Solve frac{sqrt{34}}{2}-31/2+-2/7

$$\frac { \sqrt { 34 } } { 2 } - 3 \frac { 1 } { 2 } + \frac { - 2 } { 7 }$$

Evaluate

$$\frac{\sqrt{34}}{2}-\frac{53}{14}\approx -0.870238338$$

Short Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{34}}{2}-\frac{6+1}{2}+\frac{-2}{7}$$

Add 6 and 1 to get 7.

$$\frac{\sqrt{34}}{2}-\frac{7}{2}+\frac{-2}{7}$$

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$\frac{\sqrt{34}}{2}-\frac{7}{2}-\frac{2}{7}$$

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

$$\frac{\sqrt{34}}{2}-\frac{49}{14}-\frac{4}{14}$$

Since -\frac{49}{14} and \frac{4}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{34}}{2}+\frac{-49-4}{14}$$

Subtract 4 from -49 to get -53.

$$\frac{\sqrt{34}}{2}-\frac{53}{14}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 14 is 14. Multiply \frac{\sqrt{34}}{2} times \frac{7}{7}.

$$\frac{7\sqrt{34}}{14}-\frac{53}{14}$$

Since \frac{7\sqrt{34}}{14} and \frac{53}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\sqrt{34}-53}{14}$$

Factor

$$\frac{7 \sqrt{34} - 53}{14} = -0.8702383382916352$$