Pre-Algebra Examples

$\frac{\frac{6 a^{2} b^{7}}{25 x^{3} y}}{\frac{12 a^{3} b^{4}}{5 x^{2} y^{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 a^{2} b^{7}}{25 x^{3} y} \cdot \frac{5 x^{2} y^{2}}{12 a^{3} b^{4}}$

Step 2

Combine.

$\frac{6 a^{2} b^{7} (5 x^{2} y^{2})}{25 x^{3} y (12 a^{3} b^{4})}$

Step 3

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

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Step 3.1

Factor $6$ out of $6 a^{2} b^{7} (5 x^{2} y^{2})$ .

$\frac{6 (a^{2} b^{7} (5 x^{2} y^{2}))}{25 x^{3} y (12 a^{3} b^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $25 x^{3} y (12 a^{3} b^{4})$ .

$\frac{6 (a^{2} b^{7} (5 x^{2} y^{2}))}{6 (25 x^{3} y (2 a^{3} b^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (a^{2} b^{7} (5 x^{2} y^{2}))}{6 (25 x^{3} y (2 a^{3} b^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{a^{2} b^{7} (5 x^{2} y^{2})}{25 x^{3} y (2 a^{3} b^{4})}$

Step 4

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

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Step 4.1

Factor $a^{2}$ out of $a^{2} b^{7} (5 x^{2} y^{2})$ .

$\frac{a^{2} (b^{7} (5 x^{2} y^{2}))}{25 x^{3} y (2 a^{3} b^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $25 x^{3} y (2 a^{3} b^{4})$ .

$\frac{a^{2} (b^{7} (5 x^{2} y^{2}))}{a^{2} (25 x^{3} y (2 a b^{4}))}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{2} (b^{7} (5 x^{2} y^{2}))}{a^{2} (25 x^{3} y (2 a b^{4}))}$

Step 4.2.3

Rewrite the expression.

$\frac{b^{7} (5 x^{2} y^{2})}{25 x^{3} y (2 a b^{4})}$

Step 5

Cancel the common factor of $b^{7}$ and $b^{4}$ .

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Step 5.1

Factor $b^{4}$ out of $b^{7} (5 x^{2} y^{2})$ .

$\frac{b^{4} (b^{3} (5 x^{2} y^{2}))}{25 x^{3} y (2 a b^{4})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b^{4}$ out of $25 x^{3} y (2 a b^{4})$ .

$\frac{b^{4} (b^{3} (5 x^{2} y^{2}))}{b^{4} (25 x^{3} y (2 a))}$

Step 5.2.2

Cancel the common factor.

$\frac{b^{4} (b^{3} (5 x^{2} y^{2}))}{b^{4} (25 x^{3} y (2 a))}$

Step 5.2.3

Rewrite the expression.

$\frac{b^{3} (5 x^{2} y^{2})}{25 x^{3} y (2 a)}$

Step 6

Cancel the common factor of $5$ and $25$ .

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Step 6.1

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

$\frac{5 (b^{3} (x^{2} y^{2}))}{25 x^{3} y (2 a)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $25 x^{3} y (2 a)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

Factor $x^{2}$ out of $b^{3} (x^{2} y^{2})$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $y$ out of $5 x y (2 a)$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Multiply $2$ by $5$ .

$\frac{b^{3} y}{10 x a}$