Evaluate mixed expressions

Which of the following equals 4 and 2 over 3 divided by 3 and 1 over 2?
A. 4 and 2 over 3 times 3 and 2 over 1
B. 14 over 3 times 2 over 7
C. 14 over 3 times 7 over 2
D. 42 over 3 times 2 over 31

Correct answer:

x = B

Step-by-step explanation:

$$\begin{gathered} w=4\frac{2}{3}/3\frac{1}{2}=\frac{14}{3}/\frac{7}{2}=\frac{14}{3}:\frac{7}{2}=\frac{14}{3}\cdot \frac{2}{7}=\frac{14\cdot 2}{3\cdot 7}=\frac{28}{21}=\frac{4}{3}=1\frac{1}{3}\doteq 1.3333 \\ a=3\frac{2}{3}\cdot 3\frac{2}{1}=\frac{11}{3}\cdot \frac{5}{1}=\frac{11\cdot 5}{3\cdot 1}=\frac{55}{3}\doteq 18.3333 \\ b=\frac{14}{3}\cdot \frac{2}{7}=\frac{14\cdot 2}{3\cdot 7}=\frac{28}{21}=\frac{4}{3}=1\frac{1}{3}\doteq 1.3333 \\ c=\frac{14}{3}\cdot \frac{7}{2}=\frac{14\cdot 7}{3\cdot 2}=\frac{98}{6}=\frac{49}{3}=16\frac{1}{3}\doteq 16.3333 \\ d=\frac{42}{3}\cdot \frac{2}{31}=\frac{42\cdot 2}{3\cdot 31}=\frac{84}{93}=\frac{28}{31}\doteq 0.9032 \\ w=b \\ x=B \end{gathered}$$

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