Basic Math Examples

$\frac{5}{6} + \frac{1}{9} + \frac{1}{2}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$\frac{5}{6} \cdot \frac{3}{3} + \frac{1}{9} + \frac{1}{2}$

Step 1.2

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{1}{9} + \frac{1}{2}$

Step 1.3

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{1}{9} \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.4

Multiply $\frac{1}{9}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{2}{9 \cdot 2} + \frac{1}{2}$

Step 1.5

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{2}{9 \cdot 2} + \frac{1}{2} \cdot \frac{9}{9}$

Step 1.6

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{2}{9 \cdot 2} + \frac{9}{2 \cdot 9}$

Step 1.7

Reorder the factors of $6 \cdot 3$ .

$\frac{5 \cdot 3}{3 \cdot 6} + \frac{2}{9 \cdot 2} + \frac{9}{2 \cdot 9}$

Step 1.8

Multiply $3$ by $6$ .

$\frac{5 \cdot 3}{18} + \frac{2}{9 \cdot 2} + \frac{9}{2 \cdot 9}$

Step 1.9

Reorder the factors of $9 \cdot 2$ .

$\frac{5 \cdot 3}{18} + \frac{2}{2 \cdot 9} + \frac{9}{2 \cdot 9}$

Step 1.10

Multiply $2$ by $9$ .

$\frac{5 \cdot 3}{18} + \frac{2}{18} + \frac{9}{2 \cdot 9}$

Step 1.11

Multiply $2$ by $9$ .

$\frac{5 \cdot 3}{18} + \frac{2}{18} + \frac{9}{18}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 2 + 9}{18}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $5$ by $3$ .

$\frac{15 + 2 + 9}{18}$

Step 3.2

Add $15$ and $2$ .

$\frac{17 + 9}{18}$

Step 3.3

Add $17$ and $9$ .

$\frac{26}{18}$

Step 4

Cancel the common factor of $26$ and $18$ .

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Step 4.1

Factor $2$ out of $26$ .

$\frac{2 (13)}{18}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 13}{2 \cdot 9}$

Step 4.2.2

Cancel the common factor.

$\frac{2 \cdot 13}{2 \cdot 9}$

Step 4.2.3

Rewrite the expression.

$\frac{13}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{9}$

Decimal Form:

$1.\overline{4}$

Mixed Number Form:

$1 \frac{4}{9}$