What is the value of this expression in decimal form? (44/11) + (110/44) + (44/1100)

AMC 8 2024 Problem 2

AMC8 2024 年第 2 题

表达式与运算★☆☆☆☆

What is the value of this expression in decimal form?

\displaystyle \frac{44}{11} + \frac{110}{44} + \frac{44}{1100}

请问下列表达式的值用小数可以表示为哪一项？

正确答案 · Correct Answer

解法1

我们看到

\displaystyle \frac{44}{11}

等于4；

\displaystyle \frac{110}{44}

化简为

\displaystyle \frac{5}{2}

，即2.5；而

\displaystyle \frac{44}{1100}

化简为

\displaystyle \frac{1}{25}

，即0.04；4+2.5+0.04得出$ $

\displaystyle \frac{44}{11}

$ + $

\displaystyle \frac{110}{44}

$ + $

\displaystyle \frac{44}{1100}

$ $是(C)6.54。使用直接计算，我们可以将

\displaystyle \frac{44}{11}

化为

\displaystyle \frac{4400}{1100}

，

\displaystyle \frac{110}{44}

化为

\displaystyle \frac{2750}{1100}

，再加上

\displaystyle \frac{44}{1100}

，然后相加得到

\displaystyle \frac{7194}{1100}

，化简后即为(C)6.54。

Solution 1

We see that

\displaystyle \frac{44}{11}

is 4;

\displaystyle \frac{110}{44}

simplifies to

\displaystyle \frac{5}{2}

, which is 2.5; and

\displaystyle \frac{44}{1100}

simplifies to

\displaystyle \frac{1}{25}

, which is 0.04; 4+2.5+0.04 reveals

\frac{44}{11} + \frac{110}{44} + \frac{44}{1100}

is (C) 6.54. Using brute force we can make

\displaystyle \frac{44}{11}

into

\displaystyle \frac{4400}{1100}

\displaystyle \frac{110}{44}

into

\displaystyle \frac{2750}{1100}

, and

\displaystyle \frac{44}{1100}

, and then we add and get

\displaystyle \frac{7194}{1100}

and this simplifies to (C) 6.54.

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