Basic Math Examples

$\frac{8 a^{2}}{3 y^{2}} \div \frac{4 a}{6 y^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 a^{2}}{3 y^{2}} \cdot \frac{6 y^{3}}{4 a}$

Step 2

Combine.

$\frac{8 a^{2} (6 y^{3})}{3 y^{2} (4 a)}$

Step 3

Cancel the common factor of $8$ and $4$ .

Tap for more steps...

Step 3.1

Factor $4$ out of $8 a^{2} (6 y^{3})$ .

$\frac{4 (2 a^{2} (6 y^{3}))}{3 y^{2} (4 a)}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $4$ out of $3 y^{2} (4 a)$ .

$\frac{4 (2 a^{2} (6 y^{3}))}{4 (3 y^{2} (a))}$

Step 3.2.2

Cancel the common factor.

$\frac{4 (2 a^{2} (6 y^{3}))}{4 (3 y^{2} (a))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 a^{2} (6 y^{3})}{3 y^{2} (a)}$

Step 4

Cancel the common factor of $a^{2}$ and $a$ .

Tap for more steps...

Step 4.1

Factor $a$ out of $2 a^{2} (6 y^{3})$ .

$\frac{a (2 a (6 y^{3}))}{3 y^{2} (a)}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $a$ out of $3 y^{2} (a)$ .

$\frac{a (2 a (6 y^{3}))}{a (3 y^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{a (2 a (6 y^{3}))}{a (3 y^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{2 a (6 y^{3})}{3 y^{2}}$

Step 5

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $2 a (6 y^{3})$ .

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $3$ out of $3 y^{2}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $y^{3}$ and $y^{2}$ .

Tap for more steps...

Step 6.1

Factor $y^{2}$ out of $2 a (2 y^{3})$ .

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

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Multiply by $1$ .

$\frac{y^{2} (2 a (2 y))}{y^{2} \cdot 1}$

Step 6.2.2

Cancel the common factor.

$\frac{y^{2} (2 a (2 y))}{y^{2} \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{2 a (2 y)}{1}$

Step 6.2.4

Divide $2 a (2 y)$ by $1$ .

$2 a (2 y)$

Step 7

Simplify the expression.

Tap for more steps...

Step 7.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a y$

Step 7.2

Multiply $2$ by $2$ .

$4 a y$