Basic Math Examples

\frac{1}{4} + \frac{1}{6} + \frac{1}{12}

$\frac{1}{4} + \frac{1}{6} + \frac{1}{12}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} + \frac{1}{12}

$\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} + \frac{1}{12}$

Step 1.2

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{3}{4 \cdot 3} + \frac{1}{6} + \frac{1}{12}

$\frac{3}{4 \cdot 3} + \frac{1}{6} + \frac{1}{12}$

Step 1.3

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2} + \frac{1}{12}

$\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2} + \frac{1}{12}$

Step 1.4

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{3}{4 \cdot 3} + \frac{2}{6 \cdot 2} + \frac{1}{12}

$\frac{3}{4 \cdot 3} + \frac{2}{6 \cdot 2} + \frac{1}{12}$

Step 1.5

Reorder the factors of

4 \cdot 3

$4 \cdot 3$ .

\frac{3}{3 \cdot 4} + \frac{2}{6 \cdot 2} + \frac{1}{12}

$\frac{3}{3 \cdot 4} + \frac{2}{6 \cdot 2} + \frac{1}{12}$

Step 1.6

Multiply

3

$3$ by

4

$4$ .

\frac{3}{12} + \frac{2}{6 \cdot 2} + \frac{1}{12}

$\frac{3}{12} + \frac{2}{6 \cdot 2} + \frac{1}{12}$

Step 1.7

Reorder the factors of

6 \cdot 2

$6 \cdot 2$ .

\frac{3}{12} + \frac{2}{2 \cdot 6} + \frac{1}{12}

$\frac{3}{12} + \frac{2}{2 \cdot 6} + \frac{1}{12}$

Step 1.8

Multiply

2

$2$ by

6

$6$ .

\frac{3}{12} + \frac{2}{12} + \frac{1}{12}

$\frac{3}{12} + \frac{2}{12} + \frac{1}{12}$

\frac{3}{12} + \frac{2}{12} + \frac{1}{12}

$\frac{3}{12} + \frac{2}{12} + \frac{1}{12}$

Step 2

Combine the numerators over the common denominator.

\frac{3 + 2 + 1}{12}

$\frac{3 + 2 + 1}{12}$

Step 3

Simplify by adding numbers.

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Step 3.1

Add

3

$3$ and

2

$2$ .

\frac{5 + 1}{12}

$\frac{5 + 1}{12}$

Step 3.2

Add

5

$5$ and

1

$1$ .

\frac{6}{12}

$\frac{6}{12}$

\frac{6}{12}

$\frac{6}{12}$

Step 4

Cancel the common factor of

6

$6$ and

12

$12$ .

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Step 4.1

Factor

6

$6$ out of

6

$6$ .

\frac{6 (1)}{12}

$\frac{6 (1)}{12}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

6

$6$ out of

12

$12$ .

\frac{6 \cdot 1}{6 \cdot 2}

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

Step 4.2.2

Cancel the common factor.

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

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:

$0.5$