Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{2}$ by $\frac{\frac{3}{2}}{\frac{3}{2}}$ .

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

Step 1.2

Multiply $\frac{1}{2}$ by $\frac{\frac{3}{2}}{\frac{3}{2}}$ .

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

Step 1.3

Multiply $\frac{1}{3} \div \frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{\frac{3}{2}}{2 (\frac{3}{2})} + \frac{1}{3} \div \frac{1}{2} \cdot \frac{6}{6} - \frac{1}{3}$

Step 1.4

Multiply $\frac{1}{3} \div \frac{1}{2}$ by $\frac{6}{6}$ .

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

Step 1.5

Multiply $\frac{1}{3}$ by $\frac{\frac{2}{2}}{\frac{2}{2}}$ .

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

Step 1.6

Multiply $\frac{1}{3}$ by $\frac{\frac{2}{2}}{\frac{2}{2}}$ .

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

Step 1.7

Combine $2$ and $\frac{3}{2}$ .

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

Step 1.8

Multiply $2$ by $3$ .

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

Step 1.9

Reorder the factors of $\frac{1}{2} \cdot 6$ .

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

Step 1.10

Combine $6$ and $\frac{1}{2}$ .

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

Step 1.11

Combine $3$ and $\frac{2}{2}$ .

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

Step 1.12

Multiply $3$ by $2$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Subtract $2$ from $3$ .

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $6$ .

$\frac{\frac{1}{3} \cdot (3 (2)) + \frac{1}{2}}{\frac{6}{2}}$

Step 5.2

Cancel the common factor.

$\frac{\frac{1}{3} \cdot (3 \cdot 2) + \frac{1}{2}}{\frac{6}{2}}$

Step 5.3

Rewrite the expression.

$\frac{2 + \frac{1}{2}}{\frac{6}{2}}$

Step 6

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

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

Step 7

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

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

Step 8

Combine the numerators over the common denominator.

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

Step 9

Simplify the numerator.

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Step 9.1

Multiply $2$ by $2$ .

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

Step 9.2

Add $4$ and $1$ .

$\frac{\frac{5}{2}}{\frac{6}{2}}$

Step 10

Cancel the common factor of $6$ and $2$ .

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Step 10.1

Factor $2$ out of $6$ .

$\frac{\frac{5}{2}}{\frac{2 \cdot 3}{2}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $2$ .

$\frac{\frac{5}{2}}{\frac{2 \cdot 3}{2 (1)}}$

Step 10.2.2

Cancel the common factor.

$\frac{\frac{5}{2}}{\frac{2 \cdot 3}{2 \cdot 1}}$

Step 10.2.3

Rewrite the expression.

$\frac{\frac{5}{2}}{\frac{3}{1}}$

Step 10.2.4

Divide $3$ by $1$ .

$\frac{\frac{5}{2}}{3}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{2} \cdot \frac{1}{3}$

Step 12

Multiply $\frac{5}{2} \cdot \frac{1}{3}$ .

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Step 12.1

Multiply $\frac{5}{2}$ by $\frac{1}{3}$ .

$\frac{5}{2 \cdot 3}$

Step 12.2

Multiply $2$ by $3$ .

$\frac{5}{6}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{6}$

Decimal Form:

$0.8\overline{3}$