Basic Math Examples

$\frac{3 y^{2}}{2 y^{5}} \div \frac{9 y^{3}}{4 y^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 y^{2}}{2 y^{5}} \cdot \frac{4 y^{4}}{9 y^{3}}$

Step 2

Combine.

$\frac{3 y^{2} (4 y^{4})}{2 y^{5} (9 y^{3})}$

Step 3

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

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Step 3.1

Move $y^{4}$ .

$\frac{3 (y^{4} y^{2}) \cdot 4}{2 y^{5} (9 y^{3})}$

Step 3.2

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

$\frac{3 y^{4 + 2} \cdot 4}{2 y^{5} (9 y^{3})}$

Step 3.3

Add $4$ and $2$ .

$\frac{3 y^{6} \cdot 4}{2 y^{5} (9 y^{3})}$

Step 4

Multiply $y^{5}$ by $y^{3}$ by adding the exponents.

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Step 4.1

Move $y^{3}$ .

$\frac{3 y^{6} \cdot 4}{2 (y^{3} y^{5}) \cdot 9}$

Step 4.2

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

$\frac{3 y^{6} \cdot 4}{2 y^{3 + 5} \cdot 9}$

Step 4.3

Add $3$ and $5$ .

$\frac{3 y^{6} \cdot 4}{2 y^{8} \cdot 9}$

Step 5

Cancel the common factor of $3$ and $9$ .

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Step 5.1

Factor $3$ out of $3 y^{6} \cdot 4$ .

$\frac{3 (y^{6} \cdot 4)}{2 y^{8} \cdot 9}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $2 y^{8} \cdot 9$ .

$\frac{3 (y^{6} \cdot 4)}{3 (2 y^{8} \cdot 3)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (y^{6} \cdot 4)}{3 (2 y^{8} \cdot 3)}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{6} \cdot 4}{2 y^{8} \cdot 3}$

Step 6

Cancel the common factor of $y^{6}$ and $y^{8}$ .

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Step 6.1

Factor $y^{6}$ out of $y^{6} \cdot 4$ .

$\frac{y^{6} (4)}{2 y^{8} \cdot 3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{6}$ out of $2 y^{8} \cdot 3$ .

$\frac{y^{6} (4)}{y^{6} (2 y^{2} \cdot 3)}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{6} \cdot 4}{y^{6} (2 y^{2} \cdot 3)}$

Step 6.2.3

Rewrite the expression.

$\frac{4}{2 y^{2} \cdot 3}$

Step 7

Cancel the common factor of $4$ and $2$ .

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Step 7.1

Factor $2$ out of $4$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2 y^{2} \cdot 3$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Move $3$ to the left of $y^{2}$ .

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