Basic Math Examples

$- \frac{6 a}{5 b} \cdot \frac{3 a b}{7 b} \div \frac{8 a b}{3 b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$- \frac{6 a}{5 b} \cdot \frac{3 a b}{7 b} \frac{3 b}{8 a b}$

Step 2

Cancel the common factor of $b$ .

Tap for more steps...

Step 2.1

Move the leading negative in $- \frac{6 a}{5 b}$ into the numerator.

$\frac{- 6 a}{5 b} \cdot \frac{3 a b}{7 b} \frac{3 b}{8 a b}$

Step 2.2

Factor $b$ out of $5 b$ .

$\frac{- 6 a}{b \cdot 5} \cdot \frac{3 a b}{7 b} \frac{3 b}{8 a b}$

Step 2.3

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

$\frac{- 6 a}{b \cdot 5} \cdot \frac{b (3 a)}{7 b} \frac{3 b}{8 a b}$

Step 2.4

Cancel the common factor.

$\frac{- 6 a}{b \cdot 5} \cdot \frac{b (3 a)}{7 b} \frac{3 b}{8 a b}$

Step 2.5

Rewrite the expression.

$\frac{- 6 a}{5} \cdot \frac{3 a}{7 b} \frac{3 b}{8 a b}$

Step 3

Multiply $\frac{- 6 a}{5}$ by $\frac{3 a}{7 b}$ .

$\frac{- 6 a (3 a)}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 4

Multiply $3$ by $- 6$ .

$\frac{- 18 a \cdot a}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 5

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

$\frac{- 18 (a^{1} a)}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 6

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

$\frac{- 18 (a^{1} a^{1})}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 7

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

$\frac{- 18 a^{1 + 1}}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 8

Simplify the expression.

Tap for more steps...

Step 8.1

Add $1$ and $1$ .

$\frac{- 18 a^{2}}{5 (7 b)} \cdot \frac{3 b}{8 a b}$

Step 8.2

Multiply $7$ by $5$ .

$\frac{- 18 a^{2}}{35 b} \cdot \frac{3 b}{8 a b}$

Step 9

Combine.

$\frac{- 18 a^{2} (3 b)}{35 b (8 a b)}$

Step 10

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

Tap for more steps...

Step 10.1

Move $b$ .

$\frac{- 18 a^{2} (3 b)}{35 (b \cdot b) (8 a)}$

Step 10.2

Multiply $b$ by $b$ .

$\frac{- 18 a^{2} (3 b)}{35 b^{2} (8 a)}$

Step 11

Cancel the common factor of $- 18$ and $8$ .

Tap for more steps...

Step 11.1

Factor $2$ out of $- 18 a^{2} (3 b)$ .

$\frac{2 (- 9 a^{2} (3 b))}{35 b^{2} (8 a)}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $2$ out of $35 b^{2} (8 a)$ .

$\frac{2 (- 9 a^{2} (3 b))}{2 (35 b^{2} (4 a))}$

Step 11.2.2

Cancel the common factor.

$\frac{2 (- 9 a^{2} (3 b))}{2 (35 b^{2} (4 a))}$

Step 11.2.3

Rewrite the expression.

$\frac{- 9 a^{2} (3 b)}{35 b^{2} (4 a)}$

Step 12

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

Tap for more steps...

Step 12.1

Factor $a$ out of $- 9 a^{2} (3 b)$ .

$\frac{a (- 9 a (3 b))}{35 b^{2} (4 a)}$

Step 12.2

Cancel the common factors.

Tap for more steps...

Step 12.2.1

Factor $a$ out of $35 b^{2} (4 a)$ .

$\frac{a (- 9 a (3 b))}{a (35 b^{2} \cdot (4))}$

Step 12.2.2

Cancel the common factor.

$\frac{a (- 9 a (3 b))}{a (35 b^{2} \cdot (4))}$

Step 12.2.3

Rewrite the expression.

$\frac{- 9 a (3 b)}{35 b^{2} \cdot (4)}$

Step 13

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

Tap for more steps...

Step 13.1

Factor $b$ out of $- 9 a (3 b)$ .

$\frac{b (- 9 a \cdot (3))}{35 b^{2} \cdot (4)}$

Step 13.2

Cancel the common factors.

Tap for more steps...

Step 13.2.1

Factor $b$ out of $35 b^{2} \cdot (4)$ .

$\frac{b (- 9 a \cdot (3))}{b (35 b \cdot 4)}$

Step 13.2.2

Cancel the common factor.

$\frac{b (- 9 a \cdot (3))}{b (35 b \cdot 4)}$

Step 13.2.3

Rewrite the expression.

$\frac{- 9 a \cdot (3)}{35 b \cdot 4}$

Step 14

Simplify the expression.

Tap for more steps...

Step 14.1

Multiply $3$ by $- 9$ .

$\frac{- 27 a}{35 b \cdot 4}$

Step 14.2

Multiply $4$ by $35$ .

$\frac{- 27 a}{140 b}$

Step 14.3

Move the negative in front of the fraction.

$- \frac{27 a}{140 b}$