Finite Math Examples

$\frac{11 a^{3} b^{5}}{4 a^{2} b} \div \frac{121 a^{5} b}{110 a^{4} b^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{11 a^{3} b^{5}}{4 a^{2} b} \cdot \frac{110 a^{4} b^{3}}{121 a^{5} b}$

Step 2

Combine.

$\frac{11 a^{3} b^{5} (110 a^{4} b^{3})}{4 a^{2} b (121 a^{5} b)}$

Step 3

Multiply $a^{3}$ by $a^{4}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $a^{4}$ .

$\frac{11 (a^{4} a^{3}) b^{5} (110 b^{3})}{4 a^{2} b (121 a^{5} b)}$

Step 3.2

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

$\frac{11 a^{4 + 3} b^{5} (110 b^{3})}{4 a^{2} b (121 a^{5} b)}$

Step 3.3

Add $4$ and $3$ .

$\frac{11 a^{7} b^{5} (110 b^{3})}{4 a^{2} b (121 a^{5} b)}$

Step 4

Multiply $b^{5}$ by $b^{3}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $b^{3}$ .

$\frac{11 a^{7} (b^{3} b^{5}) \cdot 110}{4 a^{2} b (121 a^{5} b)}$

Step 4.2

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

$\frac{11 a^{7} b^{3 + 5} \cdot 110}{4 a^{2} b (121 a^{5} b)}$

Step 4.3

Add $3$ and $5$ .

$\frac{11 a^{7} b^{8} \cdot 110}{4 a^{2} b (121 a^{5} b)}$

Step 5

Multiply $a^{2}$ by $a^{5}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $a^{5}$ .

$\frac{11 a^{7} b^{8} \cdot 110}{4 (a^{5} a^{2}) b (121 b)}$

Step 5.2

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

$\frac{11 a^{7} b^{8} \cdot 110}{4 a^{5 + 2} b (121 b)}$

Step 5.3

Add $5$ and $2$ .

$\frac{11 a^{7} b^{8} \cdot 110}{4 a^{7} b (121 b)}$

Step 6

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

Tap for more steps...

Step 6.1

Move $b$ .

$\frac{11 a^{7} b^{8} \cdot 110}{4 a^{7} (b \cdot b) \cdot 121}$

Step 6.2

Multiply $b$ by $b$ .

$\frac{11 a^{7} b^{8} \cdot 110}{4 a^{7} b^{2} \cdot 121}$

Step 7

Cancel the common factor of $11$ and $121$ .

Tap for more steps...

Step 7.1

Factor $11$ out of $11 a^{7} b^{8} \cdot 110$ .

$\frac{11 (a^{7} b^{8} \cdot 110)}{4 a^{7} b^{2} \cdot 121}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $11$ out of $4 a^{7} b^{2} \cdot 121$ .

$\frac{11 (a^{7} b^{8} \cdot 110)}{11 (4 a^{7} b^{2} \cdot 11)}$

Step 7.2.2

Cancel the common factor.

$\frac{11 (a^{7} b^{8} \cdot 110)}{11 (4 a^{7} b^{2} \cdot 11)}$

Step 7.2.3

Rewrite the expression.

$\frac{a^{7} b^{8} \cdot 110}{4 a^{7} b^{2} \cdot 11}$

Step 8

Cancel the common factor of $a^{7}$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

$\frac{a^{7} b^{8} \cdot 110}{4 a^{7} b^{2} \cdot 11}$

Step 8.2

Rewrite the expression.

$\frac{b^{8} \cdot 110}{4 b^{2} \cdot 11}$

Step 9

Cancel the common factor of $b^{8}$ and $b^{2}$ .

Tap for more steps...

Step 9.1

Factor $b^{2}$ out of $b^{8} \cdot 110$ .

$\frac{b^{2} (b^{6} \cdot 110)}{4 b^{2} \cdot 11}$

Step 9.2

Cancel the common factors.

Tap for more steps...

Step 9.2.1

Factor $b^{2}$ out of $4 b^{2} \cdot 11$ .

$\frac{b^{2} (b^{6} \cdot 110)}{b^{2} (4 \cdot 11)}$

Step 9.2.2

Cancel the common factor.

$\frac{b^{2} (b^{6} \cdot 110)}{b^{2} (4 \cdot 11)}$

Step 9.2.3

Rewrite the expression.

$\frac{b^{6} \cdot 110}{4 \cdot 11}$

Step 10

Cancel the common factor of $110$ and $4$ .

Tap for more steps...

Step 10.1

Factor $2$ out of $b^{6} \cdot 110$ .

$\frac{2 (b^{6} \cdot 55)}{4 \cdot 11}$

Step 10.2

Cancel the common factors.

Tap for more steps...

Step 10.2.1

Factor $2$ out of $4 \cdot 11$ .

$\frac{2 (b^{6} \cdot 55)}{2 (2 \cdot 11)}$

Step 10.2.2

Cancel the common factor.

$\frac{2 (b^{6} \cdot 55)}{2 (2 \cdot 11)}$

Step 10.2.3

Rewrite the expression.

$\frac{b^{6} \cdot 55}{2 \cdot 11}$

Step 11

Cancel the common factor of $55$ and $11$ .

Tap for more steps...

Step 11.1

Factor $11$ out of $b^{6} \cdot 55$ .

$\frac{11 (b^{6} \cdot 5)}{2 \cdot 11}$

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $11$ out of $2 \cdot 11$ .

$\frac{11 (b^{6} \cdot 5)}{11 \cdot 2}$

Step 11.2.2

Cancel the common factor.

$\frac{11 (b^{6} \cdot 5)}{11 \cdot 2}$

Step 11.2.3

Rewrite the expression.

$\frac{b^{6} \cdot 5}{2}$

Step 12

Move $5$ to the left of $b^{6}$ .

$\frac{5 b^{6}}{2}$