Pre-Algebra Examples

$\frac{6 x}{5 y} \div \frac{8 x y}{10 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 x}{5 y} \cdot \frac{10 y}{8 x y}$

Step 2

Cancel the common factor of $2 x$ .

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Step 2.1

Factor $2 x$ out of $6 x$ .

$\frac{2 x (3)}{5 y} \cdot \frac{10 y}{8 x y}$

Step 2.2

Factor $2 x$ out of $8 x y$ .

$\frac{2 x (3)}{5 y} \cdot \frac{10 y}{2 x (4 y)}$

Step 2.3

Cancel the common factor.

$\frac{2 x \cdot 3}{5 y} \cdot \frac{10 y}{2 x (4 y)}$

Step 2.4

Rewrite the expression.

$\frac{3}{5 y} \cdot \frac{10 y}{4 y}$

Step 3

Cancel the common factor of $5 y$ .

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Step 3.1

Factor $5 y$ out of $10 y$ .

$\frac{3}{5 y} \cdot \frac{5 y (2)}{4 y}$

Step 3.2

Cancel the common factor.

$\frac{3}{5 y} \cdot \frac{5 y \cdot 2}{4 y}$

Step 3.3

Rewrite the expression.

$3 \frac{2}{4 y}$

Step 4

Combine $3$ and $\frac{2}{4 y}$ .

$\frac{3 \cdot 2}{4 y}$

Step 5

Multiply $3$ by $2$ .

$\frac{6}{4 y}$

Step 6

Cancel the common factor of $6$ and $4$ .

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Step 6.1

Factor $2$ out of $6$ .

$\frac{2 (3)}{4 y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $4 y$ .

$\frac{2 (3)}{2 (2 y)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 (2 y)}$

Step 6.2.3

Rewrite the expression.

$\frac{3}{2 y}$