Pre-Algebra Examples

$\frac{5 x^{2}}{4 y^{2}} \div 20 x y$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{5 x^{2}}{4 y^{2}}}{20 x y}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 x^{2}}{4 y^{2}} \cdot \frac{1}{20 x y}$

Step 3

Combine.

$\frac{5 x^{2} \cdot 1}{4 y^{2} (20 x y)}$

Step 4

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

$\frac{5 x^{2} \cdot 1}{4 (y \cdot y^{2}) (20 x)}$

Step 4.2

Multiply $y$ by $y^{2}$ .

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Step 4.2.1

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

$\frac{5 x^{2} \cdot 1}{4 (y^{1} y^{2}) (20 x)}$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 x^{2} \cdot 1}{4 y^{1 + 2} (20 x)}$

Step 4.3

Add $1$ and $2$ .

$\frac{5 x^{2} \cdot 1}{4 y^{3} (20 x)}$

Step 5

Multiply $5 x^{2}$ by $1$ .

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

Step 6

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

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Step 6.1

Factor $5$ out of $5 x^{2}$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Multiply $4$ by $4$ .

$\frac{x}{16 y^{3}}$