Basic Math Examples

$\frac{1}{2} \cdot \sqrt{3} - 5 \sqrt{3}$

Step 1

Combine $\frac{1}{2}$ and $\sqrt{3}$ .

$\frac{\sqrt{3}}{2} - 5 \sqrt{3}$

Step 2

To write $- 5 \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\sqrt{3}}{2} - 5 \sqrt{3} \cdot \frac{2}{2}$

Step 3

Combine fractions.

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Step 3.1

Combine $- 5 \sqrt{3}$ and $\frac{2}{2}$ .

$\frac{\sqrt{3}}{2} + \frac{- 5 \sqrt{3} \cdot 2}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\sqrt{3} - 5 \sqrt{3} \cdot 2}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $2$ by $- 5$ .

$\frac{\sqrt{3} - 10 \sqrt{3}}{2}$

Step 4.2

Subtract $10 \sqrt{3}$ from $\sqrt{3}$ .

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

Step 5

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 7.79422863 \dots$