Basic Math Examples

$\frac{n}{2} + \frac{n}{4} + \frac{n}{6}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{n}{2}$ by $\frac{6}{6}$ .

$\frac{n}{2} \cdot \frac{6}{6} + \frac{n}{4} + \frac{n}{6}$

Step 1.2

Multiply $\frac{n}{2}$ by $\frac{6}{6}$ .

$\frac{n \cdot 6}{2 \cdot 6} + \frac{n}{4} + \frac{n}{6}$

Step 1.3

Multiply $\frac{n}{4}$ by $\frac{3}{3}$ .

$\frac{n \cdot 6}{2 \cdot 6} + \frac{n}{4} \cdot \frac{3}{3} + \frac{n}{6}$

Step 1.4

Multiply $\frac{n}{4}$ by $\frac{3}{3}$ .

$\frac{n \cdot 6}{2 \cdot 6} + \frac{n \cdot 3}{4 \cdot 3} + \frac{n}{6}$

Step 1.5

Multiply $\frac{n}{6}$ by $\frac{2}{2}$ .

$\frac{n \cdot 6}{2 \cdot 6} + \frac{n \cdot 3}{4 \cdot 3} + \frac{n}{6} \cdot \frac{2}{2}$

Step 1.6

Multiply $\frac{n}{6}$ by $\frac{2}{2}$ .

$\frac{n \cdot 6}{2 \cdot 6} + \frac{n \cdot 3}{4 \cdot 3} + \frac{n \cdot 2}{6 \cdot 2}$

Step 1.7

Multiply $2$ by $6$ .

$\frac{n \cdot 6}{12} + \frac{n \cdot 3}{4 \cdot 3} + \frac{n \cdot 2}{6 \cdot 2}$

Step 1.8

Reorder the factors of $4 \cdot 3$ .

$\frac{n \cdot 6}{12} + \frac{n \cdot 3}{3 \cdot 4} + \frac{n \cdot 2}{6 \cdot 2}$

Step 1.9

Multiply $3$ by $4$ .

$\frac{n \cdot 6}{12} + \frac{n \cdot 3}{12} + \frac{n \cdot 2}{6 \cdot 2}$

Step 1.10

Reorder the factors of $6 \cdot 2$ .

$\frac{n \cdot 6}{12} + \frac{n \cdot 3}{12} + \frac{n \cdot 2}{2 \cdot 6}$

Step 1.11

Multiply $2$ by $6$ .

$\frac{n \cdot 6}{12} + \frac{n \cdot 3}{12} + \frac{n \cdot 2}{12}$

Step 2

Combine the numerators over the common denominator.

$\frac{n \cdot 6 + n \cdot 3 + n \cdot 2}{12}$

Step 3

Simplify each term.

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Step 3.1

Move $6$ to the left of $n$ .

$\frac{6 \cdot n + n \cdot 3 + n \cdot 2}{12}$

Step 3.2

Move $3$ to the left of $n$ .

$\frac{6 n + 3 \cdot n + n \cdot 2}{12}$

Step 3.3

Move $2$ to the left of $n$ .

$\frac{6 n + 3 n + 2 n}{12}$

Step 4

Simplify by adding terms.

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Step 4.1

Add $6 n$ and $3 n$ .

$\frac{9 n + 2 n}{12}$

Step 4.2

Add $9 n$ and $2 n$ .

$\frac{11 n}{12}$