Evaluate 1/2+2/3-3/4

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

Step 1

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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

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

Multiply $2$ by $6$ .

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

Multiply $3$ by $4$ .

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

Reorder the factors of $4 \cdot 3$ .

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

Multiply $3$ by $4$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Multiply $2$ by $4$ .

$\frac{6 + 8 - 3 \cdot 3}{12}$

Multiply $- 3$ by $3$ .

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

Step 4

Simplify by adding and subtracting.

Add $6$ and $8$ .

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

Subtract $9$ from $14$ .

$\frac{5}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{12}$

Decimal Form:

$0.41\overline{6}$