Basic Math Examples

\frac{1}{2} + \frac{1}{3} + \frac{1}{4}

$\frac{1}{2} + \frac{1}{3} + \frac{1}{4}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.2

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{6}{6}

$\frac{6}{6}$ .

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

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

Step 1.3

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.4

Multiply

\frac{1}{3}

$\frac{1}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 1.5

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.6

Multiply

\frac{1}{4}

$\frac{1}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.7

Multiply

2

$2$ by

6

$6$ .

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

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

Step 1.8

Multiply

3

$3$ by

4

$4$ .

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

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

Step 1.9

Reorder the factors of

4 \cdot 3

$4 \cdot 3$ .

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

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

Step 1.10

Multiply

3

$3$ by

4

$4$ .

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

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

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

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

Step 2

Combine the numerators over the common denominator.

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

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

Step 3

Simplify by adding numbers.

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Step 3.1

Add

6

$6$ and

4

$4$ .

\frac{10 + 3}{12}

$\frac{10 + 3}{12}$

Step 3.2

Add

10

$10$ and

3

$3$ .

\frac{13}{12}

$\frac{13}{12}$

\frac{13}{12}

$\frac{13}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{13}{12}

$\frac{13}{12}$

Decimal Form:

1.08 ¯ 3

$1.08\overline{3}$

Mixed Number Form:

1 \frac{1}{12}

$1 \frac{1}{12}$