Solve 9(1/2)-(2frac{sqrt{3}}{3})

$$9 ( 1 / 2 ) - ( 2 \frac { \sqrt { 3 } } { 3 } )$$

Evaluate

$$-\frac{2\sqrt{3}}{3}+\frac{9}{2}\approx 3.345299462$$

Short Solution Steps

Multiply 9 and \frac{1}{2} to get \frac{9}{2}.

$$\frac{9}{2}-2\times \frac{\sqrt{3}}{3}$$

Express 2\times \frac{\sqrt{3}}{3} as a single fraction.

$$\frac{9}{2}-\frac{2\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{9}{2} times \frac{3}{3}. Multiply \frac{2\sqrt{3}}{3} times \frac{2}{2}.

$$\frac{9\times 3}{6}-\frac{2\times 2\sqrt{3}}{6}$$

Since \frac{9\times 3}{6} and \frac{2\times 2\sqrt{3}}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times 3-2\times 2\sqrt{3}}{6}$$

Do the multiplications in 9\times 3-2\times 2\sqrt{3}.

$$\frac{27-4\sqrt{3}}{6}$$

Factor

$$\frac{27 - 4 \sqrt{3}}{6} = 3.345299461620749$$