Basic Math Examples

$\frac{12 y}{a^{3}} \div \frac{4 y^{4}}{3 a^{5} y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12 y}{a^{3}} \cdot \frac{3 a^{5} y}{4 y^{4}}$

Step 2

Combine.

$\frac{12 y (3 a^{5} y)}{a^{3} (4 y^{4})}$

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

$\frac{12 (y \cdot y) (3 a^{5})}{a^{3} (4 y^{4})}$

Step 3.2

Multiply $y$ by $y$ .

$\frac{12 y^{2} (3 a^{5})}{a^{3} (4 y^{4})}$

Step 4

Cancel the common factor of $12$ and $4$ .

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Step 4.1

Factor $4$ out of $12 y^{2} (3 a^{5})$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{2}$ and $y^{4}$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $a^{5}$ and $a^{3}$ .

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

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

Step 7

Simplify the expression.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{3^{2} a^{2}}{y^{2}}$

Step 7.2

Raise $3$ to the power of $2$ .

$\frac{9 a^{2}}{y^{2}}$