Pre-Algebra Examples

$\frac{3 b}{4 a} \div \frac{12 b}{10 a b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 b}{4 a} \cdot \frac{10 a b}{12 b}$

Step 2

Cancel the common factor of $3 b$ .

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Step 2.1

Factor $3 b$ out of $12 b$ .

$\frac{3 b}{4 a} \cdot \frac{10 a b}{3 b (4)}$

Step 2.2

Cancel the common factor.

$\frac{3 b}{4 a} \cdot \frac{10 a b}{3 b \cdot 4}$

Step 2.3

Rewrite the expression.

$\frac{1}{4 a} \cdot \frac{10 a b}{4}$

Step 3

Cancel the common factor of $2 a$ .

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Step 3.1

Factor $2 a$ out of $4 a$ .

$\frac{1}{2 a (2)} \cdot \frac{10 a b}{4}$

Step 3.2

Factor $2 a$ out of $10 a b$ .

$\frac{1}{2 a (2)} \cdot \frac{2 a (5 b)}{4}$

Step 3.3

Cancel the common factor.

$\frac{1}{2 a \cdot 2} \cdot \frac{2 a (5 b)}{4}$

Step 3.4

Rewrite the expression.

$\frac{1}{2} \cdot \frac{5 b}{4}$

Step 4

Multiply $\frac{1}{2}$ by $\frac{5 b}{4}$ .

$\frac{5 b}{2 \cdot 4}$

Step 5

Multiply $2$ by $4$ .

$\frac{5 b}{8}$