Pre-Algebra Examples

\frac{11}{12} + 2 \frac{3}{12}

$\frac{11}{12} + 2 \frac{3}{12}$

Step 1

Convert

2 \frac{3}{12}

$2 \frac{3}{12}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

\frac{11}{12} + 2 + \frac{3}{12}

$\frac{11}{12} + 2 + \frac{3}{12}$

Step 1.2

Add

2

$2$ and

\frac{3}{12}

$\frac{3}{12}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{12}{12}

$\frac{12}{12}$ .

\frac{11}{12} + 2 \cdot \frac{12}{12} + \frac{3}{12}

$\frac{11}{12} + 2 \cdot \frac{12}{12} + \frac{3}{12}$

Step 1.2.2

Combine

2

$2$ and

\frac{12}{12}

$\frac{12}{12}$ .

\frac{11}{12} + \frac{2 \cdot 12}{12} + \frac{3}{12}

$\frac{11}{12} + \frac{2 \cdot 12}{12} + \frac{3}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{11}{12} + \frac{2 \cdot 12 + 3}{12}

$\frac{11}{12} + \frac{2 \cdot 12 + 3}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

12

$12$ .

\frac{11}{12} + \frac{24 + 3}{12}

$\frac{11}{12} + \frac{24 + 3}{12}$

Step 1.2.4.2

Add

24

$24$ and

3

$3$ .

\frac{11}{12} + \frac{27}{12}

$\frac{11}{12} + \frac{27}{12}$

\frac{11}{12} + \frac{27}{12}

$\frac{11}{12} + \frac{27}{12}$

\frac{11}{12} + \frac{27}{12}

$\frac{11}{12} + \frac{27}{12}$

\frac{11}{12} + \frac{27}{12}

$\frac{11}{12} + \frac{27}{12}$

Step 2

Combine the numerators over the common denominator.

\frac{11 + 27}{12}

$\frac{11 + 27}{12}$

Step 3

Add

11

$11$ and

27

$27$ .

\frac{38}{12}

$\frac{38}{12}$

Step 4

Cancel the common factor of

38

$38$ and

12

$12$ .

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Step 4.1

Factor

2

$2$ out of

38

$38$ .

\frac{2 (19)}{12}

$\frac{2 (19)}{12}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor

2

$2$ out of

12

$12$ .

\frac{2 \cdot 19}{2 \cdot 6}

$\frac{2 \cdot 19}{2 \cdot 6}$

Step 4.2.2

Cancel the common factor.

\frac{2 \cdot 19}{2 \cdot 6}

$\frac{2 \cdot 19}{2 \cdot 6}$

Step 4.2.3

Rewrite the expression.

\frac{19}{6}

$\frac{19}{6}$

\frac{19}{6}

$\frac{19}{6}$

\frac{19}{6}

$\frac{19}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{19}{6}

$\frac{19}{6}$

Decimal Form:

3.1\overline{6}

$3.1\overline{6}$

Mixed Number Form:

3 \frac{1}{6}

$3 \frac{1}{6}$