Basic Math Examples

$\frac{6 c^{3} y^{4}}{12 a^{4} b^{2}} \div \frac{36 c^{4} y^{2}}{16 a^{9} b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 c^{3} y^{4}}{12 a^{4} b^{2}} \cdot \frac{16 a^{9} b}{36 c^{4} y^{2}}$

Step 2

Combine.

$\frac{6 c^{3} y^{4} (16 a^{9} b)}{12 a^{4} b^{2} (36 c^{4} y^{2})}$

Step 3

Cancel the common factor of $6$ and $12$ .

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Step 3.1

Factor $6$ out of $6 c^{3} y^{4} (16 a^{9} b)$ .

$\frac{6 (c^{3} y^{4} (16 a^{9} b))}{12 a^{4} b^{2} (36 c^{4} y^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $12 a^{4} b^{2} (36 c^{4} y^{2})$ .

$\frac{6 (c^{3} y^{4} (16 a^{9} b))}{6 (2 a^{4} b^{2} (36 c^{4} y^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (c^{3} y^{4} (16 a^{9} b))}{6 (2 a^{4} b^{2} (36 c^{4} y^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{c^{3} y^{4} (16 a^{9} b)}{2 a^{4} b^{2} (36 c^{4} y^{2})}$

Step 4

Cancel the common factor of $c^{3}$ and $c^{4}$ .

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Step 4.1

Factor $c^{3}$ out of $c^{3} y^{4} (16 a^{9} b)$ .

$\frac{c^{3} (y^{4} (16 a^{9} b))}{2 a^{4} b^{2} (36 c^{4} y^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{3}$ out of $2 a^{4} b^{2} (36 c^{4} y^{2})$ .

$\frac{c^{3} (y^{4} (16 a^{9} b))}{c^{3} (2 a^{4} b^{2} (36 c y^{2}))}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{3} (y^{4} (16 a^{9} b))}{c^{3} (2 a^{4} b^{2} (36 c y^{2}))}$

Step 4.2.3

Rewrite the expression.

$\frac{y^{4} (16 a^{9} b)}{2 a^{4} b^{2} (36 c y^{2})}$

Step 5

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

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Step 5.1

Factor $y^{2}$ out of $y^{4} (16 a^{9} b)$ .

$\frac{y^{2} (y^{2} (16 a^{9} b))}{2 a^{4} b^{2} (36 c y^{2})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{2}$ out of $2 a^{4} b^{2} (36 c y^{2})$ .

$\frac{y^{2} (y^{2} (16 a^{9} b))}{y^{2} (2 a^{4} b^{2} (36 c))}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{2} (y^{2} (16 a^{9} b))}{y^{2} (2 a^{4} b^{2} (36 c))}$

Step 5.2.3

Rewrite the expression.

$\frac{y^{2} (16 a^{9} b)}{2 a^{4} b^{2} (36 c)}$

Step 6

Cancel the common factor of $16$ and $2$ .

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Step 6.1

Factor $2$ out of $y^{2} (16 a^{9} b)$ .

$\frac{2 (y^{2} (8 a^{9} b))}{2 a^{4} b^{2} (36 c)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 a^{4} b^{2} (36 c)$ .

$\frac{2 (y^{2} (8 a^{9} b))}{2 (a^{4} b^{2} (36 c))}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (y^{2} (8 a^{9} b))}{2 (a^{4} b^{2} (36 c))}$

Step 6.2.3

Rewrite the expression.

$\frac{y^{2} (8 a^{9} b)}{a^{4} b^{2} (36 c)}$

Step 7

Cancel the common factor of $8$ and $36$ .

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Step 7.1

Factor $4$ out of $y^{2} (8 a^{9} b)$ .

$\frac{4 (y^{2} (2 a^{9} b))}{a^{4} b^{2} (36 c)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $a^{4} b^{2} (36 c)$ .

$\frac{4 (y^{2} (2 a^{9} b))}{4 (a^{4} b^{2} (9 c))}$

Step 7.2.2

Cancel the common factor.

$\frac{4 (y^{2} (2 a^{9} b))}{4 (a^{4} b^{2} (9 c))}$

Step 7.2.3

Rewrite the expression.

$\frac{y^{2} (2 a^{9} b)}{a^{4} b^{2} (9 c)}$

Step 8

Cancel the common factor of $a^{9}$ and $a^{4}$ .

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Step 8.1

Factor $a^{4}$ out of $y^{2} (2 a^{9} b)$ .

$\frac{a^{4} (y^{2} (2 a^{5} b))}{a^{4} b^{2} (9 c)}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $a^{4}$ out of $a^{4} b^{2} (9 c)$ .

$\frac{a^{4} (y^{2} (2 a^{5} b))}{a^{4} (b^{2} (9 c))}$

Step 8.2.2

Cancel the common factor.

$\frac{a^{4} (y^{2} (2 a^{5} b))}{a^{4} (b^{2} (9 c))}$

Step 8.2.3

Rewrite the expression.

$\frac{y^{2} (2 a^{5} b)}{b^{2} (9 c)}$

Step 9

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

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Step 9.1

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

$\frac{b (y^{2} (2 a^{5}))}{b^{2} (9 c)}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $b$ out of $b^{2} (9 c)$ .

$\frac{b (y^{2} (2 a^{5}))}{b (b (9 c))}$

Step 9.2.2

Cancel the common factor.

$\frac{b (y^{2} (2 a^{5}))}{b (b (9 c))}$

Step 9.2.3

Rewrite the expression.

$\frac{y^{2} (2 a^{5})}{b (9 c)}$

Step 10

Reorder.

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Step 10.1

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

$\frac{2 \cdot y^{2} a^{5}}{b \cdot 9 c}$

Step 10.2

Move $9$ to the left of $b$ .

$\frac{2 y^{2} a^{5}}{9 b c}$