Pre-Algebra Examples

$\frac{2 y}{3 a y} \div \frac{6 y}{15 a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 y}{3 a y} \cdot \frac{15 a}{6 y}$

Step 2

Cancel the common factor of $2 y$ .

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Step 2.1

Factor $2 y$ out of $6 y$ .

$\frac{2 y}{3 a y} \cdot \frac{15 a}{2 y (3)}$

Step 2.2

Cancel the common factor.

$\frac{2 y}{3 a y} \cdot \frac{15 a}{2 y \cdot 3}$

Step 2.3

Rewrite the expression.

$\frac{1}{3 a y} \cdot \frac{15 a}{3}$

Step 3

Cancel the common factor of $3 a$ .

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Step 3.1

Factor $3 a$ out of $3 a y$ .

$\frac{1}{3 a (y)} \cdot \frac{15 a}{3}$

Step 3.2

Factor $3 a$ out of $15 a$ .

$\frac{1}{3 a (y)} \cdot \frac{3 a (5)}{3}$

Step 3.3

Cancel the common factor.

$\frac{1}{3 a y} \cdot \frac{3 a \cdot 5}{3}$

Step 3.4

Rewrite the expression.

$\frac{1}{y} \cdot \frac{5}{3}$

Step 4

Multiply $\frac{1}{y}$ by $\frac{5}{3}$ .

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

Step 5

Move $3$ to the left of $y$ .

$\frac{5}{3 y}$