Solve 13/14+75/21+19/24

$$1 \frac { 3 } { 14 } + 7 \frac { 5 } { 21 } + \frac{ 19 }{ 24 }$$

Evaluate

$$\frac{1553}{168}\approx 9.244047619$$

Solution Steps

Multiply 1 and 14 to get 14.

$$\frac{14+3}{14}+\frac{7\times 21+5}{21}+\frac{19}{24}$$

Add 14 and 3 to get 17.

$$\frac{17}{14}+\frac{7\times 21+5}{21}+\frac{19}{24}$$

Multiply 7 and 21 to get 147.

$$\frac{17}{14}+\frac{147+5}{21}+\frac{19}{24}$$

Add 147 and 5 to get 152.

$$\frac{17}{14}+\frac{152}{21}+\frac{19}{24}$$

Least common multiple of 14 and 21 is 42. Convert \frac{17}{14} and \frac{152}{21} to fractions with denominator 42.

$$\frac{51}{42}+\frac{304}{42}+\frac{19}{24}$$

Since \frac{51}{42} and \frac{304}{42} have the same denominator, add them by adding their numerators.

$$\frac{51+304}{42}+\frac{19}{24}$$

Add 51 and 304 to get 355.

$$\frac{355}{42}+\frac{19}{24}$$

Least common multiple of 42 and 24 is 168. Convert \frac{355}{42} and \frac{19}{24} to fractions with denominator 168.

$$\frac{1420}{168}+\frac{133}{168}$$

Since \frac{1420}{168} and \frac{133}{168} have the same denominator, add them by adding their numerators.

$$\frac{1420+133}{168}$$

Add 1420 and 133 to get 1553.

$$\frac{1553}{168}$$

Factor

$$\frac{1553}{2 ^ {3} \cdot 3 \cdot 7} = 9\frac{41}{168} = 9.244047619047619$$