Basic Math Examples

$\frac{5 y^{4}}{2 a y} \div \frac{15 y}{4 a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 y^{4}}{2 a y} \cdot \frac{4 a}{15 y}$

Step 2

Combine.

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

Step 3

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

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

Step 4

Cancel the common factor of $5$ and $15$ .

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Step 4.1

Factor $5$ out of $5 y^{4} (4 a)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $2 a y^{2} \cdot 15$ .

$\frac{5 (y^{4} (4 a))}{5 (2 a y^{2} \cdot 3)}$

Step 4.2.2

Cancel the common factor.

$\frac{5 (y^{4} (4 a))}{5 (2 a y^{2} \cdot 3)}$

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{2}$ out of $2 a y^{2} \cdot 3$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

Cancel the common factor of $4$ and $2$ .

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 a \cdot 3$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

Cancel the common factor of $a$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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

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

Step 8

Move $2$ to the left of $y^{2}$ .

$\frac{2 y^{2}}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$