Solve 1/36+1/37+1/39+1/43+frac{1}{45}+frac{1}{45}+frac{1}{45}+frac{1}{45}+frac{1}{55}+frac{1}{55}=

$$\frac{ 1 }{ 36 } + \frac{ 1 }{ 37 } + \frac{ 1 }{ 39 } + \frac{ 1 }{ 43 } + \frac{ 1 }{ 45 } + \frac{ 1 }{ 45 } + \frac{ 1 }{ 45 } + \frac{ 1 }{ 45 } + \frac{ 1 }{ 55 } + \frac{ 1 }{ 55 } =$$

Evaluate

$$\frac{1041801}{4550260}\approx 0.22895417$$

Solution Steps

Least common multiple of 36 and 37 is 1332. Convert \frac{1}{36} and \frac{1}{37} to fractions with denominator 1332.

$$\frac{37}{1332}+\frac{36}{1332}+\frac{1}{39}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{37}{1332} and \frac{36}{1332} have the same denominator, add them by adding their numerators.

$$\frac{37+36}{1332}+\frac{1}{39}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 37 and 36 to get 73.

$$\frac{73}{1332}+\frac{1}{39}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 1332 and 39 is 17316. Convert \frac{73}{1332} and \frac{1}{39} to fractions with denominator 17316.

$$\frac{949}{17316}+\frac{444}{17316}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{949}{17316} and \frac{444}{17316} have the same denominator, add them by adding their numerators.

$$\frac{949+444}{17316}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 949 and 444 to get 1393.

$$\frac{1393}{17316}+\frac{1}{43}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 17316 and 43 is 744588. Convert \frac{1393}{17316} and \frac{1}{43} to fractions with denominator 744588.

$$\frac{59899}{744588}+\frac{17316}{744588}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{59899}{744588} and \frac{17316}{744588} have the same denominator, add them by adding their numerators.

$$\frac{59899+17316}{744588}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 59899 and 17316 to get 77215.

$$\frac{77215}{744588}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 744588 and 45 is 3722940. Convert \frac{77215}{744588} and \frac{1}{45} to fractions with denominator 3722940.

$$\frac{386075}{3722940}+\frac{82732}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{386075}{3722940} and \frac{82732}{3722940} have the same denominator, add them by adding their numerators.

$$\frac{386075+82732}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 386075 and 82732 to get 468807.

$$\frac{468807}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Reduce the fraction \frac{468807}{3722940} to lowest terms by extracting and canceling out 3.

$$\frac{156269}{1240980}+\frac{1}{45}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 1240980 and 45 is 3722940. Convert \frac{156269}{1240980} and \frac{1}{45} to fractions with denominator 3722940.

$$\frac{468807}{3722940}+\frac{82732}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{468807}{3722940} and \frac{82732}{3722940} have the same denominator, add them by adding their numerators.

$$\frac{468807+82732}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 468807 and 82732 to get 551539.

$$\frac{551539}{3722940}+\frac{1}{45}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 3722940 and 45 is 3722940. Convert \frac{551539}{3722940} and \frac{1}{45} to fractions with denominator 3722940.

$$\frac{551539}{3722940}+\frac{82732}{3722940}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{551539}{3722940} and \frac{82732}{3722940} have the same denominator, add them by adding their numerators.

$$\frac{551539+82732}{3722940}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Add 551539 and 82732 to get 634271.

$$\frac{634271}{3722940}+\frac{1}{45}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 3722940 and 45 is 3722940. Convert \frac{634271}{3722940} and \frac{1}{45} to fractions with denominator 3722940.

$$\frac{634271}{3722940}+\frac{82732}{3722940}+\frac{1}{55}+\frac{1}{55}$$

Since \frac{634271}{3722940} and \frac{82732}{3722940} have the same denominator, add them by adding their numerators.

$$\frac{634271+82732}{3722940}+\frac{1}{55}+\frac{1}{55}$$

Add 634271 and 82732 to get 717003.

$$\frac{717003}{3722940}+\frac{1}{55}+\frac{1}{55}$$

Reduce the fraction \frac{717003}{3722940} to lowest terms by extracting and canceling out 9.

$$\frac{79667}{413660}+\frac{1}{55}+\frac{1}{55}$$

Least common multiple of 413660 and 55 is 4550260. Convert \frac{79667}{413660} and \frac{1}{55} to fractions with denominator 4550260.

$$\frac{876337}{4550260}+\frac{82732}{4550260}+\frac{1}{55}$$

Since \frac{876337}{4550260} and \frac{82732}{4550260} have the same denominator, add them by adding their numerators.

$$\frac{876337+82732}{4550260}+\frac{1}{55}$$

Add 876337 and 82732 to get 959069.

$$\frac{959069}{4550260}+\frac{1}{55}$$

Least common multiple of 4550260 and 55 is 4550260. Convert \frac{959069}{4550260} and \frac{1}{55} to fractions with denominator 4550260.

$$\frac{959069}{4550260}+\frac{82732}{4550260}$$

Since \frac{959069}{4550260} and \frac{82732}{4550260} have the same denominator, add them by adding their numerators.

$$\frac{959069+82732}{4550260}$$

Add 959069 and 82732 to get 1041801.

$$\frac{1041801}{4550260}$$

Factor

$$\frac{3 \cdot 239 \cdot 1453}{2 ^ {2} \cdot 5 \cdot 11 \cdot 13 \cdot 37 \cdot 43} = 0.22895416965184406$$