Mixed numbers

Five and two-thirds minus two and one-half equals what number?

A three and one-sixth
B three and two-thirds
C three and one-half
D three and five-sixths

Correct answer:

x = A

Step-by-step explanation:

$$\begin{gathered} a=5\frac{2}{3}=5+\frac{2}{3}=\frac{5\cdot 3+2}{3}=\frac{15+2}{3}=\frac{17}{3}=5\frac{2}{3}\doteq 5.6667 \\ b=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2\frac{1}{2}=2.5 \\ c=a-b=\frac{17}{3}-\frac{5}{2}=\frac{34}{6}-\frac{15}{6}=\frac{34-15}{6}=\frac{19}{6}=3\frac{1}{6}\doteq 3.1667 \\ x=A \end{gathered}$$

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