Simplify the Radical Expression -1/2(-5/6+1/3)

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

Step 1

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $2$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Add $- 5$ and $2$ .

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

Step 5

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factors.

Factor $3$ out of $6$ .

$- \frac{1}{2} \cdot \frac{3 \cdot - 1}{3 \cdot 2}$

Cancel the common factor.

$- \frac{1}{2} \cdot \frac{3 \cdot - 1}{3 \cdot 2}$

Rewrite the expression.

$- \frac{1}{2} \cdot \frac{- 1}{2}$

Step 6

Move the negative in front of the fraction.

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

Step 7

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

Multiply $- 1$ by $- 1$ .

$1 (\frac{1}{2}) \frac{1}{2}$

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

$\frac{1}{2} \cdot \frac{1}{2}$

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

$\frac{1}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{1}{4}$