AMC8 2001

AMC8 2001 · Q12

AMC8 2001 · Q12. It mainly tests Manipulating equations.

If $a \otimes b = \frac{a+b}{a-b}$, then $(6 \otimes 4) \otimes 3 =$

如果 $a \otimes b = \frac{a+b}{a-b}$，则 $(6 \otimes 4) \otimes 3 =$

(A) 4 4

(B) 13 13

(D) 30 30

(E) 72 72

Answer

Correct choice: (A)

正确答案：（A）

Solution

(A) $6\otimes 4=\dfrac{6+4}{6-4}=\dfrac{10}{2}=5$, and $5\otimes 3=\dfrac{5+3}{5-3}=\dfrac{8}{2}=4$. Note: $(6\otimes 4)\otimes 3\ne 6\otimes (4\otimes 3)$. Does $(6\otimes 4)\otimes 3=3\otimes (6\otimes 4)$?

（A）$6\otimes 4=\dfrac{6+4}{6-4}=\dfrac{10}{2}=5$，并且 $5\otimes 3=\dfrac{5+3}{5-3}=\dfrac{8}{2}=4$。注意：$(6\otimes 4)\otimes 3\ne 6\otimes (4\otimes 3)$。那么 $(6\otimes 4)\otimes 3=3\otimes (6\otimes 4)$ 吗？

Topics

AL.016 Manipulating equations