Solve -4frac{1/2*3sqrt{3}*9}{1/2}

$$\frac { - 4 \frac { 1 } { 2 } \times 3 \sqrt { 3 } \cdot 9 } { \frac { 1 } { 2 } }$$

Evaluate

$$-243\sqrt{3}\approx -420.888346239$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\frac{27\left(-\frac{4\times 2+1}{2}\right)\sqrt{3}}{\frac{1}{2}}$$

Multiply 4 and 2 to get 8.

$$\frac{27\left(-\frac{8+1}{2}\right)\sqrt{3}}{\frac{1}{2}}$$

Add 8 and 1 to get 9.

$$\frac{27\left(-\frac{9}{2}\right)\sqrt{3}}{\frac{1}{2}}$$

Express 27\left(-\frac{9}{2}\right) as a single fraction.

$$\frac{\frac{27\left(-9\right)}{2}\sqrt{3}}{\frac{1}{2}}$$

Multiply 27 and -9 to get -243.

$$\frac{\frac{-243}{2}\sqrt{3}}{\frac{1}{2}}$$

Fraction \frac{-243}{2} can be rewritten as -\frac{243}{2} by extracting the negative sign.

$$\frac{-\frac{243}{2}\sqrt{3}}{\frac{1}{2}}$$

Divide -\frac{243}{2}\sqrt{3} by \frac{1}{2} by multiplying -\frac{243}{2}\sqrt{3} by the reciprocal of \frac{1}{2}.

$$-\frac{243}{2}\sqrt{3}\times 2$$

Cancel out 2 and 2.

$$-243\sqrt{3}$$