Pre-Algebra Examples

$\frac{\frac{16 x^{2} y}{24 x y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 1

Cancel the common factor of $16$ and $24$ .

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Step 1.1

Factor $8$ out of $16 x^{2} y$ .

$\frac{\frac{8 (2 x^{2} y)}{24 x y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $24 x y^{3}$ .

$\frac{\frac{8 (2 x^{2} y)}{8 (3 x y^{3})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{8 (2 x^{2} y)}{8 (3 x y^{3})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{2 x^{2} y}{3 x y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 2

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

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Step 2.1

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

$\frac{\frac{x (2 x y)}{3 x y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x$ out of $3 x y^{3}$ .

$\frac{\frac{x (2 x y)}{x (3 y^{3})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{x (2 x y)}{x (3 y^{3})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{2 x y}{3 y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 3

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

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Step 3.1

Factor $y$ out of $2 x y$ .

$\frac{\frac{y (2 x)}{3 y^{3}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{\frac{y (2 x)}{y (3 y^{2})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 3.2.2

Cancel the common factor.

$\frac{\frac{y (2 x)}{y (3 y^{2})}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 3.2.3

Rewrite the expression.

$\frac{\frac{2 x}{3 y^{2}}}{\frac{9 x y}{8 x^{2} y^{2}}}$

Step 4

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

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Step 4.1

Factor $x$ out of $9 x y$ .

$\frac{\frac{2 x}{3 y^{2}}}{\frac{x (9 y)}{8 x^{2} y^{2}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $8 x^{2} y^{2}$ .

$\frac{\frac{2 x}{3 y^{2}}}{\frac{x (9 y)}{x (8 x y^{2})}}$

Step 4.2.2

Cancel the common factor.

$\frac{\frac{2 x}{3 y^{2}}}{\frac{x (9 y)}{x (8 x y^{2})}}$

Step 4.2.3

Rewrite the expression.

$\frac{\frac{2 x}{3 y^{2}}}{\frac{9 y}{8 x y^{2}}}$

Step 5

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

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Step 5.1

Factor $y$ out of $9 y$ .

$\frac{\frac{2 x}{3 y^{2}}}{\frac{y \cdot 9}{8 x y^{2}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y$ out of $8 x y^{2}$ .

$\frac{\frac{2 x}{3 y^{2}}}{\frac{y \cdot 9}{y (8 x y)}}$

Step 5.2.2

Cancel the common factor.

$\frac{\frac{2 x}{3 y^{2}}}{\frac{y \cdot 9}{y (8 x y)}}$

Step 5.2.3

Rewrite the expression.

$\frac{\frac{2 x}{3 y^{2}}}{\frac{9}{8 x y}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x}{3 y^{2}} \cdot \frac{8 x y}{9}$

Step 7

Combine.

$\frac{2 x (8 x y)}{3 y^{2} \cdot 9}$

Step 8

Multiply $x$ by $x$ by adding the exponents.

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Step 8.1

Move $x$ .

$\frac{2 (x \cdot x) (8 y)}{3 y^{2} \cdot 9}$

Step 8.2

Multiply $x$ by $x$ .

$\frac{2 x^{2} (8 y)}{3 y^{2} \cdot 9}$

Step 9

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

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Step 9.1

Factor $y$ out of $2 x^{2} (8 y)$ .

$\frac{y (2 x^{2} \cdot (8))}{3 y^{2} \cdot 9}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $y$ out of $3 y^{2} \cdot 9$ .

$\frac{y (2 x^{2} \cdot (8))}{y (3 y \cdot 9)}$

Step 9.2.2

Cancel the common factor.

$\frac{y (2 x^{2} \cdot (8))}{y (3 y \cdot 9)}$

Step 9.2.3

Rewrite the expression.

$\frac{2 x^{2} \cdot (8)}{3 y \cdot 9}$

Step 10

Multiply $8$ by $2$ .

$\frac{16 x^{2}}{3 y \cdot 9}$

Step 11

Multiply $9$ by $3$ .

$\frac{16 x^{2}}{27 y}$