Basic Math Examples

\frac{1}{18} + \frac{1}{9} + \frac{1}{12} + \frac{1}{4}

$\frac{1}{18} + \frac{1}{9} + \frac{1}{12} + \frac{1}{4}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

$\frac{1}{18}$ by

$\frac{2}{2}$ .

$\frac{1}{18} \cdot \frac{2}{2} + \frac{1}{9} + \frac{1}{12} + \frac{1}{4}$

Step 1.2

Multiply

$\frac{1}{18}$ by

$\frac{2}{2}$ .

$\frac{2}{18 \cdot 2} + \frac{1}{9} + \frac{1}{12} + \frac{1}{4}$

Step 1.3

Multiply

$\frac{1}{9}$ by

$\frac{4}{4}$ .

$\frac{2}{18 \cdot 2} + \frac{1}{9} \cdot \frac{4}{4} + \frac{1}{12} + \frac{1}{4}$

Step 1.4

Multiply

$\frac{1}{9}$ by

$\frac{4}{4}$ .

$\frac{2}{18 \cdot 2} + \frac{4}{9 \cdot 4} + \frac{1}{12} + \frac{1}{4}$

Step 1.5

Multiply

$\frac{1}{12}$ by

$\frac{3}{3}$ .

$\frac{2}{18 \cdot 2} + \frac{4}{9 \cdot 4} + \frac{1}{12} \cdot \frac{3}{3} + \frac{1}{4}$

Step 1.6

Multiply

$\frac{1}{12}$ by

$\frac{3}{3}$ .

$\frac{2}{18 \cdot 2} + \frac{4}{9 \cdot 4} + \frac{3}{12 \cdot 3} + \frac{1}{4}$

Step 1.7

Multiply

$\frac{1}{4}$ by

$\frac{9}{9}$ .

$\frac{2}{18 \cdot 2} + \frac{4}{9 \cdot 4} + \frac{3}{12 \cdot 3} + \frac{1}{4} \cdot \frac{9}{9}$

Step 1.8

Multiply

$\frac{1}{4}$ by

$\frac{9}{9}$ .

$\frac{2}{18 \cdot 2} + \frac{4}{9 \cdot 4} + \frac{3}{12 \cdot 3} + \frac{9}{4 \cdot 9}$

Step 1.9

Reorder the factors of

$18 \cdot 2$ .

$\frac{2}{2 \cdot 18} + \frac{4}{9 \cdot 4} + \frac{3}{12 \cdot 3} + \frac{9}{4 \cdot 9}$

Step 1.10

Multiply

$2$ by

$18$ .

$\frac{2}{36} + \frac{4}{9 \cdot 4} + \frac{3}{12 \cdot 3} + \frac{9}{4 \cdot 9}$

Step 1.11

Reorder the factors of

$9 \cdot 4$ .

$\frac{2}{36} + \frac{4}{4 \cdot 9} + \frac{3}{12 \cdot 3} + \frac{9}{4 \cdot 9}$

Step 1.12

Multiply

$4$ by

$9$ .

$\frac{2}{36} + \frac{4}{36} + \frac{3}{12 \cdot 3} + \frac{9}{4 \cdot 9}$

Step 1.13

Reorder the factors of

$12 \cdot 3$ .

$\frac{2}{36} + \frac{4}{36} + \frac{3}{3 \cdot 12} + \frac{9}{4 \cdot 9}$

Step 1.14

Multiply

$3$ by

$12$ .

$\frac{2}{36} + \frac{4}{36} + \frac{3}{36} + \frac{9}{4 \cdot 9}$

Step 1.15

Multiply

$4$ by

$9$ .

$\frac{2}{36} + \frac{4}{36} + \frac{3}{36} + \frac{9}{36}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 + 4 + 3 + 9}{36}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add

$2$ and

$4$ .

$\frac{6 + 3 + 9}{36}$

Step 3.2

Add

$6$ and

$3$ .

$\frac{9 + 9}{36}$

Step 3.3

Add

$9$ and

$9$ .

$\frac{18}{36}$

Step 4

Cancel the common factor of

$18$ and

$36$ .

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Step 4.1

Factor

$18$ out of

$18$ .

$\frac{18 (1)}{36}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

$18$ out of

$36$ .

$\frac{18 \cdot 1}{18 \cdot 2}$

Step 4.2.2

Cancel the common factor.

$\frac{18 \cdot 1}{18 \cdot 2}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$