Solve 11+10+3+1+7/9+1/5+1/5+1/6+frac{2}{21}+1=

$$11+10+3+1+ \frac{ 7 }{ 9 } + \frac{ 1 }{ 5 } + \frac{ 1 }{ 5 } + \frac{ 1 }{ 6 } + \frac{ 2 }{ 21 } +1=$$

Evaluate

$$\frac{17287}{630}\approx 27.43968254$$

Solution Steps

Add 11 and 10 to get 21.

$$21+3+1+\frac{7}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Add 21 and 3 to get 24.

$$24+1+\frac{7}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Add 24 and 1 to get 25.

$$25+\frac{7}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Convert 25 to fraction \frac{225}{9}.

$$\frac{225}{9}+\frac{7}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Since \frac{225}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\frac{225+7}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Add 225 and 7 to get 232.

$$\frac{232}{9}+\frac{1}{5}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Least common multiple of 9 and 5 is 45. Convert \frac{232}{9} and \frac{1}{5} to fractions with denominator 45.

$$\frac{1160}{45}+\frac{9}{45}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Since \frac{1160}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{1160+9}{45}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Add 1160 and 9 to get 1169.

$$\frac{1169}{45}+\frac{1}{5}+\frac{1}{6}+\frac{2}{21}+1$$

Least common multiple of 45 and 5 is 45. Convert \frac{1169}{45} and \frac{1}{5} to fractions with denominator 45.

$$\frac{1169}{45}+\frac{9}{45}+\frac{1}{6}+\frac{2}{21}+1$$

Since \frac{1169}{45} and \frac{9}{45} have the same denominator, add them by adding their numerators.

$$\frac{1169+9}{45}+\frac{1}{6}+\frac{2}{21}+1$$

Add 1169 and 9 to get 1178.

$$\frac{1178}{45}+\frac{1}{6}+\frac{2}{21}+1$$

Least common multiple of 45 and 6 is 90. Convert \frac{1178}{45} and \frac{1}{6} to fractions with denominator 90.

$$\frac{2356}{90}+\frac{15}{90}+\frac{2}{21}+1$$

Since \frac{2356}{90} and \frac{15}{90} have the same denominator, add them by adding their numerators.

$$\frac{2356+15}{90}+\frac{2}{21}+1$$

Add 2356 and 15 to get 2371.

$$\frac{2371}{90}+\frac{2}{21}+1$$

Least common multiple of 90 and 21 is 630. Convert \frac{2371}{90} and \frac{2}{21} to fractions with denominator 630.

$$\frac{16597}{630}+\frac{60}{630}+1$$

Since \frac{16597}{630} and \frac{60}{630} have the same denominator, add them by adding their numerators.

$$\frac{16597+60}{630}+1$$

Add 16597 and 60 to get 16657.

$$\frac{16657}{630}+1$$

Convert 1 to fraction \frac{630}{630}.

$$\frac{16657}{630}+\frac{630}{630}$$

Since \frac{16657}{630} and \frac{630}{630} have the same denominator, add them by adding their numerators.

$$\frac{16657+630}{630}$$

Add 16657 and 630 to get 17287.

$$\frac{17287}{630}$$

Factor

$$\frac{59 \cdot 293}{2 \cdot 3 ^ {2} \cdot 5 \cdot 7} = 27\frac{277}{630} = 27.43968253968254$$