Pre-Algebra Examples

$\frac{8 m^{2}}{12 m^{3} - 48 m^{2}} \div \frac{6}{12 m - 48}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 m^{2}}{12 m^{3} - 48 m^{2}} \cdot \frac{12 m - 48}{6}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $8 m^{2}$ .

$\frac{2 (4 m^{2})}{12 m^{3} - 48 m^{2}} \cdot \frac{12 m - 48}{6}$

Step 2.1.2

Factor $2$ out of $6$ .

$\frac{2 (4 m^{2})}{12 m^{3} - 48 m^{2}} \cdot \frac{12 m - 48}{2 (3)}$

Step 2.1.3

Cancel the common factor.

$\frac{2 (4 m^{2})}{12 m^{3} - 48 m^{2}} \cdot \frac{12 m - 48}{2 \cdot 3}$

Step 2.1.4

Rewrite the expression.

$\frac{4 m^{2}}{12 m^{3} - 48 m^{2}} \cdot \frac{12 m - 48}{3}$

Step 2.2

Multiply $\frac{4 m^{2}}{12 m^{3} - 48 m^{2}}$ by $\frac{12 m - 48}{3}$ .

$\frac{4 m^{2} (12 m - 48)}{(12 m^{3} - 48 m^{2}) \cdot 3}$

Step 2.3

Cancel the common factor of $12 m - 48$ and $3$ .

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Step 2.3.1

Factor $3$ out of $4 m^{2} (12 m - 48)$ .

$\frac{3 (4 m^{2} (4 m - 16))}{(12 m^{3} - 48 m^{2}) \cdot 3}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $3$ out of $(12 m^{3} - 48 m^{2}) \cdot 3$ .

$\frac{3 (4 m^{2} (4 m - 16))}{3 ((4 m^{3} - 16 m^{2}) \cdot 3)}$

Step 2.3.2.2

Cancel the common factor.

$\frac{3 (4 m^{2} (4 m - 16))}{3 ((4 m^{3} - 16 m^{2}) \cdot 3)}$

Step 2.3.2.3

Rewrite the expression.

$\frac{4 m^{2} (4 m - 16)}{(4 m^{3} - 16 m^{2}) \cdot 3}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $4$ out of $4 m - 16$ .

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Step 3.1.1

Factor $4$ out of $4 m$ .

$\frac{4 m^{2} (4 (m) - 16)}{(4 m^{3} - 16 m^{2}) \cdot 3}$

Step 3.1.2

Factor $4$ out of $- 16$ .

$\frac{4 m^{2} (4 m + 4 \cdot - 4)}{(4 m^{3} - 16 m^{2}) \cdot 3}$

Step 3.1.3

Factor $4$ out of $4 m + 4 \cdot - 4$ .

$\frac{4 m^{2} (4 (m - 4))}{(4 m^{3} - 16 m^{2}) \cdot 3}$

$\frac{4 m^{2} \cdot 4 (m - 4)}{(4 m^{3} - 16 m^{2}) \cdot 3}$

Step 3.2

Multiply $4$ by $4$ .

$\frac{16 m^{2} (m - 4)}{(4 m^{3} - 16 m^{2}) \cdot 3}$

Step 4

Simplify the denominator.

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Step 4.1

Factor $4 m^{2}$ out of $4 m^{3} - 16 m^{2}$ .

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Step 4.1.1

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

$\frac{16 m^{2} (m - 4)}{(4 m^{2} (m) - 16 m^{2}) \cdot 3}$

Step 4.1.2

Factor $4 m^{2}$ out of $- 16 m^{2}$ .

$\frac{16 m^{2} (m - 4)}{(4 m^{2} (m) + 4 m^{2} (- 4)) \cdot 3}$

Step 4.1.3

Factor $4 m^{2}$ out of $4 m^{2} (m) + 4 m^{2} (- 4)$ .

$\frac{16 m^{2} (m - 4)}{4 m^{2} (m - 4) \cdot 3}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{16 m^{2} (m - 4)}{12 m^{2} (m - 4)}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $16$ and $12$ .

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Step 5.1.1

Factor $4$ out of $16 m^{2} (m - 4)$ .

$\frac{4 (4 m^{2} (m - 4))}{12 m^{2} (m - 4)}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $4$ out of $12 m^{2} (m - 4)$ .

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

Step 5.1.2.2

Cancel the common factor.

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

Step 5.1.2.3

Rewrite the expression.

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

Step 5.2

Cancel the common factor of $m^{2}$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Rewrite the expression.

$\frac{4 (m - 4)}{3 (m - 4)}$

Step 5.3

Cancel the common factor of $m - 4$ .

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Step 5.3.1

Cancel the common factor.

$\frac{4 (m - 4)}{3 (m - 4)}$

Step 5.3.2

Rewrite the expression.

$\frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$