Basic Math Examples

$\frac{4}{5 u} + \frac{2}{u v}$

Step 1

To write $\frac{4}{5 u}$ as a fraction with a common denominator, multiply by $\frac{v}{v}$ .

$\frac{4}{5 u} \cdot \frac{v}{v} + \frac{2}{u v}$

Step 2

To write $\frac{2}{u v}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4}{5 u} \cdot \frac{v}{v} + \frac{2}{u v} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $5 u v$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{5 u}$ by $\frac{v}{v}$ .

$\frac{4 v}{5 u v} + \frac{2}{u v} \cdot \frac{5}{5}$

Step 3.2

Multiply $\frac{2}{u v}$ by $\frac{5}{5}$ .

$\frac{4 v}{5 u v} + \frac{2 \cdot 5}{u v \cdot 5}$

Step 3.3

Reorder the factors of $u v \cdot 5$ .

$\frac{4 v}{5 u v} + \frac{2 \cdot 5}{5 u v}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 v + 2 \cdot 5}{5 u v}$

Step 5

Factor $2$ out of $4 v + 2 \cdot 5$ .

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Step 5.1

Factor $2$ out of $4 v$ .

$\frac{2 (2 v) + 2 \cdot 5}{5 u v}$

Step 5.2

Factor $2$ out of $2 \cdot 5$ .

$\frac{2 (2 v) + 2 (5)}{5 u v}$

Step 5.3

Factor $2$ out of $2 (2 v) + 2 (5)$ .

$\frac{2 (2 v + 5)}{5 u v}$