Simplify (-( square root of 2)/2)÷(( square root of 2)/2)

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

To divide by a fraction, multiply by its reciprocal.

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

Cancel the common factor of $\sqrt{2}$ .

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

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

Factor $\sqrt{2}$ out of $- \sqrt{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- 1$