Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Step 2.1.2

Factor $3$ out of $- 3$ .

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

Combine $\sqrt{5}$ and $\frac{- 1}{2}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

Move $- 1$ to the left of $\sqrt{5}$ .

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

Step 3.2

Rewrite $- 1 \sqrt{5}$ as $- \sqrt{5}$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.11803398 \dots$