Solve -4(frac{3/sqrt{2})}{9(sqrt{2})}

$$\frac { - 4 ( \frac { 3 } { \sqrt { 2 } } ) } { 9 ( \sqrt { 2 } ) }$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-4\times \frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{9\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-4\times \frac{3\sqrt{2}}{2}}{9\sqrt{2}}$$

Cancel out 2, the greatest common factor in 4 and 2.

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

Cancel out 3\sqrt{2} in both numerator and denominator.

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

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

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

Factor

$$-\frac{2}{3} = -0.6666666666666666$$