Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Factor $4$ out of $4 a$ .

$\frac{4 (a)}{3 y} \cdot \frac{10 a y}{12 y}$

Step 2.2

Factor $4$ out of $12 y$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

$\frac{a}{3 y} \cdot \frac{10 a y}{3 y}$

Step 3

Cancel the common factor of $y$ .

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Step 3.1

Factor $y$ out of $3 y$ .

$\frac{a}{y \cdot 3} \cdot \frac{10 a y}{3 y}$

Step 3.2

Factor $y$ out of $10 a y$ .

$\frac{a}{y \cdot 3} \cdot \frac{y (10 a)}{3 y}$

Step 3.3

Cancel the common factor.

$\frac{a}{y \cdot 3} \cdot \frac{y (10 a)}{3 y}$

Step 3.4

Rewrite the expression.

$\frac{a}{3} \cdot \frac{10 a}{3 y}$

Step 4

Multiply $\frac{a}{3}$ by $\frac{10 a}{3 y}$ .

$\frac{a (10 a)}{3 (3 y)}$

Step 5

Raise $a$ to the power of $1$ .

$\frac{10 (a^{1} a)}{3 (3 y)}$

Step 6

Raise $a$ to the power of $1$ .

$\frac{10 (a^{1} a^{1})}{3 (3 y)}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 a^{1 + 1}}{3 (3 y)}$

Step 8

Add $1$ and $1$ .

$\frac{10 a^{2}}{3 (3 y)}$

Step 9

Multiply $3$ by $3$ .

$\frac{10 a^{2}}{9 y}$