AMC12 2022 A

AMC12 2022 A · Q1

AMC12 2022 A · Q1. It mainly tests Fractions.

What is the value of \[3+\frac{1}{3+\frac{1}{3+\frac13}}?\]

求\[3+\frac{1}{3+\frac{1}{3+\frac13}}\]的值。

(A) \ \frac{31}{10} \ \frac{31}{10}

(B) \ \frac{49}{15} \ \frac{49}{15}

(D) \ \frac{109}{33} \ \frac{109}{33}

(E) \ \frac{15}{4} \ \frac{15}{4}

Answer

Correct choice: (D)

正确答案：（D）

Solution

We have \begin{align*} 3+\frac{1}{3+\frac{1}{3+\frac13}} &= 3+\frac{1}{3+\frac{1}{\left(\frac{10}{3}\right)}} \\ &= 3+\frac{1}{3+\frac{3}{10}} \\ &= 3+\frac{1}{\left(\frac{33}{10}\right)} \\ &= 3+\frac{10}{33} \\ &= \boxed{\textbf{(D)}\ \frac{109}{33}}. \end{align*}

我们有 \begin{align*} 3+\frac{1}{3+\frac{1}{3+\frac13}} &= 3+\frac{1}{3+\frac{1}{\left(\frac{10}{3}\right)}} \\ &= 3+\frac{1}{3+\frac{3}{10}} \\ &= 3+\frac{1}{\left(\frac{33}{10}\right)} \\ &= 3+\frac{10}{33} \\ &= \boxed{\textbf{(D)}\ \frac{109}{33}}. \end{align*}

Topics

AR.001 Fractions