Pre-Algebra Examples

$\frac{x + 4}{30 x - 70} \cdot \frac{30 x - 70}{2}$

Step 1

Factor $10$ out of $30 x - 70$ .

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Step 1.1

Factor $10$ out of $30 x$ .

$\frac{x + 4}{10 (3 x) - 70} \cdot \frac{30 x - 70}{2}$

Step 1.2

Factor $10$ out of $- 70$ .

$\frac{x + 4}{10 (3 x) + 10 (- 7)} \cdot \frac{30 x - 70}{2}$

Step 1.3

Factor $10$ out of $10 (3 x) + 10 (- 7)$ .

$\frac{x + 4}{10 (3 x - 7)} \cdot \frac{30 x - 70}{2}$

Step 2

Factor $10$ out of $30 x - 70$ .

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Step 2.1

Factor $10$ out of $30 x$ .

$\frac{x + 4}{10 (3 x - 7)} \cdot \frac{10 (3 x) - 70}{2}$

Step 2.2

Factor $10$ out of $- 70$ .

$\frac{x + 4}{10 (3 x - 7)} \cdot \frac{10 (3 x) + 10 (- 7)}{2}$

Step 2.3

Factor $10$ out of $10 (3 x) + 10 (- 7)$ .

$\frac{x + 4}{10 (3 x - 7)} \cdot \frac{10 (3 x - 7)}{2}$

Step 3

Cancel the common factor of $10 (3 x - 7)$ .

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Step 3.1

Cancel the common factor.

$\frac{x + 4}{10 (3 x - 7)} \cdot \frac{10 (3 x - 7)}{2}$

Step 3.2

Rewrite the expression.

$(x + 4) \cdot \frac{1}{2}$

Step 4

Apply the distributive property.

$x \frac{1}{2} + 4 (\frac{1}{2})$

Step 5

Combine $x$ and $\frac{1}{2}$ .

$\frac{x}{2} + 4 (\frac{1}{2})$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $4$ .

$\frac{x}{2} + 2 (2) \frac{1}{2}$

Step 6.2

Cancel the common factor.

$\frac{x}{2} + 2 \cdot 2 \frac{1}{2}$

Step 6.3

Rewrite the expression.

$\frac{x}{2} + 2$

Step 7

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} + 2 \cdot \frac{2}{2}$

Step 8

Combine $2$ and $\frac{2}{2}$ .

$\frac{x}{2} + \frac{2 \cdot 2}{2}$

Step 9

Combine the numerators over the common denominator.

$\frac{x + 2 \cdot 2}{2}$

Step 10

Multiply $2$ by $2$ .

$\frac{x + 4}{2}$