Pre-Algebra Examples

$\frac{4 m^{3}}{n^{2}} \div \frac{2 m}{n}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 m^{3}}{n^{2}} \cdot \frac{n}{2 m}$

Step 2

Combine.

$\frac{4 m^{3} n}{n^{2} (2 m)}$

Step 3

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

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Step 3.1

Factor $2$ out of $4 m^{3} n$ .

$\frac{2 (2 m^{3} n)}{n^{2} (2 m)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $n^{2} (2 m)$ .

$\frac{2 (2 m^{3} n)}{2 (n^{2} (m))}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (2 m^{3} n)}{2 (n^{2} (m))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 m^{3} n}{n^{2} (m)}$

$\frac{2 m^{3} n}{n^{2} (m)}$

$\frac{2 m^{3} n}{n^{2} (m)}$

Step 4

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

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Step 4.1

Factor $m$ out of $2 m^{3} n$ .

$\frac{m (2 m^{2} n)}{n^{2} (m)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m$ out of $n^{2} (m)$ .

$\frac{m (2 m^{2} n)}{m n^{2}}$

Step 4.2.2

Cancel the common factor.

$\frac{m (2 m^{2} n)}{m n^{2}}$

Step 4.2.3

Rewrite the expression.

$\frac{2 m^{2} n}{n^{2}}$

$\frac{2 m^{2} n}{n^{2}}$

$\frac{2 m^{2} n}{n^{2}}$

Step 5

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

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Step 5.1

Factor $n$ out of $2 m^{2} n$ .

$\frac{n (2 m^{2})}{n^{2}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $n$ out of $n^{2}$ .

$\frac{n (2 m^{2})}{n \cdot n}$

Step 5.2.2

Cancel the common factor.

$\frac{n (2 m^{2})}{n \cdot n}$

Step 5.2.3

Rewrite the expression.

$\frac{2 m^{2}}{n}$

$\frac{2 m^{2}}{n}$

$\frac{2 m^{2}}{n}$

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