Simplify ((a^2)/(12b))÷((ab)/36)

$\frac{a^{2}}{12 b} \div \frac{a b}{36}$

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2}}{12 b} \cdot \frac{36}{a b}$

Combine.

$\frac{a^{2} \cdot 36}{12 b (a b)}$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{a^{2} \cdot 36}{12 (b \cdot b) a}$

Multiply $b$ by $b$ .

$\frac{a^{2} \cdot 36}{12 b^{2} a}$

$\frac{a^{2} \cdot 36}{12 b^{2} a}$

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

Factor $a$ out of $a^{2} \cdot 36$ .

$\frac{a (a \cdot 36)}{12 b^{2} a}$

Cancel the common factors.

Factor $a$ out of $12 b^{2} a$ .

$\frac{a (a \cdot 36)}{a (12 b^{2})}$

Cancel the common factor.

$\frac{a (a \cdot 36)}{a (12 b^{2})}$

Rewrite the expression.

$\frac{a \cdot 36}{12 b^{2}}$

$\frac{a \cdot 36}{12 b^{2}}$

$\frac{a \cdot 36}{12 b^{2}}$

Cancel the common factor of $36$ and $12$ .

Factor $12$ out of $a \cdot 36$ .

$\frac{12 (a \cdot 3)}{12 b^{2}}$

Cancel the common factors.

Factor $12$ out of $12 b^{2}$ .

$\frac{12 (a \cdot 3)}{12 (b^{2})}$

Cancel the common factor.

$\frac{12 (a \cdot 3)}{12 b^{2}}$

Rewrite the expression.

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

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

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

Move $3$ to the left of $a$ .

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

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