Question

use properties to evaluate \\(\frac{3}{4}\left(-\frac{2}{3} \div \frac{1}{6}\
ight)\frac{1}{2}\\). \
\
\\(\bigcirc\\) a. \\(-3\\)\
\\(\bigcirc\\) b. \\(-\frac{3}{2}\\)\
\\(\bigcirc\\) c. \\(3\\)\
\\(\bigcirc\\) d. \\(\frac{3}{2}\\)

Explanation:

Step1: Evaluate the division inside parentheses

Dividing by a fraction is multiplying by its reciprocal:
$$-\frac{2}{3} \div \frac{1}{6} = -\frac{2}{3} \times 6 = -4$$

Step2: Multiply the remaining fractions

Multiply all terms together:
$$\frac{3}{4} \times (-4) \times \frac{1}{2} = \frac{3 \times (-4) \times 1}{4 \times 2}$$

Step3: Simplify the expression

Cancel and compute the result:
$$\frac{-12}{8} = -3$$

Answer:

A. $-3$