Solve 1/2+4/7+7/12+10/17

$$\frac { 1 } { 2 } + \frac { 4 } { 7 } + \frac { 7 } { 12 } + \frac { 10 } { 17 }$$

Evaluate

$$\frac{3203}{1428}\approx 2.242997199$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{4}{7} to fractions with denominator 14.

$$\frac{7}{14}+\frac{8}{14}+\frac{7}{12}+\frac{10}{17}$$

Since \frac{7}{14} and \frac{8}{14} have the same denominator, add them by adding their numerators.

$$\frac{7+8}{14}+\frac{7}{12}+\frac{10}{17}$$

Add 7 and 8 to get 15.

$$\frac{15}{14}+\frac{7}{12}+\frac{10}{17}$$

Least common multiple of 14 and 12 is 84. Convert \frac{15}{14} and \frac{7}{12} to fractions with denominator 84.

$$\frac{90}{84}+\frac{49}{84}+\frac{10}{17}$$

Since \frac{90}{84} and \frac{49}{84} have the same denominator, add them by adding their numerators.

$$\frac{90+49}{84}+\frac{10}{17}$$

Add 90 and 49 to get 139.

$$\frac{139}{84}+\frac{10}{17}$$

Least common multiple of 84 and 17 is 1428. Convert \frac{139}{84} and \frac{10}{17} to fractions with denominator 1428.

$$\frac{2363}{1428}+\frac{840}{1428}$$

Since \frac{2363}{1428} and \frac{840}{1428} have the same denominator, add them by adding their numerators.

$$\frac{2363+840}{1428}$$

Add 2363 and 840 to get 3203.

$$\frac{3203}{1428}$$

Factor

$$\frac{3203}{2 ^ {2} \cdot 3 \cdot 7 \cdot 17} = 2\frac{347}{1428} = 2.242997198879552$$