Evaluate 5-2/3+1/2

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

Step 1

Find the common denominator.

Write $5$ as a fraction with denominator $1$ .

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

Multiply $\frac{5}{1}$ by $\frac{6}{6}$ .

$\frac{5}{1} \cdot \frac{6}{6} - \frac{2}{3} + \frac{1}{2}$

Multiply $\frac{5}{1}$ by $\frac{6}{6}$ .

$\frac{5 \cdot 6}{6} - \frac{2}{3} + \frac{1}{2}$

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

$\frac{5 \cdot 6}{6} - (\frac{2}{3} \cdot \frac{2}{2}) + \frac{1}{2}$

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

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{2}$

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

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}$

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

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{3 \cdot 2} + \frac{3}{2 \cdot 3}$

Reorder the factors of $3 \cdot 2$ .

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{2 \cdot 3} + \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{6} + \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{5 \cdot 6}{6} - \frac{2 \cdot 2}{6} + \frac{3}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 6 - 2 \cdot 2 + 3}{6}$

Step 3

Simplify each term.

Multiply $5$ by $6$ .

$\frac{30 - 2 \cdot 2 + 3}{6}$

Multiply $- 2$ by $2$ .

$\frac{30 - 4 + 3}{6}$

Step 4

Simplify by adding and subtracting.

Subtract $4$ from $30$ .

$\frac{26 + 3}{6}$

Add $26$ and $3$ .

$\frac{29}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{6}$

Decimal Form:

$4.8\overline{3}$

Mixed Number Form:

$4 \frac{5}{6}$