Simplify 3/4-1/2+2/3-1/6

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

Step 1

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Reorder the factors of $4 \cdot 3$ .

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

Multiply $3$ by $4$ .

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

Multiply $2$ by $6$ .

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

Multiply $3$ by $4$ .

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

Reorder the factors of $6 \cdot 2$ .

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

Multiply $2$ by $6$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Multiply $3$ by $3$ .

$\frac{9 - 6 + 2 \cdot 4 - 2}{12}$

Multiply $2$ by $4$ .

$\frac{9 - 6 + 8 - 2}{12}$

Step 4

Reduce the expression by cancelling the common factors.

Subtract $6$ from $9$ .

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

Simplify by adding and subtracting.

Add $3$ and $8$ .

$\frac{11 - 2}{12}$

Subtract $2$ from $11$ .

$\frac{9}{12}$

Cancel the common factor of $9$ and $12$ .

Factor $3$ out of $9$ .

$\frac{3 (3)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$

Simplify 3/4-1/2+2/3-1/6

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