Pre-Algebra Examples

$\frac{6 m^{7}}{30 n} \div \frac{12 m^{3} n}{25}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 m^{7}}{30 n} \cdot \frac{25}{12 m^{3} n}$

Step 2

Combine.

$\frac{6 m^{7} \cdot 25}{30 n (12 m^{3} n)}$

Step 3

Multiply $n$ by $n$ by adding the exponents.

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Step 3.1

Move $n$ .

$\frac{6 m^{7} \cdot 25}{30 (n \cdot n) (12 m^{3})}$

Step 3.2

Multiply $n$ by $n$ .

$\frac{6 m^{7} \cdot 25}{30 n^{2} (12 m^{3})}$

Step 4

Cancel the common factor of $6$ and $30$ .

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Step 4.1

Factor $6$ out of $6 m^{7} \cdot 25$ .

$\frac{6 (m^{7} \cdot 25)}{30 n^{2} (12 m^{3})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $6$ out of $30 n^{2} (12 m^{3})$ .

$\frac{6 (m^{7} \cdot 25)}{6 (5 n^{2} (12 m^{3}))}$

Step 4.2.2

Cancel the common factor.

$\frac{6 (m^{7} \cdot 25)}{6 (5 n^{2} (12 m^{3}))}$

Step 4.2.3

Rewrite the expression.

$\frac{m^{7} \cdot 25}{5 n^{2} (12 m^{3})}$

Step 5

Cancel the common factor of $m^{7}$ and $m^{3}$ .

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Step 5.1

Factor $m^{3}$ out of $m^{7} \cdot 25$ .

$\frac{m^{3} (m^{4} \cdot 25)}{5 n^{2} (12 m^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $m^{3}$ out of $5 n^{2} (12 m^{3})$ .

$\frac{m^{3} (m^{4} \cdot 25)}{m^{3} (5 n^{2} \cdot (12))}$

Step 5.2.2

Cancel the common factor.

$\frac{m^{3} (m^{4} \cdot 25)}{m^{3} (5 n^{2} \cdot (12))}$

Step 5.2.3

Rewrite the expression.

$\frac{m^{4} \cdot 25}{5 n^{2} \cdot (12)}$

Step 6

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

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Step 6.1

Factor $5$ out of $m^{4} \cdot 25$ .

$\frac{5 (m^{4} \cdot 5)}{5 n^{2} \cdot (12)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 n^{2} \cdot (12)$ .

$\frac{5 (m^{4} \cdot 5)}{5 (n^{2} \cdot (12))}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (m^{4} \cdot 5)}{5 (n^{2} \cdot (12))}$

Step 6.2.3

Rewrite the expression.

$\frac{m^{4} \cdot 5}{n^{2} \cdot (12)}$

Step 7

Move $5$ to the left of $m^{4}$ .

$\frac{5 \cdot m^{4}}{n^{2} \cdot 12}$

Step 8

Move $12$ to the left of $n^{2}$ .

$\frac{5 m^{4}}{12 n^{2}}$