Evaluate 3/8+1/8+2/3-1/2

$\frac{3}{8} + \frac{1}{8} + \frac{2}{3} - \frac{1}{2}$

Step 1

Combine the numerators over the common denominator.

$\frac{3 + 1}{8} + \frac{2}{3} + \frac{- 1}{2}$

Step 2

Add $3$ and $1$ .

$\frac{4}{8} + \frac{2}{3} + \frac{- 1}{2}$

Step 3

Find the common denominator.

Multiply $\frac{4}{8}$ by $\frac{3}{3}$ .

$\frac{4}{8} \cdot \frac{3}{3} + \frac{2}{3} + \frac{- 1}{2}$

Multiply $\frac{4}{8}$ by $\frac{3}{3}$ .

$\frac{4 \cdot 3}{8 \cdot 3} + \frac{2}{3} + \frac{- 1}{2}$

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{4 \cdot 3}{8 \cdot 3} + \frac{2}{3} \cdot \frac{8}{8} + \frac{- 1}{2}$

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{4 \cdot 3}{8 \cdot 3} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{- 1}{2}$

Multiply $\frac{- 1}{2}$ by $\frac{12}{12}$ .

$\frac{4 \cdot 3}{8 \cdot 3} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{- 1}{2} \cdot \frac{12}{12}$

Multiply $\frac{- 1}{2}$ by $\frac{12}{12}$ .

$\frac{4 \cdot 3}{8 \cdot 3} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{- 1 \cdot 12}{2 \cdot 12}$

Reorder the factors of $8 \cdot 3$ .

$\frac{4 \cdot 3}{3 \cdot 8} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{- 1 \cdot 12}{2 \cdot 12}$

Multiply $3$ by $8$ .

$\frac{4 \cdot 3}{24} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{- 1 \cdot 12}{2 \cdot 12}$

Multiply $3$ by $8$ .

$\frac{4 \cdot 3}{24} + \frac{2 \cdot 8}{24} + \frac{- 1 \cdot 12}{2 \cdot 12}$

Multiply $2$ by $12$ .

$\frac{4 \cdot 3}{24} + \frac{2 \cdot 8}{24} + \frac{- 1 \cdot 12}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 2 \cdot 8 - 1 \cdot 12}{24}$

Step 5

Simplify each term.

Multiply $4$ by $3$ .

$\frac{12 + 2 \cdot 8 - 1 \cdot 12}{24}$

Multiply $2$ by $8$ .

$\frac{12 + 16 - 1 \cdot 12}{24}$

Multiply $- 1$ by $12$ .

$\frac{12 + 16 - 12}{24}$

Step 6

Reduce the expression by cancelling the common factors.

Add $12$ and $16$ .

$\frac{28 - 12}{24}$

Subtract $12$ from $28$ .

$\frac{16}{24}$

Cancel the common factor of $16$ and $24$ .

Factor $8$ out of $16$ .

$\frac{8 (2)}{24}$

Cancel the common factors.

Factor $8$ out of $24$ .

$\frac{8 \cdot 2}{8 \cdot 3}$

Cancel the common factor.

$\frac{8 \cdot 2}{8 \cdot 3}$

Rewrite the expression.

$\frac{2}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

Evaluate 3/8+1/8+2/3-1/2

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