Solve {l}{1/4+1/9+1/10}{+4422}

$$\left. \begin{array} { l } { \frac { 1 } { 4 } + \frac { 1 } { 9 } + \frac { 1 } { 10 } } \\ { + 4422 } \end{array} \right.$$

Evaluate

$$\frac{796043}{180}\approx 4422.461111111$$

Solution Steps

Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{1}{9} to fractions with denominator 36.

$$\frac{9}{36}+\frac{4}{36}+\frac{1}{10}+4422$$

Since \frac{9}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{9+4}{36}+\frac{1}{10}+4422$$

Add 9 and 4 to get 13.

$$\frac{13}{36}+\frac{1}{10}+4422$$

Least common multiple of 36 and 10 is 180. Convert \frac{13}{36} and \frac{1}{10} to fractions with denominator 180.

$$\frac{65}{180}+\frac{18}{180}+4422$$

Since \frac{65}{180} and \frac{18}{180} have the same denominator, add them by adding their numerators.

$$\frac{65+18}{180}+4422$$

Add 65 and 18 to get 83.

$$\frac{83}{180}+4422$$

Convert 4422 to fraction \frac{795960}{180}.

$$\frac{83}{180}+\frac{795960}{180}$$

Since \frac{83}{180} and \frac{795960}{180} have the same denominator, add them by adding their numerators.

$$\frac{83+795960}{180}$$

Add 83 and 795960 to get 796043.

$$\frac{796043}{180}$$

Factor

$$\frac{19 \cdot 41897}{2 ^ {2} \cdot 3 ^ {2} \cdot 5} = 4422\frac{83}{180} = 4422.461111111111$$