Solve 1/80+1/120+1/168+1/224+frac{1}{288}+frac{1}{360}

$$\frac{ 1 }{ 80 } + \frac{ 1 }{ 120 } + \frac{ 1 }{ 168 } + \frac{ 1 }{ 224 } + \frac{ 1 }{ 288 } + \frac{ 1 }{ 360 }$$

Evaluate

$$\frac{3}{80}=0.0375$$

Solution Steps

Least common multiple of 80 and 120 is 240. Convert \frac{1}{80} and \frac{1}{120} to fractions with denominator 240.

$$\frac{3}{240}+\frac{2}{240}+\frac{1}{168}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Since \frac{3}{240} and \frac{2}{240} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{240}+\frac{1}{168}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Add 3 and 2 to get 5.

$$\frac{5}{240}+\frac{1}{168}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Reduce the fraction \frac{5}{240} to lowest terms by extracting and canceling out 5.

$$\frac{1}{48}+\frac{1}{168}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Least common multiple of 48 and 168 is 336. Convert \frac{1}{48} and \frac{1}{168} to fractions with denominator 336.

$$\frac{7}{336}+\frac{2}{336}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Since \frac{7}{336} and \frac{2}{336} have the same denominator, add them by adding their numerators.

$$\frac{7+2}{336}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Add 7 and 2 to get 9.

$$\frac{9}{336}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Reduce the fraction \frac{9}{336} to lowest terms by extracting and canceling out 3.

$$\frac{3}{112}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Least common multiple of 112 and 224 is 224. Convert \frac{3}{112} and \frac{1}{224} to fractions with denominator 224.

$$\frac{6}{224}+\frac{1}{224}+\frac{1}{288}+\frac{1}{360}$$

Since \frac{6}{224} and \frac{1}{224} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{224}+\frac{1}{288}+\frac{1}{360}$$

Add 6 and 1 to get 7.

$$\frac{7}{224}+\frac{1}{288}+\frac{1}{360}$$

Reduce the fraction \frac{7}{224} to lowest terms by extracting and canceling out 7.

$$\frac{1}{32}+\frac{1}{288}+\frac{1}{360}$$

Least common multiple of 32 and 288 is 288. Convert \frac{1}{32} and \frac{1}{288} to fractions with denominator 288.

$$\frac{9}{288}+\frac{1}{288}+\frac{1}{360}$$

Since \frac{9}{288} and \frac{1}{288} have the same denominator, add them by adding their numerators.

$$\frac{9+1}{288}+\frac{1}{360}$$

Add 9 and 1 to get 10.

$$\frac{10}{288}+\frac{1}{360}$$

Reduce the fraction \frac{10}{288} to lowest terms by extracting and canceling out 2.

$$\frac{5}{144}+\frac{1}{360}$$

Least common multiple of 144 and 360 is 720. Convert \frac{5}{144} and \frac{1}{360} to fractions with denominator 720.

$$\frac{25}{720}+\frac{2}{720}$$

Since \frac{25}{720} and \frac{2}{720} have the same denominator, add them by adding their numerators.

$$\frac{25+2}{720}$$

Add 25 and 2 to get 27.

$$\frac{27}{720}$$

Reduce the fraction \frac{27}{720} to lowest terms by extracting and canceling out 9.

$$\frac{3}{80}$$

Factor

$$\frac{3}{2 ^ {4} \cdot 5} = 0.0375$$