Solve 17/5+17/5-(1/3+1/2)

$$\frac { 17 } { 5 } + \frac { 17 } { 5 } - ( \frac { 1 } { 3 } + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{179}{30}\approx 5.966666667$$

Solution Steps

Since \frac{17}{5} and \frac{17}{5} have the same denominator, add them by adding their numerators.

$$\frac{17+17}{5}-\left(\frac{1}{3}+\frac{1}{2}\right)$$

Add 17 and 17 to get 34.

$$\frac{34}{5}-\left(\frac{1}{3}+\frac{1}{2}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{34}{5}-\left(\frac{2}{6}+\frac{3}{6}\right)$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{34}{5}-\frac{2+3}{6}$$

Add 2 and 3 to get 5.

$$\frac{34}{5}-\frac{5}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{34}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{204}{30}-\frac{25}{30}$$

Since \frac{204}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{204-25}{30}$$

Subtract 25 from 204 to get 179.

$$\frac{179}{30}$$

Factor

$$\frac{179}{2 \cdot 3 \cdot 5} = 5\frac{29}{30} = 5.966666666666667$$