2020 AMC 10B 第 1 题

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1.

求下式的值: 1(2)3(4)5(6)? \begin{aligned} &1 - (-2) - 3 - (-4) \\ &\quad {}- 5 - (-6)? \end{aligned}

What is the value of 1(2)3(4)5(6)? \begin{aligned} &1 - (-2) - 3 - (-4) \\ &\quad {}- 5 - (-6)? \end{aligned}

20-20

3-3

33

55

2121

答案:D
知识点:整数运算
难度评级:450
解答:

减去负数等于加上对应的正数,所以 合并各项可得 1(2)3(4)5(6)=1+23+45+6. \begin{aligned} &1-(-2)-3-(-4) \\ &\quad {}-5-(-6) \\ &\quad = 1+2-3+4-5+6. \end{aligned} (1+2+4+6)(3+5)=138=5. \begin{aligned} &(1+2+4+6)-(3+5) \\ &\quad = 13-8=5. \end{aligned}

所以正确答案是 D

Subtracting a negative is the same as adding the corresponding positive number, so 1(2)3(4)5(6)=1+23+45+6. \begin{aligned} &1-(-2)-3-(-4) \\ &\quad {}-5-(-6) \\ &\quad = 1+2-3+4-5+6. \end{aligned} Now combine the terms: (1+2+4+6)(3+5)=138=5. \begin{aligned} &(1+2+4+6)-(3+5) \\ &\quad = 13-8=5. \end{aligned}

Thus, D is the correct answer.

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