Solve 1+0.5+1/3+0.25+0.2+1/6+1/7+0.125+1/9+0.1+frac{1}{11}+frac{1}{12}

$$1+0.5+ \frac{ 1 }{ 3 } +0.25+0.2+ \frac{ 1 }{ 6 } + \frac{ 1 }{ 7 } +0.125+ \frac{ 1 }{ 9 } +0.1+ \frac{ 1 }{ 11 } + \frac{ 1 }{ 12 }$$

Evaluate

$$\frac{86021}{27720}\approx 3.103210678$$

Solution Steps

Add 1 and 0.5 to get 1.5.

$$1.5+\frac{1}{3}+0.25+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}+\frac{1}{3}+0.25+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{9}{6}+\frac{2}{6}+0.25+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{6}+0.25+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 9 and 2 to get 11.

$$\frac{11}{6}+0.25+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{11}{6}+\frac{1}{4}+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 6 and 4 is 12. Convert \frac{11}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{22}{12}+\frac{3}{12}+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{22}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{22+3}{12}+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 22 and 3 to get 25.

$$\frac{25}{12}+0.2+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{25}{12}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 12 and 5 is 60. Convert \frac{25}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{125}{60}+\frac{12}{60}+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{125}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{125+12}{60}+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 125 and 12 to get 137.

$$\frac{137}{60}+\frac{1}{6}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 60 and 6 is 60. Convert \frac{137}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{137}{60}+\frac{10}{60}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{137}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{137+10}{60}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 137 and 10 to get 147.

$$\frac{147}{60}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Reduce the fraction \frac{147}{60} to lowest terms by extracting and canceling out 3.

$$\frac{49}{20}+\frac{1}{7}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 20 and 7 is 140. Convert \frac{49}{20} and \frac{1}{7} to fractions with denominator 140.

$$\frac{343}{140}+\frac{20}{140}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{343}{140} and \frac{20}{140} have the same denominator, add them by adding their numerators.

$$\frac{343+20}{140}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 343 and 20 to get 363.

$$\frac{363}{140}+0.125+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Convert decimal number 0.125 to fraction \frac{125}{1000}. Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{363}{140}+\frac{1}{8}+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 140 and 8 is 280. Convert \frac{363}{140} and \frac{1}{8} to fractions with denominator 280.

$$\frac{726}{280}+\frac{35}{280}+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{726}{280} and \frac{35}{280} have the same denominator, add them by adding their numerators.

$$\frac{726+35}{280}+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 726 and 35 to get 761.

$$\frac{761}{280}+\frac{1}{9}+0.1+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 280 and 9 is 2520. Convert \frac{761}{280} and \frac{1}{9} to fractions with denominator 2520.

$$\frac{6849}{2520}+\frac{280}{2520}+0.1+\frac{1}{11}+\frac{1}{12}$$

Since \frac{6849}{2520} and \frac{280}{2520} have the same denominator, add them by adding their numerators.

$$\frac{6849+280}{2520}+0.1+\frac{1}{11}+\frac{1}{12}$$

Add 6849 and 280 to get 7129.

$$\frac{7129}{2520}+0.1+\frac{1}{11}+\frac{1}{12}$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{7129}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 2520 and 10 is 2520. Convert \frac{7129}{2520} and \frac{1}{10} to fractions with denominator 2520.

$$\frac{7129}{2520}+\frac{252}{2520}+\frac{1}{11}+\frac{1}{12}$$

Since \frac{7129}{2520} and \frac{252}{2520} have the same denominator, add them by adding their numerators.

$$\frac{7129+252}{2520}+\frac{1}{11}+\frac{1}{12}$$

Add 7129 and 252 to get 7381.

$$\frac{7381}{2520}+\frac{1}{11}+\frac{1}{12}$$

Least common multiple of 2520 and 11 is 27720. Convert \frac{7381}{2520} and \frac{1}{11} to fractions with denominator 27720.

$$\frac{81191}{27720}+\frac{2520}{27720}+\frac{1}{12}$$

Since \frac{81191}{27720} and \frac{2520}{27720} have the same denominator, add them by adding their numerators.

$$\frac{81191+2520}{27720}+\frac{1}{12}$$

Add 81191 and 2520 to get 83711.

$$\frac{83711}{27720}+\frac{1}{12}$$

Least common multiple of 27720 and 12 is 27720. Convert \frac{83711}{27720} and \frac{1}{12} to fractions with denominator 27720.

$$\frac{83711}{27720}+\frac{2310}{27720}$$

Since \frac{83711}{27720} and \frac{2310}{27720} have the same denominator, add them by adding their numerators.

$$\frac{83711+2310}{27720}$$

Add 83711 and 2310 to get 86021.

$$\frac{86021}{27720}$$

Factor

$$\frac{509 \cdot 13 ^ {2}}{5 \cdot 7 \cdot 11 \cdot 2 ^ {3} \cdot 3 ^ {2}} = 3\frac{2861}{27720} = 3.103210678210678$$