Solve 112+1/3+1/8+1/5+1/4

$$112 + 1 / 3 + 1 / 8 + 1 / 5 + 1 / 4$$

Evaluate

$$\frac{13549}{120}\approx 112.908333333$$

Solution Steps

Convert 112 to fraction \frac{336}{3}.

$$\frac{336}{3}+\frac{1}{3}+\frac{1}{8}+\frac{1}{5}+\frac{1}{4}$$

Since \frac{336}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{336+1}{3}+\frac{1}{8}+\frac{1}{5}+\frac{1}{4}$$

Add 336 and 1 to get 337.

$$\frac{337}{3}+\frac{1}{8}+\frac{1}{5}+\frac{1}{4}$$

Least common multiple of 3 and 8 is 24. Convert \frac{337}{3} and \frac{1}{8} to fractions with denominator 24.

$$\frac{2696}{24}+\frac{3}{24}+\frac{1}{5}+\frac{1}{4}$$

Since \frac{2696}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{2696+3}{24}+\frac{1}{5}+\frac{1}{4}$$

Add 2696 and 3 to get 2699.

$$\frac{2699}{24}+\frac{1}{5}+\frac{1}{4}$$

Least common multiple of 24 and 5 is 120. Convert \frac{2699}{24} and \frac{1}{5} to fractions with denominator 120.

$$\frac{13495}{120}+\frac{24}{120}+\frac{1}{4}$$

Since \frac{13495}{120} and \frac{24}{120} have the same denominator, add them by adding their numerators.

$$\frac{13495+24}{120}+\frac{1}{4}$$

Add 13495 and 24 to get 13519.

$$\frac{13519}{120}+\frac{1}{4}$$

Least common multiple of 120 and 4 is 120. Convert \frac{13519}{120} and \frac{1}{4} to fractions with denominator 120.

$$\frac{13519}{120}+\frac{30}{120}$$

Since \frac{13519}{120} and \frac{30}{120} have the same denominator, add them by adding their numerators.

$$\frac{13519+30}{120}$$

Add 13519 and 30 to get 13549.

$$\frac{13549}{120}$$

Factor

$$\frac{17 \cdot 797}{2 ^ {3} \cdot 3 \cdot 5} = 112\frac{109}{120} = 112.90833333333333$$