Pre-Algebra Examples

$\frac{5 x^{2}}{9 y^{3}} \cdot \frac{18 y}{20 x^{4}}$

Step 1

Combine.

$\frac{5 x^{2} (18 y)}{9 y^{3} (20 x^{4})}$

Step 2

Cancel the common factor of $5$ and $20$ .

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Step 2.1

Factor $5$ out of $5 x^{2} (18 y)$ .

$\frac{5 (x^{2} (18 y))}{9 y^{3} (20 x^{4})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $9 y^{3} (20 x^{4})$ .

$\frac{5 (x^{2} (18 y))}{5 (9 y^{3} (4 x^{4}))}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (x^{2} (18 y))}{5 (9 y^{3} (4 x^{4}))}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2} (18 y)}{9 y^{3} (4 x^{4})}$

$\frac{x^{2} (18 y)}{9 y^{3} (4 x^{4})}$

$\frac{x^{2} (18 y)}{9 y^{3} (4 x^{4})}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $x^{2}$ out of $9 y^{3} (4 x^{4})$ .

$\frac{x^{2} (18 y)}{x^{2} (9 y^{3} (4 x^{2}))}$

Step 3.2

Cancel the common factor.

$\frac{x^{2} (18 y)}{x^{2} (9 y^{3} (4 x^{2}))}$

Step 3.3

Rewrite the expression.

$\frac{18 y}{9 y^{3} (4 x^{2})}$

$\frac{18 y}{9 y^{3} (4 x^{2})}$

Step 4

Cancel the common factor of $18$ and $9$ .

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Step 4.1

Factor $9$ out of $18 y$ .

$\frac{9 (2 y)}{9 y^{3} (4 x^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $9$ out of $9 y^{3} (4 x^{2})$ .

$\frac{9 (2 y)}{9 (y^{3} (4 x^{2}))}$

Step 4.2.2

Cancel the common factor.

$\frac{9 (2 y)}{9 (y^{3} (4 x^{2}))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 y}{y^{3} (4 x^{2})}$

$\frac{2 y}{y^{3} (4 x^{2})}$

$\frac{2 y}{y^{3} (4 x^{2})}$

Step 5

Cancel the common factor of $2$ and $4$ .

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Step 5.1

Factor $2$ out of $2 y$ .

$\frac{2 (y)}{y^{3} (4 x^{2})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $y^{3} (4 x^{2})$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

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

$\frac{y^{1}}{y^{3} (2 x^{2})}$

Step 6.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1}{y^{3} (2 x^{2})}$

Step 6.3

Cancel the common factors.

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Step 6.3.1

Factor $y$ out of $y^{3} (2 x^{2})$ .

$\frac{y \cdot 1}{y (y^{2} (2 x^{2}))}$

Step 6.3.2

Cancel the common factor.

$\frac{y \cdot 1}{y (y^{2} (2 x^{2}))}$

Step 6.3.3

Rewrite the expression.

$\frac{1}{y^{2} (2 x^{2})}$

$\frac{1}{y^{2} (2 x^{2})}$

$\frac{1}{y^{2} (2 x^{2})}$

Step 7

Move $2$ to the left of $y^{2}$ .

$\frac{1}{2 y^{2} x^{2}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$