Pre-Algebra Examples

$\frac{80 x + 50}{6} \div \frac{96 x + 60}{6 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{80 x + 50}{6} \cdot \frac{6 x}{96 x + 60}$

Step 2

Cancel the common factor of $6$ .

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Step 2.1

Factor $6$ out of $6 x$ .

$\frac{80 x + 50}{6} \cdot \frac{6 (x)}{96 x + 60}$

Step 2.2

Cancel the common factor.

$\frac{80 x + 50}{6} \cdot \frac{6 x}{96 x + 60}$

Step 2.3

Rewrite the expression.

$(80 x + 50) \frac{x}{96 x + 60}$

Step 3

Factor $12$ out of $96 x + 60$ .

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Step 3.1

Factor $12$ out of $96 x$ .

$(80 x + 50) \frac{x}{12 (8 x) + 60}$

Step 3.2

Factor $12$ out of $60$ .

$(80 x + 50) \frac{x}{12 (8 x) + 12 (5)}$

Step 3.3

Factor $12$ out of $12 (8 x) + 12 (5)$ .

$(80 x + 50) \frac{x}{12 (8 x + 5)}$

Step 4

Multiply $80 x + 50$ by $\frac{x}{12 (8 x + 5)}$ .

$\frac{(80 x + 50) x}{12 (8 x + 5)}$

Step 5

Cancel the common factor of $80 x + 50$ and $12$ .

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Step 5.1

Factor $2$ out of $(80 x + 50) x$ .

$\frac{2 ((40 x + 25) x)}{12 (8 x + 5)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $12 (8 x + 5)$ .

$\frac{2 ((40 x + 25) x)}{2 (6 (8 x + 5))}$

Step 5.2.2

Cancel the common factor.

$\frac{2 ((40 x + 25) x)}{2 (6 (8 x + 5))}$

Step 5.2.3

Rewrite the expression.

$\frac{(40 x + 25) x}{6 (8 x + 5)}$

Step 6

Factor $5$ out of $40 x + 25$ .

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Step 6.1

Factor $5$ out of $40 x$ .

$\frac{(5 (8 x) + 25) x}{6 (8 x + 5)}$

Step 6.2

Factor $5$ out of $25$ .

$\frac{(5 (8 x) + 5 (5)) x}{6 (8 x + 5)}$

Step 6.3

Factor $5$ out of $5 (8 x) + 5 (5)$ .

$\frac{5 (8 x + 5) x}{6 (8 x + 5)}$

Step 7

Cancel the common factor of $8 x + 5$ .

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Step 7.1

Cancel the common factor.

$\frac{5 (8 x + 5) x}{6 (8 x + 5)}$

Step 7.2

Rewrite the expression.

$\frac{5 x}{6}$