Antonio

Antonio is thinking of an improper fraction and a mixed fraction with a sum of 5 5/12. The improper fraction is 8/3. What is the mixed number?

Correct answer:

x =  2 ³⁄₄ = 11/4

Step-by-step explanation:

$$\begin{gathered} s=5\frac{5}{12}=5+\frac{5}{12}=\frac{5\cdot 12+5}{12}=\frac{60+5}{12}=\frac{65}{12}=5\frac{5}{12}\doteq 5.4167 \\ y=8/3=\frac{8}{3}=2\frac{2}{3}\doteq 2.6667 \\ s=x+y \\ x=s-y=\frac{65}{12}-\frac{8}{3}=\frac{65}{12}-\frac{32}{12}=\frac{65-32}{12}=\frac{33}{12}=\frac{11}{4}=2\frac{3}{4}=2.75 \end{gathered}$$

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