Basic Math Examples

$\frac{5 y^{3}}{7} \div \frac{14 y}{30 y^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 y^{3}}{7} \cdot \frac{30 y^{2}}{14 y}$

Step 2

Combine.

$\frac{5 y^{3} (30 y^{2})}{7 (14 y)}$

Step 3

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $y^{2}$ .

$\frac{5 (y^{2} y^{3}) \cdot 30}{7 (14 y)}$

Step 3.2

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

$\frac{5 y^{2 + 3} \cdot 30}{7 (14 y)}$

Step 3.3

Add $2$ and $3$ .

$\frac{5 y^{5} \cdot 30}{7 (14 y)}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of $y^{5}$ and $y$ .

Tap for more steps...

Step 4.1.1

Factor $y$ out of $5 y^{5} \cdot 30$ .

$\frac{y (5 y^{4} \cdot 30)}{7 (14 y)}$

Step 4.1.2

Cancel the common factors.

Tap for more steps...

Step 4.1.2.1

Factor $y$ out of $7 (14 y)$ .

$\frac{y (5 y^{4} \cdot 30)}{y (7 \cdot (14))}$

Step 4.1.2.2

Cancel the common factor.

$\frac{y (5 y^{4} \cdot 30)}{y (7 \cdot (14))}$

Step 4.1.2.3

Rewrite the expression.

$\frac{5 y^{4} \cdot 30}{7 \cdot (14)}$

Step 4.2

Cancel the common factor of $30$ and $14$ .

Tap for more steps...

Step 4.2.1

Factor $2$ out of $5 y^{4} \cdot 30$ .

$\frac{2 (5 y^{4} \cdot 15)}{7 \cdot (14)}$

Step 4.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.2.1

Factor $2$ out of $7 \cdot (14)$ .

$\frac{2 (5 y^{4} \cdot 15)}{2 (7 \cdot (7))}$

Step 4.2.2.2

Cancel the common factor.

$\frac{2 (5 y^{4} \cdot 15)}{2 (7 \cdot (7))}$

Step 4.2.2.3

Rewrite the expression.

$\frac{5 y^{4} \cdot 15}{7 \cdot (7)}$

Step 4.3

Multiply $15$ by $5$ .

$\frac{75 y^{4}}{7 \cdot (7)}$

Step 5

Multiply $7$ by $7$ .

$\frac{75 y^{4}}{49}$