Pre-Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

Multiply $y$ by $y$ .

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

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

Step 4

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

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Step 4.1

Factor $5$ out of $15 b y^{2} \cdot 4$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $2 y^{4} (5 b)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $b$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

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

Step 6

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

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Step 6.1

Factor $y^{2}$ out of $3 y^{2} \cdot 4$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y^{2}$ out of $2 y^{4}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

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

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Step 7.1

Factor $2$ out of $3 \cdot 4$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

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

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

Step 8

Multiply $3$ by $2$ .

$\frac{6}{y^{2}}$

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