding their numerators.

$$\frac{335+24}{60}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 335 and 24 to get 359.

$$\frac{359}{60}+\frac{8}{3}+1+1+\frac{5}{2}+\frac{7}{11}$$

Least common multiple of 60 and 3 is 60. Convert \frac{359}{60} and \frac{8}{3} to fractions with denominator 60.

$$\frac{359}{60}+\frac{160}{60}+1+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{359}{60} and \frac{160}{60} have the same denominator, add them by adding their numerators.

$$\frac{359+160}{60}+1+1+\frac{5}{2}+\frac{7}{11}$$

Add 359 and 160 to get 519.

$$\frac{519}{60}+1+1+\frac{5}{2}+\frac{7}{11}$$

Reduce the fraction \frac{519}{60} to lowest terms by extracting and canceling out 3.

$$\frac{173}{20}+1+1+\frac{5}{2}+\frac{7}{11}$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{173}{20}+\frac{20}{20}+1+\frac{5}{2}+\frac{7}{11}$$

Since \frac{173}{20} and \frac{20}{20} have the same denominator, add them by adding their numerators.

$$\frac{173+20}{20}+1+\frac{5}{2}+\frac{7}{11}$$

Add 173 and 20 to get 193.

$$\frac{193}{20}+1+\frac{5}{2}+\frac{7}{11}$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{193}{20}+\frac{20}{20}+\frac{5}{2}+\frac{7}{11}$$

Since \frac{193}{20} and \frac{20}{20} have the same denominator, add them by adding their numerators.

$$\frac{193+20}{20}+\frac{5}{2}+\frac{7}{11}$$

Add 193 and 20 to get 213.

$$\frac{213}{20}+\frac{5}{2}+\frac{7}{11}$$

Least common multiple of 20 and 2 is 20. Convert \frac{213}{20} and \frac{5}{2} to fractions with denominator 20.

$$\frac{213}{20}+\frac{50}{20}+\frac{7}{11}$$

Since \frac{213}{20} and \frac{50}{20} have the same denominator, add them by adding their numerators.

$$\frac{213+50}{20}+\frac{7}{11}$$

Add 213 and 50 to get 263.

$$\frac{263}{20}+\frac{7}{11}$$

Least common multiple of 20 and 11 is 220. Convert \frac{263}{20} and \frac{7}{11} to fractions with denominator 220.

$$\frac{2893}{220}+\frac{140}{220}$$

Since \frac{2893}{220} and \frac{140}{220} have the same denominator, add them by adding their numerators.

$$\frac{2893+140}{220}$$

Add 2893 and 140 to get 3033.

$$\frac{3033}{220}$$

Factor

$$\frac{3 ^ {2} \cdot 337}{2 ^ {2} \cdot 5 \cdot 11} = 13\frac{173}{220} = 13.786363636363637$$