Algebra Examples

$\frac{28 n + 40}{35 n + 50} \cdot \frac{12 n + 24}{8 n + 16}$

Step 1

Factor $4$ out of $28 n + 40$ .

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Step 1.1

Factor $4$ out of $28 n$ .

$\frac{4 (7 n) + 40}{35 n + 50} \cdot \frac{12 n + 24}{8 n + 16}$

Step 1.2

Factor $4$ out of $40$ .

$\frac{4 (7 n) + 4 (10)}{35 n + 50} \cdot \frac{12 n + 24}{8 n + 16}$

Step 1.3

Factor $4$ out of $4 (7 n) + 4 (10)$ .

$\frac{4 (7 n + 10)}{35 n + 50} \cdot \frac{12 n + 24}{8 n + 16}$

Step 2

Factor $5$ out of $35 n + 50$ .

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Step 2.1

Factor $5$ out of $35 n$ .

$\frac{4 (7 n + 10)}{5 (7 n) + 50} \cdot \frac{12 n + 24}{8 n + 16}$

Step 2.2

Factor $5$ out of $50$ .

$\frac{4 (7 n + 10)}{5 (7 n) + 5 (10)} \cdot \frac{12 n + 24}{8 n + 16}$

Step 2.3

Factor $5$ out of $5 (7 n) + 5 (10)$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 n + 24}{8 n + 16}$

Step 3

Factor $12$ out of $12 n + 24$ .

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Step 3.1

Factor $12$ out of $12 n$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n) + 24}{8 n + 16}$

Step 3.2

Factor $12$ out of $24$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 n + 12 \cdot 2}{8 n + 16}$

Step 3.3

Factor $12$ out of $12 n + 12 \cdot 2$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{8 n + 16}$

Step 4

Factor $8$ out of $8 n + 16$ .

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Step 4.1

Factor $8$ out of $8 n$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{8 (n) + 16}$

Step 4.2

Factor $8$ out of $16$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{8 n + 8 \cdot 2}$

Step 4.3

Factor $8$ out of $8 n + 8 \cdot 2$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{8 (n + 2)}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $8 (n + 2)$ .

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{4 (2 (n + 2))}$

Step 5.2

Cancel the common factor.

$\frac{4 (7 n + 10)}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{4 (2 (n + 2))}$

Step 5.3

Rewrite the expression.

$\frac{7 n + 10}{5 (7 n + 10)} \cdot \frac{12 (n + 2)}{2 (n + 2)}$

Step 6

Multiply $\frac{7 n + 10}{5 (7 n + 10)}$ by $\frac{12 (n + 2)}{2 (n + 2)}$ .

$\frac{(7 n + 10) (12 (n + 2))}{5 (7 n + 10) (2 (n + 2))}$

Step 7

Multiply $2$ by $5$ .

$\frac{(7 n + 10) (12 (n + 2))}{10 (7 n + 10) (n + 2)}$

Step 8

Cancel the common factor of $7 n + 10$ .

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Step 8.1

Cancel the common factor.

$\frac{(7 n + 10) (12 (n + 2))}{10 (7 n + 10) (n + 2)}$

Step 8.2

Rewrite the expression.

$\frac{12 (n + 2)}{10 (n + 2)}$

Step 9

Cancel the common factor of $12$ and $10$ .

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Step 9.1

Factor $2$ out of $12 (n + 2)$ .

$\frac{2 (6 (n + 2))}{10 (n + 2)}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $10 (n + 2)$ .

$\frac{2 (6 (n + 2))}{2 (5 (n + 2))}$

Step 9.2.2

Cancel the common factor.

$\frac{2 (6 (n + 2))}{2 (5 (n + 2))}$

Step 9.2.3

Rewrite the expression.

$\frac{6 (n + 2)}{5 (n + 2)}$

Step 10

Cancel the common factor of $n + 2$ .

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Step 10.1

Cancel the common factor.

$\frac{6 (n + 2)}{5 (n + 2)}$

Step 10.2

Rewrite the expression.

$\frac{6}{5}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{5}$

Decimal Form:

$1.2$

Mixed Number Form:

$1 \frac{1}{5}$