Basic Math Examples

$\frac{8 y}{3 b} \div \frac{2 y^{4}}{9 b y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 y}{3 b} \cdot \frac{9 b y}{2 y^{4}}$

Step 2

Combine.

$\frac{8 y (9 b y)}{3 b (2 y^{4})}$

Step 3

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

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Step 3.1

Move $y$ .

$\frac{8 (y \cdot y) (9 b)}{3 b (2 y^{4})}$

Step 3.2

Multiply $y$ by $y$ .

$\frac{8 y^{2} (9 b)}{3 b (2 y^{4})}$

$\frac{8 y^{2} (9 b)}{3 b (2 y^{4})}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $8$ and $2$ .

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Step 4.1.1

Factor $2$ out of $8 y^{2} (9 b)$ .

$\frac{2 (4 y^{2} (9 b))}{3 b (2 y^{4})}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

$\frac{2 (4 y^{2} (9 b))}{2 (3 b (y^{4}))}$

Step 4.1.2.2

Cancel the common factor.

$\frac{2 (4 y^{2} (9 b))}{2 (3 b (y^{4}))}$

Step 4.1.2.3

Rewrite the expression.

$\frac{4 y^{2} (9 b)}{3 b (y^{4})}$

$\frac{4 y^{2} (9 b)}{3 b (y^{4})}$

$\frac{4 y^{2} (9 b)}{3 b (y^{4})}$

Step 4.2

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

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Step 4.2.1

Factor $y^{2}$ out of $4 y^{2} (9 b)$ .

$\frac{y^{2} (4 (9 b))}{3 b (y^{4})}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

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

$\frac{y^{2} (4 (9 b))}{y^{2} (3 b (y^{2}))}$

Step 4.2.2.2

Cancel the common factor.

$\frac{y^{2} (4 (9 b))}{y^{2} (3 b (y^{2}))}$

Step 4.2.2.3

Rewrite the expression.

$\frac{4 (9 b)}{3 b (y^{2})}$

$\frac{4 (9 b)}{3 b (y^{2})}$

$\frac{4 (9 b)}{3 b (y^{2})}$

Step 4.3

Cancel the common factor of $9$ and $3$ .

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Step 4.3.1

Factor $3$ out of $4 (9 b)$ .

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

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

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

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

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

Step 4.4

Cancel the common factor of $b$ .

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Step 4.4.1

Cancel the common factor.

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

Step 4.4.2

Rewrite the expression.

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

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

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

Step 5

Multiply $4$ by $3$ .

$\frac{12}{y^{2}}$

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