Pre-Algebra Examples

$\frac{3}{10 n} + \frac{7}{15 n^{2}}$

Step 1

To write $\frac{3}{10 n}$ as a fraction with a common denominator, multiply by $\frac{3 n}{3 n}$ .

$\frac{3}{10 n} \cdot \frac{3 n}{3 n} + \frac{7}{15 n^{2}}$

Step 2

To write $\frac{7}{15 n^{2}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{10 n} \cdot \frac{3 n}{3 n} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $30 n^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{10 n}$ by $\frac{3 n}{3 n}$ .

$\frac{3 (3 n)}{10 n (3 n)} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.2

Multiply $3$ by $10$ .

$\frac{3 (3 n)}{30 n \cdot n} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.3

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

$\frac{3 (3 n)}{30 (n^{1} n)} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.4

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

$\frac{3 (3 n)}{30 (n^{1} n^{1})} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.5

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

$\frac{3 (3 n)}{30 n^{1 + 1}} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.6

Add $1$ and $1$ .

$\frac{3 (3 n)}{30 n^{2}} + \frac{7}{15 n^{2}} \cdot \frac{2}{2}$

Step 3.7

Multiply $\frac{7}{15 n^{2}}$ by $\frac{2}{2}$ .

$\frac{3 (3 n)}{30 n^{2}} + \frac{7 \cdot 2}{15 n^{2} \cdot 2}$

Step 3.8

Multiply $2$ by $15$ .

$\frac{3 (3 n)}{30 n^{2}} + \frac{7 \cdot 2}{30 n^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (3 n) + 7 \cdot 2}{30 n^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 n + 7 \cdot 2}{30 n^{2}}$

Step 5.2

Multiply $7$ by $2$ .

$\frac{9 n + 14}{30 n^{2}}$