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

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

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

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

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

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - 1$

Step 4

Multiply $- 1$ by $- 1$ .

$1$