Basic Math Examples

$\frac{z^{2}}{5 w^{2}} \div \frac{z}{w^{3}} \cdot \frac{w}{2 z}$

Step 1

Combine fractions.

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Step 1.1

Combine.

$\frac{\frac{z^{2}}{5 w^{2}} w}{\frac{z}{w^{3}} (2 z)}$

Step 1.2

Combine $\frac{z^{2}}{5 w^{2}}$ and $w$ .

$\frac{\frac{z^{2} w}{5 w^{2}}}{\frac{z}{w^{3}} (2 z)}$

Step 2

Simplify the denominator.

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Step 2.1

Combine $2$ and $\frac{z}{w^{3}}$ .

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

Step 2.2

Combine $\frac{2 z}{w^{3}}$ and $z$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{\frac{z^{2} w}{5 w^{2}}}{\frac{2 (z^{1} z)}{w^{3}}}$

Step 3.2

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

$\frac{\frac{z^{2} w}{5 w^{2}}}{\frac{2 (z^{1} z^{1})}{w^{3}}}$

Step 3.3

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

$\frac{\frac{z^{2} w}{5 w^{2}}}{\frac{2 z^{1 + 1}}{w^{3}}}$

Step 3.4

Add $1$ and $1$ .

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

Step 4

Reduce the expression $\frac{z^{2} w}{5 w^{2}}$ by cancelling the common factors.

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Step 4.1

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

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

Step 4.2

Factor $w$ out of $5 w^{2}$ .

$\frac{\frac{w z^{2}}{w (5 w)}}{\frac{2 z^{2}}{w^{3}}}$

Step 4.3

Cancel the common factor.

$\frac{\frac{w z^{2}}{w (5 w)}}{\frac{2 z^{2}}{w^{3}}}$

Step 4.4

Rewrite the expression.

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

Simplify terms.

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Step 6.1

Combine.

$\frac{z^{2} w^{3}}{5 w (2 z^{2})}$

Step 6.2

Cancel the common factor of $z^{2}$ .

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Step 6.2.1

Cancel the common factor.

$\frac{z^{2} w^{3}}{5 w (2 z^{2})}$

Step 6.2.2

Rewrite the expression.

$\frac{w^{3}}{5 w \cdot (2)}$

Step 6.3

Cancel the common factor of $w^{3}$ and $w$ .

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Step 6.3.1

Factor $w$ out of $w^{3}$ .

$\frac{w \cdot w^{2}}{5 w \cdot (2)}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor $w$ out of $5 w \cdot (2)$ .

$\frac{w \cdot w^{2}}{w (5 \cdot (2))}$

Step 6.3.2.2

Cancel the common factor.

$\frac{w \cdot w^{2}}{w (5 \cdot (2))}$

Step 6.3.2.3

Rewrite the expression.

$\frac{w^{2}}{5 \cdot (2)}$

Step 7

Multiply $5$ by $2$ .

$\frac{w^{2}}{10}$