Pre-Algebra Examples

$\frac{12 y^{3}}{a^{5} y} \div \frac{10 y}{3 a^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12 y^{3}}{a^{5} y} \cdot \frac{3 a^{3}}{10 y}$

Step 2

Combine.

$\frac{12 y^{3} (3 a^{3})}{a^{5} y (10 y)}$

Step 3

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

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Step 3.1

Move $y$ .

$\frac{12 y^{3} (3 a^{3})}{a^{5} (y \cdot y) \cdot 10}$

Step 3.2

Multiply $y$ by $y$ .

$\frac{12 y^{3} (3 a^{3})}{a^{5} y^{2} \cdot 10}$

Step 4

Cancel the common factor of $12$ and $10$ .

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Step 4.1

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

$\frac{2 (6 y^{3} (3 a^{3}))}{a^{5} y^{2} \cdot 10}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $a^{5} y^{2} \cdot 10$ .

$\frac{2 (6 y^{3} (3 a^{3}))}{2 (a^{5} y^{2} \cdot 5)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (6 y^{3} (3 a^{3}))}{2 (a^{5} y^{2} \cdot 5)}$

Step 4.2.3

Rewrite the expression.

$\frac{6 y^{3} (3 a^{3})}{a^{5} y^{2} \cdot 5}$

Step 5

Cancel the common factor of $y^{3}$ and $y^{2}$ .

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Step 5.1

Factor $y^{2}$ out of $6 y^{3} (3 a^{3})$ .

$\frac{y^{2} (6 y (3 a^{3}))}{a^{5} y^{2} \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{2}$ out of $a^{5} y^{2} \cdot 5$ .

$\frac{y^{2} (6 y (3 a^{3}))}{y^{2} (a^{5} \cdot 5)}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{2} (6 y (3 a^{3}))}{y^{2} (a^{5} \cdot 5)}$

Step 5.2.3

Rewrite the expression.

$\frac{6 y (3 a^{3})}{a^{5} \cdot 5}$

Step 6

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

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Step 6.1

Factor $a^{3}$ out of $6 y (3 a^{3})$ .

$\frac{a^{3} (6 y \cdot (3))}{a^{5} \cdot 5}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $a^{3}$ out of $a^{5} \cdot 5$ .

$\frac{a^{3} (6 y \cdot (3))}{a^{3} (a^{2} \cdot 5)}$

Step 6.2.2

Cancel the common factor.

$\frac{a^{3} (6 y \cdot (3))}{a^{3} (a^{2} \cdot 5)}$

Step 6.2.3

Rewrite the expression.

$\frac{6 y \cdot (3)}{a^{2} \cdot 5}$

Step 7

Multiply $3$ by $6$ .

$\frac{18 y}{a^{2} \cdot 5}$

Step 8

Move $5$ to the left of $a^{2}$ .

$\frac{18 y}{5 a^{2}}$