Basic Math Examples

$\frac{- 2 a}{5 b} \cdot \frac{3 a b}{5 b} \div \frac{5 a b}{9 b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{- 2 a}{5 b} \cdot \frac{3 a b}{5 b} \frac{9 b}{5 a b}$

Step 2

Cancel the common factor of $b$ .

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Step 2.1

Factor $b$ out of $5 b$ .

$\frac{- 2 a}{b \cdot 5} \cdot \frac{3 a b}{5 b} \frac{9 b}{5 a b}$

Step 2.2

Factor $b$ out of $3 a b$ .

$\frac{- 2 a}{b \cdot 5} \cdot \frac{b (3 a)}{5 b} \frac{9 b}{5 a b}$

Step 2.3

Cancel the common factor.

$\frac{- 2 a}{b \cdot 5} \cdot \frac{b (3 a)}{5 b} \frac{9 b}{5 a b}$

Step 2.4

Rewrite the expression.

$\frac{- 2 a}{5} \cdot \frac{3 a}{5 b} \frac{9 b}{5 a b}$

Step 3

Multiply $\frac{- 2 a}{5}$ by $\frac{3 a}{5 b}$ .

$\frac{- 2 a (3 a)}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 4

Multiply $3$ by $- 2$ .

$\frac{- 6 a \cdot a}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 5

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

$\frac{- 6 (a^{1} a)}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 6

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

$\frac{- 6 (a^{1} a^{1})}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 7

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

$\frac{- 6 a^{1 + 1}}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 8

Simplify the expression.

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Step 8.1

Add $1$ and $1$ .

$\frac{- 6 a^{2}}{5 (5 b)} \cdot \frac{9 b}{5 a b}$

Step 8.2

Multiply $5$ by $5$ .

$\frac{- 6 a^{2}}{25 b} \cdot \frac{9 b}{5 a b}$

Step 9

Combine.

$\frac{- 6 a^{2} (9 b)}{25 b (5 a b)}$

Step 10

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

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Step 10.1

Move $b$ .

$\frac{- 6 a^{2} (9 b)}{25 (b \cdot b) (5 a)}$

Step 10.2

Multiply $b$ by $b$ .

$\frac{- 6 a^{2} (9 b)}{25 b^{2} (5 a)}$

Step 11

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

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Step 11.1

Factor $a$ out of $- 6 a^{2} (9 b)$ .

$\frac{a (- 6 a (9 b))}{25 b^{2} (5 a)}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $a$ out of $25 b^{2} (5 a)$ .

$\frac{a (- 6 a (9 b))}{a (25 b^{2} \cdot (5))}$

Step 11.2.2

Cancel the common factor.

$\frac{a (- 6 a (9 b))}{a (25 b^{2} \cdot (5))}$

Step 11.2.3

Rewrite the expression.

$\frac{- 6 a (9 b)}{25 b^{2} \cdot (5)}$

Step 12

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

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Step 12.1

Factor $b$ out of $- 6 a (9 b)$ .

$\frac{b (- 6 a \cdot (9))}{25 b^{2} \cdot (5)}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $b$ out of $25 b^{2} \cdot (5)$ .

$\frac{b (- 6 a \cdot (9))}{b (25 b \cdot 5)}$

Step 12.2.2

Cancel the common factor.

$\frac{b (- 6 a \cdot (9))}{b (25 b \cdot 5)}$

Step 12.2.3

Rewrite the expression.

$\frac{- 6 a \cdot (9)}{25 b \cdot 5}$

Step 13

Simplify the expression.

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Step 13.1

Multiply $9$ by $- 6$ .

$\frac{- 54 a}{25 b \cdot 5}$

Step 13.2

Multiply $5$ by $25$ .

$\frac{- 54 a}{125 b}$

Step 13.3

Move the negative in front of the fraction.

$- \frac{54 a}{125 b}$