Basic Math Examples

$\frac{- 7 a}{9 b} \cdot \frac{2 a b}{9 b} \div \frac{7 a b}{4 b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{- 7 a}{9 b} \cdot \frac{2 a b}{9 b} \frac{4 b}{7 a b}$

Step 2

Cancel the common factor of $b$ .

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Step 2.1

Factor $b$ out of $9 b$ .

$\frac{- 7 a}{b \cdot 9} \cdot \frac{2 a b}{9 b} \frac{4 b}{7 a b}$

Step 2.2

Factor $b$ out of $2 a b$ .

$\frac{- 7 a}{b \cdot 9} \cdot \frac{b (2 a)}{9 b} \frac{4 b}{7 a b}$

Step 2.3

Cancel the common factor.

$\frac{- 7 a}{b \cdot 9} \cdot \frac{b (2 a)}{9 b} \frac{4 b}{7 a b}$

Step 2.4

Rewrite the expression.

$\frac{- 7 a}{9} \cdot \frac{2 a}{9 b} \frac{4 b}{7 a b}$

Step 3

Multiply $\frac{- 7 a}{9}$ by $\frac{2 a}{9 b}$ .

$\frac{- 7 a (2 a)}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 4

Multiply $2$ by $- 7$ .

$\frac{- 14 a \cdot a}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 5

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

$\frac{- 14 (a^{1} a)}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 6

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

$\frac{- 14 (a^{1} a^{1})}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 7

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

$\frac{- 14 a^{1 + 1}}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 8

Simplify the expression.

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Step 8.1

Add $1$ and $1$ .

$\frac{- 14 a^{2}}{9 (9 b)} \cdot \frac{4 b}{7 a b}$

Step 8.2

Multiply $9$ by $9$ .

$\frac{- 14 a^{2}}{81 b} \cdot \frac{4 b}{7 a b}$

Step 9

Combine.

$\frac{- 14 a^{2} (4 b)}{81 b (7 a b)}$

Step 10

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

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Step 10.1

Move $b$ .

$\frac{- 14 a^{2} (4 b)}{81 (b \cdot b) (7 a)}$

Step 10.2

Multiply $b$ by $b$ .

$\frac{- 14 a^{2} (4 b)}{81 b^{2} (7 a)}$

Step 11

Cancel the common factor of $- 14$ and $7$ .

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Step 11.1

Factor $7$ out of $- 14 a^{2} (4 b)$ .

$\frac{7 (- 2 a^{2} (4 b))}{81 b^{2} (7 a)}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $7$ out of $81 b^{2} (7 a)$ .

$\frac{7 (- 2 a^{2} (4 b))}{7 (81 b^{2} (a))}$

Step 11.2.2

Cancel the common factor.

$\frac{7 (- 2 a^{2} (4 b))}{7 (81 b^{2} (a))}$

Step 11.2.3

Rewrite the expression.

$\frac{- 2 a^{2} (4 b)}{81 b^{2} (a)}$

Step 12

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

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Step 12.1

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

$\frac{a (- 2 a (4 b))}{81 b^{2} (a)}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $a$ out of $81 b^{2} (a)$ .

$\frac{a (- 2 a (4 b))}{a (81 b^{2})}$

Step 12.2.2

Cancel the common factor.

$\frac{a (- 2 a (4 b))}{a (81 b^{2})}$

Step 12.2.3

Rewrite the expression.

$\frac{- 2 a (4 b)}{81 b^{2}}$

Step 13

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

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Step 13.1

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

$\frac{b (- 2 a \cdot (4))}{81 b^{2}}$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $b$ out of $81 b^{2}$ .

$\frac{b (- 2 a \cdot (4))}{b (81 b)}$

Step 13.2.2

Cancel the common factor.

$\frac{b (- 2 a \cdot (4))}{b (81 b)}$

Step 13.2.3

Rewrite the expression.

$\frac{- 2 a \cdot (4)}{81 b}$

Step 14

Simplify the expression.

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Step 14.1

Multiply $4$ by $- 2$ .

$\frac{- 8 a}{81 b}$

Step 14.2

Move the negative in front of the fraction.

$- \frac{8 a}{81 b}$