Algebra Examples

$\frac{3}{4} + (\frac{1}{3} \div \frac{1}{6}) - (- \frac{1}{2})$

Step 1

Remove parentheses.

$\frac{3}{4} + \frac{1}{3} \div \frac{1}{6} - (- \frac{1}{2})$

Step 2

Simplify each term.

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Step 2.1

To divide by a fraction, multiply by its reciprocal.

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

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Factor $3$ out of $6$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Multiply $- (- \frac{1}{2})$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

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

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

Step 3

Find the common denominator.

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Step 3.1

Write $2$ as a fraction with denominator $1$ .

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

Step 3.2

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

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

Step 3.3

Multiply $\frac{2}{1}$ by $\frac{4}{4}$ .

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

Multiply $2$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the expression.

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Step 5.1

Multiply $2$ by $4$ .

$\frac{3 + 8 + 2}{4}$

Step 5.2

Add $3$ and $8$ .

$\frac{11 + 2}{4}$

Step 5.3

Add $11$ and $2$ .

$\frac{13}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{4}$

Decimal Form:

$3.25$

Mixed Number Form:

$3 \frac{1}{4}$