Pre-Algebra Examples

$\frac{4 x}{9} \div \frac{20 x + 40}{9 x + 18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 x}{9} \cdot \frac{9 x + 18}{20 x + 40}$

Step 2

Factor $9$ out of $9 x + 18$ .

Tap for more steps...

Step 2.1

Factor $9$ out of $9 x$ .

$\frac{4 x}{9} \cdot \frac{9 (x) + 18}{20 x + 40}$

Step 2.2

Factor $9$ out of $18$ .

$\frac{4 x}{9} \cdot \frac{9 x + 9 \cdot 2}{20 x + 40}$

Step 2.3

Factor $9$ out of $9 x + 9 \cdot 2$ .

$\frac{4 x}{9} \cdot \frac{9 (x + 2)}{20 x + 40}$

Step 3

Factor $20$ out of $20 x + 40$ .

Tap for more steps...

Step 3.1

Factor $20$ out of $20 x$ .

$\frac{4 x}{9} \cdot \frac{9 (x + 2)}{20 (x) + 40}$

Step 3.2

Factor $20$ out of $40$ .

$\frac{4 x}{9} \cdot \frac{9 (x + 2)}{20 x + 20 \cdot 2}$

Step 3.3

Factor $20$ out of $20 x + 20 \cdot 2$ .

$\frac{4 x}{9} \cdot \frac{9 (x + 2)}{20 (x + 2)}$

Step 4

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $4 x$ .

$\frac{4 (x)}{9} \cdot \frac{9 (x + 2)}{20 (x + 2)}$

Step 4.2

Factor $4$ out of $20 (x + 2)$ .

$\frac{4 (x)}{9} \cdot \frac{9 (x + 2)}{4 (5 (x + 2))}$

Step 4.3

Cancel the common factor.

$\frac{4 x}{9} \cdot \frac{9 (x + 2)}{4 (5 (x + 2))}$

Step 4.4

Rewrite the expression.

$\frac{x}{9} \cdot \frac{9 (x + 2)}{5 (x + 2)}$

Step 5

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{x}{9} \cdot \frac{9 (x + 2)}{5 (x + 2)}$

Step 5.2

Rewrite the expression.

$x \frac{x + 2}{5 (x + 2)}$

Step 6

Combine $x$ and $\frac{x + 2}{5 (x + 2)}$ .

$\frac{x (x + 2)}{5 (x + 2)}$

Step 7

Cancel the common factor of $x + 2$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{x (x + 2)}{5 (x + 2)}$

Step 7.2

Rewrite the expression.

$\frac{x}{5}$