Pre-Algebra Examples

$\frac{\frac{6 a^{2}}{b^{3}}}{\frac{3 a}{2 b}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 a^{2}}{b^{3}} \cdot \frac{2 b}{3 a}$

Step 2

Combine.

$\frac{6 a^{2} (2 b)}{b^{3} (3 a)}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

Factor $b$ out of $2 a (2 b)$ .

$\frac{b (2 a \cdot (2))}{b^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $b$ out of $b^{3}$ .

$\frac{b (2 a \cdot (2))}{b \cdot b^{2}}$

Step 5.2.2

Cancel the common factor.

$\frac{b (2 a \cdot (2))}{b \cdot b^{2}}$

Step 5.2.3

Rewrite the expression.

$\frac{2 a \cdot (2)}{b^{2}}$

$\frac{2 a \cdot (2)}{b^{2}}$

$\frac{2 a \cdot (2)}{b^{2}}$

Step 6

Multiply $2$ by $2$ .

$\frac{4 a}{b^{2}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$