Solve 4*(1-1/3+1/5-1/7+1/9-frac{1}{11}+frac{1}{13})

$$4 \times ( 1 - \frac { 1 } { 3 } + \frac { 1 } { 5 } - \frac { 1 } { 7 } + \frac { 1 } { 9 } - \frac { 1 } { 11 } + \frac { 1 } { 13 } )$$

Evaluate

$$\frac{147916}{45045}\approx 3.283738484$$

Solution Steps

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

$$4\left(\frac{3}{3}-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{3-1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

Subtract 1 from 3 to get 2.

$$4\left(\frac{2}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{10}{15}+\frac{3}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{10+3}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

Add 10 and 3 to get 13.

$$4\left(\frac{13}{15}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{91}{105}-\frac{15}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{91-15}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

Subtract 15 from 91 to get 76.

$$4\left(\frac{76}{105}+\frac{1}{9}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{228}{315}+\frac{35}{315}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{228+35}{315}-\frac{1}{11}+\frac{1}{13}\right)$$

Add 228 and 35 to get 263.

$$4\left(\frac{263}{315}-\frac{1}{11}+\frac{1}{13}\right)$$

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

$$4\left(\frac{2893}{3465}-\frac{315}{3465}+\frac{1}{13}\right)$$

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

$$4\left(\frac{2893-315}{3465}+\frac{1}{13}\right)$$

Subtract 315 from 2893 to get 2578.

$$4\left(\frac{2578}{3465}+\frac{1}{13}\right)$$

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

$$4\left(\frac{33514}{45045}+\frac{3465}{45045}\right)$$

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

$$4\times \frac{33514+3465}{45045}$$

Add 33514 and 3465 to get 36979.

$$4\times \frac{36979}{45045}$$

Express 4\times \frac{36979}{45045} as a single fraction.

$$\frac{4\times 36979}{45045}$$

Multiply 4 and 36979 to get 147916.

$$\frac{147916}{45045}$$

Factor

$$\frac{2 ^ {2} \cdot 36979}{3 ^ {2} \cdot 5 \cdot 7 \cdot 11 \cdot 13} = 3\frac{12781}{45045} = 3.2837384837384835$$