Solve 1/3+1/7+1/9+1/11+frac{1}{32}

$$\frac { 1 } { 3 } + \frac { 1 } { 7 } + \frac { 1 } { 9 } + \frac { 1 } { 11 } + \frac { 1 } { 32 }$$

Evaluate

$$\frac{15733}{22176}\approx 0.709460678$$

Solution Steps

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{1}{7} to fractions with denominator 21.

$$\frac{7}{21}+\frac{3}{21}+\frac{1}{9}+\frac{1}{11}+\frac{1}{32}$$

Since \frac{7}{21} and \frac{3}{21} have the same denominator, add them by adding their numerators.

$$\frac{7+3}{21}+\frac{1}{9}+\frac{1}{11}+\frac{1}{32}$$

Add 7 and 3 to get 10.

$$\frac{10}{21}+\frac{1}{9}+\frac{1}{11}+\frac{1}{32}$$

Least common multiple of 21 and 9 is 63. Convert \frac{10}{21} and \frac{1}{9} to fractions with denominator 63.

$$\frac{30}{63}+\frac{7}{63}+\frac{1}{11}+\frac{1}{32}$$

Since \frac{30}{63} and \frac{7}{63} have the same denominator, add them by adding their numerators.

$$\frac{30+7}{63}+\frac{1}{11}+\frac{1}{32}$$

Add 30 and 7 to get 37.

$$\frac{37}{63}+\frac{1}{11}+\frac{1}{32}$$

Least common multiple of 63 and 11 is 693. Convert \frac{37}{63} and \frac{1}{11} to fractions with denominator 693.

$$\frac{407}{693}+\frac{63}{693}+\frac{1}{32}$$

Since \frac{407}{693} and \frac{63}{693} have the same denominator, add them by adding their numerators.

$$\frac{407+63}{693}+\frac{1}{32}$$

Add 407 and 63 to get 470.

$$\frac{470}{693}+\frac{1}{32}$$

Least common multiple of 693 and 32 is 22176. Convert \frac{470}{693} and \frac{1}{32} to fractions with denominator 22176.

$$\frac{15040}{22176}+\frac{693}{22176}$$

Since \frac{15040}{22176} and \frac{693}{22176} have the same denominator, add them by adding their numerators.

$$\frac{15040+693}{22176}$$

Add 15040 and 693 to get 15733.

$$\frac{15733}{22176}$$

Factor

$$\frac{15733}{2 ^ {5} \cdot 3 ^ {2} \cdot 7 \cdot 11} = 0.7094606782106783$$