2020 AMC 10B 第 1 题

Question

下式的值是多少

\begin{aligned} &1 - (-2) - 3 - (-4) \\ &\quad {}- 5 - (-6) \end{aligned}\text{？}

What is the value of

\begin{aligned} &1 - (-2) - 3 - (-4) \\ &\quad {}- 5 - (-6)? \end{aligned}

-20

-3

3

5

21

先把减去负数改写成加上正数，再合并各项。

Turn subtraction of a negative into addition before combining terms

把正项和负项分别配对，计算会更小。

Pair the positive and negative terms so the arithmetic stays small

减去负数等于加上对应的正数，所以

\begin{aligned} &1-(-2)-3-(-4) \\ &\quad {}-5-(-6) \\ &\quad = 1+2-3+4-5+6\text{。} \end{aligned}

合并各项可得

\begin{aligned} &(1+2+4+6)-(3+5) \\ &\quad = 13-8=5\text{。} \end{aligned}

所以正确答案是 D。

Subtracting a negative is the same as adding the corresponding positive number, so

\begin{aligned} &1-(-2)-3-(-4) \\ &\quad {}-5-(-6) \\ &\quad = 1+2-3+4-5+6. \end{aligned}

Now combine the terms:

\begin{aligned} &(1+2+4+6)-(3+5) \\ &\quad = 13-8=5. \end{aligned}

Thus, D is the correct answer.

其他年份的第 1 题