Pre-Algebra Examples

$- \frac{2}{3} + \frac{11}{6} - \frac{3}{4}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$- (\frac{2}{3} \cdot \frac{4}{4}) + \frac{11}{6} - \frac{3}{4}$

Step 1.2

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$- \frac{2 \cdot 4}{3 \cdot 4} + \frac{11}{6} - \frac{3}{4}$

Step 1.3

Multiply $\frac{11}{6}$ by $\frac{2}{2}$ .

$- \frac{2 \cdot 4}{3 \cdot 4} + \frac{11}{6} \cdot \frac{2}{2} - \frac{3}{4}$

Step 1.4

Multiply $\frac{11}{6}$ by $\frac{2}{2}$ .

$- \frac{2 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 2}{6 \cdot 2} - \frac{3}{4}$

Step 1.5

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$- \frac{2 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 2}{6 \cdot 2} - (\frac{3}{4} \cdot \frac{3}{3})$

Step 1.6

Multiply $\frac{3}{4}$ by $\frac{3}{3}$ .

$- \frac{2 \cdot 4}{3 \cdot 4} + \frac{11 \cdot 2}{6 \cdot 2} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 1.7

Multiply $3$ by $4$ .

$- \frac{2 \cdot 4}{12} + \frac{11 \cdot 2}{6 \cdot 2} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 1.8

Reorder the factors of $6 \cdot 2$ .

$- \frac{2 \cdot 4}{12} + \frac{11 \cdot 2}{2 \cdot 6} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 1.9

Multiply $2$ by $6$ .

$- \frac{2 \cdot 4}{12} + \frac{11 \cdot 2}{12} - \frac{3 \cdot 3}{4 \cdot 3}$

Step 1.10

Reorder the factors of $4 \cdot 3$ .

$- \frac{2 \cdot 4}{12} + \frac{11 \cdot 2}{12} - \frac{3 \cdot 3}{3 \cdot 4}$

Step 1.11

Multiply $3$ by $4$ .

$- \frac{2 \cdot 4}{12} + \frac{11 \cdot 2}{12} - \frac{3 \cdot 3}{12}$

Step 2

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 4 + 11 \cdot 2 - 3 \cdot 3}{12}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 2$ by $4$ .

$\frac{- 8 + 11 \cdot 2 - 3 \cdot 3}{12}$

Step 3.2

Multiply $11$ by $2$ .

$\frac{- 8 + 22 - 3 \cdot 3}{12}$

Step 3.3

Multiply $- 3$ by $3$ .

$\frac{- 8 + 22 - 9}{12}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $- 8$ and $22$ .

$\frac{14 - 9}{12}$

Step 4.2

Subtract $9$ from $14$ .

$\frac{5}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$