Algebra Examples

$\frac{3}{4} - \frac{2}{3} + (\frac{1}{2} + \frac{1}{3})$

Step 1

Remove parentheses.

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Add $- 2$ and $1$ .

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

Step 4

Find the common denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Multiply $\frac{- 1}{3}$ by $\frac{4}{4}$ .

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

Step 4.4

Multiply $\frac{- 1}{3}$ by $\frac{4}{4}$ .

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

Step 4.5

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

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

Step 4.6

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

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

Step 4.7

Reorder the factors of $4 \cdot 3$ .

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

Step 4.8

Multiply $3$ by $4$ .

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

Step 4.9

Multiply $3$ by $4$ .

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

Step 4.10

Multiply $2$ by $6$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify each term.

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Step 6.1

Multiply $3$ by $3$ .

$\frac{9 - 1 \cdot 4 + 6}{12}$

Step 6.2

Multiply $- 1$ by $4$ .

$\frac{9 - 4 + 6}{12}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $4$ from $9$ .

$\frac{5 + 6}{12}$

Step 7.2

Add $5$ and $6$ .

$\frac{11}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{12}$

Decimal Form:

$0.91\overline{6}$