Basic Math Examples

$\frac{3}{10 q^{2}} + \frac{1}{4 q^{3}}$

Step 1

To write $\frac{3}{10 q^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 q}{2 q}$ .

$\frac{3}{10 q^{2}} \cdot \frac{2 q}{2 q} + \frac{1}{4 q^{3}}$

Step 2

To write $\frac{1}{4 q^{3}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{10 q^{2}} \cdot \frac{2 q}{2 q} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $20 q^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{10 q^{2}}$ by $\frac{2 q}{2 q}$ .

$\frac{3 (2 q)}{10 q^{2} (2 q)} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3.2

Multiply $2$ by $10$ .

$\frac{3 (2 q)}{20 q^{2} q} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3.3

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

$\frac{3 (2 q)}{20 (q^{1} q^{2})} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3.4

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

$\frac{3 (2 q)}{20 q^{1 + 2}} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3.5

Add $1$ and $2$ .

$\frac{3 (2 q)}{20 q^{3}} + \frac{1}{4 q^{3}} \cdot \frac{5}{5}$

Step 3.6

Multiply $\frac{1}{4 q^{3}}$ by $\frac{5}{5}$ .

$\frac{3 (2 q)}{20 q^{3}} + \frac{5}{4 q^{3} \cdot 5}$

Step 3.7

Multiply $5$ by $4$ .

$\frac{3 (2 q)}{20 q^{3}} + \frac{5}{20 q^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (2 q) + 5}{20 q^{3}}$

Step 5

Multiply $3$ by $2$ .

$\frac{6 q + 5}{20 q^{3}}$