Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Combine.

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

Step 3

Multiply $b$ by $b$ by adding the exponents.

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Step 3.1

Move $b$ .

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

Step 3.2

Multiply $b$ by $b$ .

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

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

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Step 4.1.1

Factor $5$ out of $15 b^{2} (4 a)$ .

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

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

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

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

Step 4.2

Cancel the common factor of $b^{2}$ and $b^{5}$ .

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

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

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

Step 4.2.2.2

Cancel the common factor.

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

Step 4.2.2.3

Rewrite the expression.

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

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

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

Step 4.3

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

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Step 4.3.1

Factor $2$ out of $3 (4 a)$ .

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

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

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

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

Step 4.3.2.2

Cancel the common factor.

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

Step 4.3.2.3

Rewrite the expression.

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

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

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

Step 4.4

Cancel the common factor of $a$ .

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Step 4.4.1

Cancel the common factor.

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

Step 4.4.2

Rewrite the expression.

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

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

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

Step 5

Multiply $3$ by $2$ .

$\frac{6}{b^{3}}$

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