Solve 19/18+61/72+13/210+1/10+frac{8}{5}

$$\frac{ 19 }{ 18 } + \frac{ 61 }{ 72 } + \frac{ 13 }{ 210 } + \frac{ 1 }{ 10 } + \frac{ 8 }{ 5 }$$

Evaluate

$$\frac{1847}{504}\approx 3.66468254$$

Solution Steps

Least common multiple of 18 and 72 is 72. Convert \frac{19}{18} and \frac{61}{72} to fractions with denominator 72.

$$\frac{76}{72}+\frac{61}{72}+\frac{13}{210}+\frac{1}{10}+\frac{8}{5}$$

Since \frac{76}{72} and \frac{61}{72} have the same denominator, add them by adding their numerators.

$$\frac{76+61}{72}+\frac{13}{210}+\frac{1}{10}+\frac{8}{5}$$

Add 76 and 61 to get 137.

$$\frac{137}{72}+\frac{13}{210}+\frac{1}{10}+\frac{8}{5}$$

Least common multiple of 72 and 210 is 2520. Convert \frac{137}{72} and \frac{13}{210} to fractions with denominator 2520.

$$\frac{4795}{2520}+\frac{156}{2520}+\frac{1}{10}+\frac{8}{5}$$

Since \frac{4795}{2520} and \frac{156}{2520} have the same denominator, add them by adding their numerators.

$$\frac{4795+156}{2520}+\frac{1}{10}+\frac{8}{5}$$

Add 4795 and 156 to get 4951.

$$\frac{4951}{2520}+\frac{1}{10}+\frac{8}{5}$$

Least common multiple of 2520 and 10 is 2520. Convert \frac{4951}{2520} and \frac{1}{10} to fractions with denominator 2520.

$$\frac{4951}{2520}+\frac{252}{2520}+\frac{8}{5}$$

Since \frac{4951}{2520} and \frac{252}{2520} have the same denominator, add them by adding their numerators.

$$\frac{4951+252}{2520}+\frac{8}{5}$$

Add 4951 and 252 to get 5203.

$$\frac{5203}{2520}+\frac{8}{5}$$

Least common multiple of 2520 and 5 is 2520. Convert \frac{5203}{2520} and \frac{8}{5} to fractions with denominator 2520.

$$\frac{5203}{2520}+\frac{4032}{2520}$$

Since \frac{5203}{2520} and \frac{4032}{2520} have the same denominator, add them by adding their numerators.

$$\frac{5203+4032}{2520}$$

Add 5203 and 4032 to get 9235.

$$\frac{9235}{2520}$$

Reduce the fraction \frac{9235}{2520} to lowest terms by extracting and canceling out 5.

$$\frac{1847}{504}$$

Factor

$$\frac{1847}{2 ^ {3} \cdot 3 ^ {2} \cdot 7} = 3\frac{335}{504} = 3.6646825396825395$$