Solve 1-1/3+1/5-1/7+1/9-frac{1}{11}+frac{1}{13}-frac{1}{15}+frac{1}{17}-frac{1}{19}*4^

$$1- \frac{ 1 }{ 3 } + \frac{ 1 }{ 5 } - \frac{ 1 }{ 7 } + \frac{ 1 }{ 9 } - \frac{ 1 }{ 11 } + \frac{ 1 }{ 13 } - \frac{ 1 }{ 15 } + \frac{ 1 }{ 17 } - \frac{ 1 }{ 19 } \times { 4 }^{ }$$

Evaluate

$$\frac{8767043}{14549535}\approx 0.602565168$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{3}{3}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Subtract 1 from 3 to get 2.

$$\frac{2}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{10}{15}+\frac{3}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, add them by adding their numerators.

$$\frac{10+3}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Add 10 and 3 to get 13.

$$\frac{13}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 15 and 7 is 105. Convert \frac{13}{15} and \frac{1}{7} to fractions with denominator 105.

$$\frac{91}{105}-\frac{15}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{91}{105} and \frac{15}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-15}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Subtract 15 from 91 to get 76.

$$\frac{76}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 105 and 9 is 315. Convert \frac{76}{105} and \frac{1}{9} to fractions with denominator 315.

$$\frac{228}{315}+\frac{35}{315}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{228}{315} and \frac{35}{315} have the same denominator, add them by adding their numerators.

$$\frac{228+35}{315}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Add 228 and 35 to get 263.

$$\frac{263}{315}-\frac{1}{11}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 315 and 11 is 3465. Convert \frac{263}{315} and \frac{1}{11} to fractions with denominator 3465.

$$\frac{2893}{3465}-\frac{315}{3465}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{2893}{3465} and \frac{315}{3465} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2893-315}{3465}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Subtract 315 from 2893 to get 2578.

$$\frac{2578}{3465}+\frac{1}{13}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 3465 and 13 is 45045. Convert \frac{2578}{3465} and \frac{1}{13} to fractions with denominator 45045.

$$\frac{33514}{45045}+\frac{3465}{45045}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{33514}{45045} and \frac{3465}{45045} have the same denominator, add them by adding their numerators.

$$\frac{33514+3465}{45045}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Add 33514 and 3465 to get 36979.

$$\frac{36979}{45045}-\frac{1}{15}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 45045 and 15 is 45045. Convert \frac{36979}{45045} and \frac{1}{15} to fractions with denominator 45045.

$$\frac{36979}{45045}-\frac{3003}{45045}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Since \frac{36979}{45045} and \frac{3003}{45045} have the same denominator, subtract them by subtracting their numerators.

$$\frac{36979-3003}{45045}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Subtract 3003 from 36979 to get 33976.

$$\frac{33976}{45045}+\frac{1}{17}-\frac{1}{19}\times 4^{1}$$

Least common multiple of 45045 and 17 is 765765. Convert \frac{33976}{45045} and \frac{1}{17} to fractions with denominator 765765.

$$\frac{577592}{765765}+\frac{45045}{765765}-\frac{1}{19}\times 4^{1}$$

Since \frac{577592}{765765} and \frac{45045}{765765} have the same denominator, add them by adding their numerators.

$$\frac{577592+45045}{765765}-\frac{1}{19}\times 4^{1}$$

Add 577592 and 45045 to get 622637.

$$\frac{622637}{765765}-\frac{1}{19}\times 4^{1}$$

Calculate 4 to the power of 1 and get 4.

$$\frac{622637}{765765}-\frac{1}{19}\times 4$$

Multiply \frac{1}{19} and 4 to get \frac{4}{19}.

$$\frac{622637}{765765}-\frac{4}{19}$$

Least common multiple of 765765 and 19 is 14549535. Convert \frac{622637}{765765} and \frac{4}{19} to fractions with denominator 14549535.

$$\frac{11830103}{14549535}-\frac{3063060}{14549535}$$

Since \frac{11830103}{14549535} and \frac{3063060}{14549535} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11830103-3063060}{14549535}$$

Subtract 3063060 from 11830103 to get 8767043.

$$\frac{8767043}{14549535}$$

Factor

$$\frac{1061 \cdot 8263}{3 ^ {2} \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19} = 0.6025651678902453$$