Answer:
D. -4½
Step-by-step explanation:
Remember PEMDAS:
Parentheses
Exponents
Multiply and Divide (in any order)
Add and Subtract (in any order)
[tex]\begin{array}{rl}& \dfrac{3}{4}\left(\dfrac{2}{3} + \dfrac{4}{3} \right ) - 9 \div\dfrac{1}{2} \times\dfrac{1}{3} \\\\\text{Do the addition inside parentheses} &\dfrac{3}{4}\left(\dfrac{6}{3} \right ) - 9 \div\dfrac{1}{2} \times\dfrac{1}{3} \\ \\\text{Simplify the new fraction} &\dfrac{3}{4}(2) - 9 \div\dfrac{1}{2} \times\dfrac{1}{3} \\ \\\text{Multiply} &\dfrac{3}{2} - 9 \div\dfrac{1}{2} \times\dfrac{1}{3} \\\\\end{array}[/tex]
[tex]\begin{array}{rl}\text{Invert the fraction and change divide to multiply} &\dfrac{3}{2} - 9 \times 2 \times\dfrac{1}{3} \\\\\text{Cancel the threes} &\dfrac{3}{2} - 3 \times 2\\\\\text{Multiply} &\dfrac{3}{2} - 6 \\\\\text{Find lowest common denominator } &\dfrac{3}{2} - \dfrac{12}{2} \\\\\text{Add the numerators} &\dfrac{-9}{2} \\\\\text{Convert to a mixed number} &=\mathbf{-4\frac{1}{2}} \\\\\end{array}[/tex]
