Pre-Algebra Examples

$\frac{1}{2} + \frac{1}{3} + \frac{5}{6}$

Step 1

Find the common denominator.

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Step 1.1

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

$\frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} + \frac{5}{6}$

Step 1.2

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

$\frac{3}{2 \cdot 3} + \frac{1}{3} + \frac{5}{6}$

Step 1.3

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

$\frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2} + \frac{5}{6}$

Step 1.4

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

$\frac{3}{2 \cdot 3} + \frac{2}{3 \cdot 2} + \frac{5}{6}$

Step 1.5

Multiply $2$ by $3$ .

$\frac{3}{6} + \frac{2}{3 \cdot 2} + \frac{5}{6}$

Step 1.6

Reorder the factors of $3 \cdot 2$ .

$\frac{3}{6} + \frac{2}{2 \cdot 3} + \frac{5}{6}$

Step 1.7

Multiply $2$ by $3$ .

$\frac{3}{6} + \frac{2}{6} + \frac{5}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 + 2 + 5}{6}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add $3$ and $2$ .

$\frac{5 + 5}{6}$

Step 3.2

Add $5$ and $5$ .

$\frac{10}{6}$

Step 4

Cancel the common factor of $10$ and $6$ .

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Step 4.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{6}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 4.2.3

Rewrite the expression.

$\frac{5}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$