Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{3}{12}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

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

Step 1.2.2

Combine $2$ and $\frac{12}{12}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $12$ .

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

Step 1.2.4.2

Add $24$ and $3$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Add $11$ and $27$ .

$\frac{38}{12}$

Step 4

Cancel the common factor of $38$ and $12$ .

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Step 4.1

Factor $2$ out of $38$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $12$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{19}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{6}$

Decimal Form:

$3.1\overline{6}$

Mixed Number Form:

$3 \frac{1}{6}$