Basic Math Examples

$(\frac{1}{2}) + 2 + \frac{2}{3}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{1}{2} \cdot \frac{3}{3} + 2 + \frac{2}{3}$

Step 1.2

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{3}{2 \cdot 3} + 2 + \frac{2}{3}$

Step 1.3

Write $2$ as a fraction with denominator $1$ .

$\frac{3}{2 \cdot 3} + \frac{2}{1} + \frac{2}{3}$

Step 1.4

Multiply $\frac{2}{1}$ by $\frac{6}{6}$ .

$\frac{3}{2 \cdot 3} + \frac{2}{1} \cdot \frac{6}{6} + \frac{2}{3}$

Step 1.5

Multiply $\frac{2}{1}$ by $\frac{6}{6}$ .

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

Step 1.6

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

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

Step 1.7

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

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

Step 1.8

Multiply $2$ by $3$ .

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

Step 1.9

Reorder the factors of $3 \cdot 2$ .

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

Step 1.10

Multiply $2$ by $3$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $6$ .

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

Step 3.2

Multiply $2$ by $2$ .

$\frac{3 + 12 + 4}{6}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $3$ and $12$ .

$\frac{15 + 4}{6}$

Step 4.2

Add $15$ and $4$ .

$\frac{19}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{6}$

Decimal Form:

$3.1\overline{6}$

Mixed Number Form:

$3 \frac{1}{6}$