Basic Math Examples

$\frac{3 a^{2}}{b} \div \frac{{(2 a)}^{2}}{b^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 a^{2}}{b} \cdot \frac{b^{3}}{{(2 a)}^{2}}$

Step 2

Simplify terms.

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Step 2.1

Combine.

$\frac{3 a^{2} b^{3}}{b {(2 a)}^{2}}$

Step 2.2

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

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Step 2.2.1

Factor $b$ out of $3 a^{2} b^{3}$ .

$\frac{b (3 a^{2} b^{2})}{b {(2 a)}^{2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $b$ out of $b {(2 a)}^{2}$ .

$\frac{b (3 a^{2} b^{2})}{b ({(2 a)}^{2})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{b (3 a^{2} b^{2})}{b {(2 a)}^{2}}$

Step 2.2.2.3

Rewrite the expression.

$\frac{3 a^{2} b^{2}}{{(2 a)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $2 a$ .

$\frac{3 a^{2} b^{2}}{2^{2} a^{2}}$

Step 3.2

Raise $2$ to the power of $2$ .

$\frac{3 a^{2} b^{2}}{4 a^{2}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{3 a^{2} b^{2}}{4 a^{2}}$

Step 4.2

Rewrite the expression.

$\frac{3 b^{2}}{4}$