Solve 1/3+12/13-(1/2+1/17)

$$\frac { 1 } { 3 } + \frac { 12 } { 13 } - ( \frac { 1 } { 2 } + \frac { 1 } { 17 } )$$

Evaluate

$$\frac{925}{1326}\approx 0.697586727$$

Solution Steps

Least common multiple of 3 and 13 is 39. Convert \frac{1}{3} and \frac{12}{13} to fractions with denominator 39.

$$\frac{13}{39}+\frac{36}{39}-\left(\frac{1}{2}+\frac{1}{17}\right)$$

Since \frac{13}{39} and \frac{36}{39} have the same denominator, add them by adding their numerators.

$$\frac{13+36}{39}-\left(\frac{1}{2}+\frac{1}{17}\right)$$

Add 13 and 36 to get 49.

$$\frac{49}{39}-\left(\frac{1}{2}+\frac{1}{17}\right)$$

Least common multiple of 2 and 17 is 34. Convert \frac{1}{2} and \frac{1}{17} to fractions with denominator 34.

$$\frac{49}{39}-\left(\frac{17}{34}+\frac{2}{34}\right)$$

Since \frac{17}{34} and \frac{2}{34} have the same denominator, add them by adding their numerators.

$$\frac{49}{39}-\frac{17+2}{34}$$

Add 17 and 2 to get 19.

$$\frac{49}{39}-\frac{19}{34}$$

Least common multiple of 39 and 34 is 1326. Convert \frac{49}{39} and \frac{19}{34} to fractions with denominator 1326.

$$\frac{1666}{1326}-\frac{741}{1326}$$

Since \frac{1666}{1326} and \frac{741}{1326} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1666-741}{1326}$$

Subtract 741 from 1666 to get 925.

$$\frac{925}{1326}$$

Factor

$$\frac{5 ^ {2} \cdot 37}{2 \cdot 3 \cdot 13 \cdot 17} = 0.6975867269984917$$