Basic Math Examples

$\frac{4 a}{15 b} \div \frac{2 a^{5} b^{3}}{5 b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 a}{15 b} \cdot \frac{5 b}{2 a^{5} b^{3}}$

Step 2

Combine.

$\frac{4 a (5 b)}{15 b (2 a^{5} b^{3})}$

Step 3

Multiply $b$ by $b^{3}$ by adding the exponents.

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Step 3.1

Move $b^{3}$ .

$\frac{4 a (5 b)}{15 (b^{3} b) (2 a^{5})}$

Step 3.2

Multiply $b^{3}$ by $b$ .

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Step 3.2.1

Raise $b$ to the power of $1$ .

$\frac{4 a (5 b)}{15 (b^{3} b^{1}) (2 a^{5})}$

Step 3.2.2

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

$\frac{4 a (5 b)}{15 b^{3 + 1} (2 a^{5})}$

$\frac{4 a (5 b)}{15 b^{3 + 1} (2 a^{5})}$

Step 3.3

Add $3$ and $1$ .

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

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

Step 4

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

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Step 4.1

Factor $2$ out of $4 a (5 b)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

Factor $a$ out of $2 a (5 b)$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

Factor $5$ out of $2 (5 b)$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

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

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Step 7.1

Factor $b$ out of $2 (b)$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

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

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

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