AMC10 2009 A

AMC10 2009 A · Q3

AMC10 2009 A · Q3. It mainly tests Manipulating equations.

Which of the following is equal to $1 + \frac{1}{1 + \frac{1}{1+1}}$?

以下哪个等于 $1 + \frac{1}{1 + \frac{1}{1+1}}$？

(A) $\frac{5}{4}$ $\frac{5}{4}$

(B) $\frac{3}{2}$ $\frac{3}{2}$

(D) 2 2

(E) 3 3

Answer

Correct choice: (C)

正确答案：（C）

Solution

Simplifying the expression, $1 + \frac{1}{1 + \frac{1}{1+1}} = 1 + \frac{1}{1 + \frac{1}{2}} = 1 + \frac{1}{\frac{3}{2}} = 1 + \frac{2}{3} = \frac{5}{3}$.

化简该表达式，$1 + \frac{1}{1 + \frac{1}{1+1}} = 1 + \frac{1}{1 + \frac{1}{2}} = 1 + \frac{1}{\frac{3}{2}} = 1 + \frac{2}{3} = \frac{5}{3}$。

Topics

AL.016 Manipulating equations