Pre-Algebra Examples

$\frac{15 x y^{2}}{2 z} \div \frac{5 x^{2} y^{2}}{10 z^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{15 x y^{2}}{2 z} \cdot \frac{10 z^{2}}{5 x^{2} y^{2}}$

Step 2

Combine.

$\frac{15 x y^{2} (10 z^{2})}{2 z (5 x^{2} y^{2})}$

Step 3

Cancel the common factor of $15$ and $5$ .

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Step 3.1

Factor $5$ out of $15 x y^{2} (10 z^{2})$ .

$\frac{5 (3 x y^{2} (10 z^{2}))}{2 z (5 x^{2} y^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{5 (3 x y^{2} (10 z^{2}))}{5 (2 z (x^{2} y^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (3 x y^{2} (10 z^{2}))}{5 (2 z (x^{2} y^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 x y^{2} (10 z^{2})}{2 z (x^{2} y^{2})}$

Step 4

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

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Step 4.1

Factor $x$ out of $3 x y^{2} (10 z^{2})$ .

$\frac{x (3 y^{2} (10 z^{2}))}{2 z (x^{2} y^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{x (3 y^{2} (10 z^{2}))}{x (2 z (x y^{2}))}$

Step 4.2.2

Cancel the common factor.

$\frac{x (3 y^{2} (10 z^{2}))}{x (2 z (x y^{2}))}$

Step 4.2.3

Rewrite the expression.

$\frac{3 y^{2} (10 z^{2})}{2 z (x y^{2})}$

Step 5

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

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Step 5.1

Cancel the common factor.

$\frac{3 y^{2} (10 z^{2})}{2 z (x y^{2})}$

Step 5.2

Rewrite the expression.

$\frac{3 (10 z^{2})}{2 z (x)}$

Step 6

Cancel the common factor of $10$ and $2$ .

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Step 6.1

Factor $2$ out of $3 (10 z^{2})$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 z (x)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

Factor $z$ out of $3 (5 z^{2})$ .

$\frac{z (3 (5 z))}{z (x)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Cancel the common factor.

$\frac{z (3 (5 z))}{z x}$

Step 7.2.2

Rewrite the expression.

$\frac{3 (5 z)}{x}$

Step 8

Multiply $3$ by $5$ .

$\frac{15 z}{x}$