Basic Math Examples

$\frac{6 z}{2} \div \frac{10}{2 z}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 z}{2} \cdot \frac{2 z}{10}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $6 z$ .

$\frac{2 (3 z)}{2} \cdot \frac{2 z}{10}$

Step 2.2

Factor $2$ out of $10$ .

$\frac{2 (3 z)}{2} \cdot \frac{2 z}{2 (5)}$

Step 2.3

Cancel the common factor.

$\frac{2 (3 z)}{2} \cdot \frac{2 z}{2 \cdot 5}$

Step 2.4

Rewrite the expression.

$\frac{3 z}{2} \cdot \frac{2 z}{5}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $2 z$ .

$\frac{3 z}{2} \cdot \frac{2 (z)}{5}$

Step 3.2

Cancel the common factor.

$\frac{3 z}{2} \cdot \frac{2 z}{5}$

Step 3.3

Rewrite the expression.

$3 z \frac{z}{5}$

Step 4

Combine $3$ and $\frac{z}{5}$ .

$z \frac{3 z}{5}$

Step 5

Combine $z$ and $\frac{3 z}{5}$ .

$\frac{z (3 z)}{5}$

Step 6

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

$\frac{3 (z^{1} z)}{5}$

Step 7

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

$\frac{3 (z^{1} z^{1})}{5}$

Step 8

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

$\frac{3 z^{1 + 1}}{5}$

Step 9

Add $1$ and $1$ .

$\frac{3 z^{2}}{5}$