Basic Math Examples

$\frac{4}{z} \cdot (z) \div \frac{8}{z} \cdot (- z)$

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{4}{z} \cdot (z) \div \frac{8}{z} z$

Step 2

To divide by a fraction, multiply by its reciprocal.

$- (\frac{4}{z} \cdot (z) \frac{z}{8}) z$

Step 3

Multiply $z$ by $z$ by adding the exponents.

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Step 3.1

Move $z$ .

$- (\frac{4}{z} \cdot (z \cdot z) \frac{z}{8})$

Step 3.2

Multiply $z$ by $z$ .

$- (\frac{4}{z} \cdot z^{2} \frac{z}{8})$

Step 4

Cancel the common factor of $z$ .

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Step 4.1

Factor $z$ out of $z^{2}$ .

$- (\frac{4}{z} \cdot (z \cdot z) \frac{z}{8})$

Step 4.2

Cancel the common factor.

$- (\frac{4}{z} \cdot (z \cdot z) \frac{z}{8})$

Step 4.3

Rewrite the expression.

$- (4 \cdot z \frac{z}{8})$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $4 \cdot z$ .

$- (4 (z) \frac{z}{8})$

Step 5.2

Factor $4$ out of $8$ .

$- (4 (z) \frac{z}{4 (2)})$

Step 5.3

Cancel the common factor.

$- (4 z \frac{z}{4 \cdot 2})$

Step 5.4

Rewrite the expression.

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

Step 6

Combine $z$ and $\frac{z}{2}$ .

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

Step 7

Raise $z$ to the power of $1$ .

$- \frac{z^{1} z}{2}$

Step 8

Raise $z$ to the power of $1$ .

$- \frac{z^{1} z^{1}}{2}$

Step 9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{z^{1 + 1}}{2}$

Step 10

Add $1$ and $1$ .

$- \frac{z^{2}}{2}$