Basic Math Examples

$\frac{15 z^{5}}{24 y^{8}} \div \frac{4 z^{2}}{8 y^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{15 z^{5}}{24 y^{8}} \cdot \frac{8 y^{4}}{4 z^{2}}$

Step 2

Combine.

$\frac{15 z^{5} (8 y^{4})}{24 y^{8} (4 z^{2})}$

Step 3

Cancel the common factor of $15$ and $24$ .

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Step 3.1

Factor $3$ out of $15 z^{5} (8 y^{4})$ .

$\frac{3 (5 z^{5} (8 y^{4}))}{24 y^{8} (4 z^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $24 y^{8} (4 z^{2})$ .

$\frac{3 (5 z^{5} (8 y^{4}))}{3 (8 y^{8} (4 z^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (5 z^{5} (8 y^{4}))}{3 (8 y^{8} (4 z^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{5 z^{5} (8 y^{4})}{8 y^{8} (4 z^{2})}$

Step 4

Cancel the common factor of $z^{5}$ and $z^{2}$ .

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Step 4.1

Factor $z^{2}$ out of $5 z^{5} (8 y^{4})$ .

$\frac{z^{2} (5 z^{3} (8 y^{4}))}{8 y^{8} (4 z^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $z^{2}$ out of $8 y^{8} (4 z^{2})$ .

$\frac{z^{2} (5 z^{3} (8 y^{4}))}{z^{2} (8 y^{8} \cdot (4))}$

Step 4.2.2

Cancel the common factor.

$\frac{z^{2} (5 z^{3} (8 y^{4}))}{z^{2} (8 y^{8} \cdot (4))}$

Step 4.2.3

Rewrite the expression.

$\frac{5 z^{3} (8 y^{4})}{8 y^{8} \cdot (4)}$

Step 5

Cancel the common factor of $8$ .

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Step 5.1

Cancel the common factor.

$\frac{5 z^{3} (8 y^{4})}{8 y^{8} \cdot 4}$

Step 5.2

Rewrite the expression.

$\frac{5 z^{3} (y^{4})}{y^{8} \cdot (4)}$

Step 6

Cancel the common factor of $y^{4}$ and $y^{8}$ .

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Step 6.1

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

$\frac{y^{4} (5 z^{3})}{y^{8} \cdot (4)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{4}$ out of $y^{8} \cdot (4)$ .

$\frac{y^{4} (5 z^{3})}{y^{4} (y^{4} \cdot 4)}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{4} (5 z^{3})}{y^{4} (y^{4} \cdot 4)}$

Step 6.2.3

Rewrite the expression.

$\frac{5 z^{3}}{y^{4} \cdot 4}$

Step 7

Move $4$ to the left of $y^{4}$ .

$\frac{5 z^{3}}{4 y^{4}}$