Pre-Algebra Examples

$(2 n^{3} + 3 n^{2} + 24 n) \div 6 n^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{2 n^{3} + 3 n^{2} + 24 n}{6 n^{2}}$

Step 2

Factor $n$ out of $2 n^{3} + 3 n^{2} + 24 n$ .

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Step 2.1

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

$\frac{n (2 n^{2}) + 3 n^{2} + 24 n}{6 n^{2}}$

Step 2.2

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

$\frac{n (2 n^{2}) + n (3 n) + 24 n}{6 n^{2}}$

Step 2.3

Factor $n$ out of $24 n$ .

$\frac{n (2 n^{2}) + n (3 n) + n \cdot 24}{6 n^{2}}$

Step 2.4

Factor $n$ out of $n (2 n^{2}) + n (3 n)$ .

$\frac{n (2 n^{2} + 3 n) + n \cdot 24}{6 n^{2}}$

Step 2.5

Factor $n$ out of $n (2 n^{2} + 3 n) + n \cdot 24$ .

$\frac{n (2 n^{2} + 3 n + 24)}{6 n^{2}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $n$ out of $6 n^{2}$ .

$\frac{n (2 n^{2} + 3 n + 24)}{n (6 n)}$

Step 3.2

Cancel the common factor.

$\frac{n (2 n^{2} + 3 n + 24)}{n (6 n)}$

Step 3.3

Rewrite the expression.

$\frac{2 n^{2} + 3 n + 24}{6 n}$

Step 4

Split the fraction $\frac{2 n^{2} + 3 n + 24}{6 n}$ into two fractions.

$\frac{2 n^{2} + 3 n}{6 n} + \frac{24}{6 n}$

Step 5

Split the fraction $\frac{2 n^{2} + 3 n}{6 n}$ into two fractions.

$\frac{2 n^{2}}{6 n} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 6

Cancel the common factor of $2$ and $6$ .

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Step 6.1

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

$\frac{2 (n^{2})}{6 n} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $6 n$ .

$\frac{2 (n^{2})}{2 (3 n)} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 6.2.2

Cancel the common factor.

$\frac{2 n^{2}}{2 (3 n)} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 6.2.3

Rewrite the expression.

$\frac{n^{2}}{3 n} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 7

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

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Step 7.1

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

$\frac{n \cdot n}{3 n} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $n$ out of $3 n$ .

$\frac{n \cdot n}{n \cdot 3} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 7.2.2

Cancel the common factor.

$\frac{n \cdot n}{n \cdot 3} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 7.2.3

Rewrite the expression.

$\frac{n}{3} + \frac{3 n}{6 n} + \frac{24}{6 n}$

Step 8

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

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Step 8.1

Factor $3$ out of $3 n$ .

$\frac{n}{3} + \frac{3 (n)}{6 n} + \frac{24}{6 n}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $6 n$ .

$\frac{n}{3} + \frac{3 (n)}{3 (2 n)} + \frac{24}{6 n}$

Step 8.2.2

Cancel the common factor.

$\frac{n}{3} + \frac{3 n}{3 (2 n)} + \frac{24}{6 n}$

Step 8.2.3

Rewrite the expression.

$\frac{n}{3} + \frac{n}{2 n} + \frac{24}{6 n}$

Step 9

Cancel the common factor of $n$ .

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Step 9.1

Cancel the common factor.

$\frac{n}{3} + \frac{n}{2 n} + \frac{24}{6 n}$

Step 9.2

Rewrite the expression.

$\frac{n}{3} + \frac{1}{2} + \frac{24}{6 n}$

Step 10

Cancel the common factor of $24$ and $6$ .

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Step 10.1

Factor $6$ out of $24$ .

$\frac{n}{3} + \frac{1}{2} + \frac{6 \cdot 4}{6 n}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $6$ out of $6 n$ .

$\frac{n}{3} + \frac{1}{2} + \frac{6 \cdot 4}{6 (n)}$

Step 10.2.2

Cancel the common factor.

$\frac{n}{3} + \frac{1}{2} + \frac{6 \cdot 4}{6 n}$

Step 10.2.3

Rewrite the expression.

$\frac{n}{3} + \frac{1}{2} + \frac{4}{n}$