Pre-Algebra Examples

$\frac{1}{12 m^{3} n} + \frac{8}{22 m^{2} n^{2}}$

Step 1

Cancel the common factor of $8$ and $22$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $8$ .

$\frac{1}{12 m^{3} n} + \frac{2 (4)}{22 m^{2} n^{2}}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $2$ out of $22 m^{2} n^{2}$ .

$\frac{1}{12 m^{3} n} + \frac{2 (4)}{2 (11 m^{2} n^{2})}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{12 m^{3} n} + \frac{2 \cdot 4}{2 (11 m^{2} n^{2})}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{12 m^{3} n} + \frac{4}{11 m^{2} n^{2}}$

Step 2

To write $\frac{1}{12 m^{3} n}$ as a fraction with a common denominator, multiply by $\frac{11 n}{11 n}$ .

$\frac{1}{12 m^{3} n} \cdot \frac{11 n}{11 n} + \frac{4}{11 m^{2} n^{2}}$

Step 3

To write $\frac{4}{11 m^{2} n^{2}}$ as a fraction with a common denominator, multiply by $\frac{12 m}{12 m}$ .

$\frac{1}{12 m^{3} n} \cdot \frac{11 n}{11 n} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4

Write each expression with a common denominator of $132 m^{3} n^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{1}{12 m^{3} n}$ by $\frac{11 n}{11 n}$ .

$\frac{11 n}{12 m^{3} n (11 n)} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.2

Multiply $11$ by $12$ .

$\frac{11 n}{132 m^{3} n \cdot n} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.3

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

$\frac{11 n}{132 m^{3} (n^{1} n)} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.4

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

$\frac{11 n}{132 m^{3} (n^{1} n^{1})} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.5

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

$\frac{11 n}{132 m^{3} n^{1 + 1}} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.6

Add $1$ and $1$ .

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4}{11 m^{2} n^{2}} \cdot \frac{12 m}{12 m}$

Step 4.7

Multiply $\frac{4}{11 m^{2} n^{2}}$ by $\frac{12 m}{12 m}$ .

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4 (12 m)}{11 m^{2} n^{2} (12 m)}$

Step 4.8

Multiply $12$ by $11$ .

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4 (12 m)}{132 m^{2} n^{2} m}$

Step 4.9

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

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4 (12 m)}{132 (m^{1} m^{2}) n^{2}}$

Step 4.10

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

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4 (12 m)}{132 m^{1 + 2} n^{2}}$

Step 4.11

Add $1$ and $2$ .

$\frac{11 n}{132 m^{3} n^{2}} + \frac{4 (12 m)}{132 m^{3} n^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 n + 4 (12 m)}{132 m^{3} n^{2}}$

Step 6

Multiply $4$ by $12$ .

$\frac{11 n + 48 m}{132 m^{3} n^{2}}$