Pre-Algebra Examples

$\frac{\frac{3 x^{2}}{2 y}}{\frac{6 x y}{9}}$

Step 1

Cancel the common factor of $6$ and $9$ .

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Step 1.1

Factor $3$ out of $6 x y$ .

$\frac{\frac{3 x^{2}}{2 y}}{\frac{3 (2 x y)}{9}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9$ .

$\frac{\frac{3 x^{2}}{2 y}}{\frac{3 (2 x y)}{3 (3)}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{3 x^{2}}{2 y}}{\frac{3 (2 x y)}{3 \cdot 3}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{3 x^{2}}{2 y}}{\frac{2 x y}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{3 x^{2}}{2 y} \cdot \frac{3}{2 x y}$

Step 3

Combine.

$\frac{3 x^{2} \cdot 3}{2 y (2 x y)}$

Step 4

Multiply $y$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

$\frac{3 x^{2} \cdot 3}{2 (y \cdot y) (2 x)}$

Step 4.2

Multiply $y$ by $y$ .

$\frac{3 x^{2} \cdot 3}{2 y^{2} (2 x)}$

Step 5

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

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Step 5.1

Factor $x$ out of $3 x^{2} \cdot 3$ .

$\frac{x (3 x \cdot 3)}{2 y^{2} (2 x)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $2 y^{2} (2 x)$ .

$\frac{x (3 x \cdot 3)}{x (2 y^{2} \cdot (2))}$

Step 5.2.2

Cancel the common factor.

$\frac{x (3 x \cdot 3)}{x (2 y^{2} \cdot (2))}$

Step 5.2.3

Rewrite the expression.

$\frac{3 x \cdot 3}{2 y^{2} \cdot (2)}$

Step 6

Multiply $3$ by $3$ .

$\frac{9 x}{2 y^{2} \cdot 2}$

Step 7

Multiply $2$ by $2$ .

$\frac{9 x}{4 y^{2}}$