11.10同号整数的差

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  同号整数的差

  

  [Figure 1]

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  Candace's school is doing a Jump Rope for Heart event to raise money for the American Heart Association. Technically, it is about raising money for a worthy cause, but, unofficially, the students all keep track of their jump rope high scores and try to beat each other. Last year, Candace's friend, Lauren, got the most jumps without missing: 487. Candace only made 324 jumps without missing, but she's been practicing all year. Assuming that Lauren does about the same this year as last, how many more jumps will Candace need to do to beat her?
  ::坎迪斯的学校正在为美国心脏协会筹募钱。在技术上,这是为了一个值得的事业筹集资金,但非正式地说,学生们都跟踪他们的跳绳高分,并试图相互打斗。去年,坎迪斯的朋友劳伦在没有失踪的情况下跳得最多:487次。坎迪斯只跳了324次而没有失踪,但她全年都在练习。假设劳伦今年和去年一样,要跳多少次坎迪斯才能打败她?

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  In this concept, you will learn to take the  difference  between two integers with the same sign.
  ::在此概念中, 您将学会用同一个符号取两个整数的差 。

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  Subtracting Integers with the Same Sign
  ::减少带有相同符号的整数

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  A  positive  number  is a number greater than  zero . It can be written with or without a + symbol in front of it. A gain in something is written with a positive number. 
  ::正数是大于零的数。 它可以在前面有或没有 + 符号来写。 某事物的增益会写成正数 。

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  A  negative number  is a number that is less than zero. It is always written with a - symbol in front of it. A loss is written with a negative number. 
  ::负数是一个小于零的数字。它总是在前面写上一个符号。损失则用负数写上。

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  An  integer  is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa.
  ::整数是正整数或正整数。 这里, 反整数是指符号。 正整数是负整数, 反整数是负整数, 反整数是正整数。

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  The rules are different when subtracting two  positive numbers  or two  negative numbers . When subtracting two positive numbers, first take the smaller number out of the larger number. Then, look at which number was bigger in the original problem. If the bigger number was first, then the answer is positive, as in this example:
  ::当减去两个正数或两个负数时,规则是不同的。当减去两个正数时,首先从较大数字中取取较小数字。然后,看看在最初的问题中哪个数字更大。如果较大数字是第一个,那么答案是正数,例如:

  $$\begin{array}{r}9–4=5\end{array}$$

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  If the bigger number was second, then the answer is negative, as in this example:
  ::如果较大的数字是第二,那么答案是否定的,例如:

  $$\begin{array}{r}4-9=-5\end{array}$$

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  The process is longer when subtracting negative numbers because you end up subtracting a negative number, which is the same as adding a positive number, as in this example:
  ::当减去负数时,该过程较长,因为最终会减去负数,这与增加正数相同,例如:

  $$\begin{array}{r}-8--5=-8+5\end{array}$$

    

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  The subtraction became addition. This is always the case when subtracting a negative number.
  ::减法成为加法。减去负数时总是这样。

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  So, when subtracting two negative numbers, the first step is always to change the subtraction to an addition and re-write the problem. Then, you have an addition problem between a positive number and a negative number. Next, re-write the problem so that it looks like the difference between two positive numbers.
  ::因此,当减去两个负数时,第一步总是将减法改为加法并重写问题。然后,在正数和负数之间出现一个加法问题。接下来,重写问题,使之看起来像两个正数之间的差别。

  $$\begin{array}{r}-8+5=5-8\end{array}$$

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  Finally, solve it as you did the difference between two positive numbers.
  ::最后,解决它,就像你所做的两个正数的差别一样。

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  In this example, the difference between 8 and 5 is 3, and because the bigger integer was second, the answer is negative.
  ::在这个例子中,8和5之间的差别是3,由于较大的整数是第二,答案是否定的。

  $$\begin{array}{r}5-8=-3\end{array}$$

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  Here is another example.
  ::下面是另一个例子。

  $$\begin{array}{r}-3–-6=\end{array}$$

   

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  First, re-write as an addition problem.
  ::首先,重写是一个附加问题。

  $$\begin{array}{r}-3+6=\end{array}$$

  
  

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  Next, re-write as the difference of two positive numbers.
  ::接下来,重写两个正数的差数。

  $$\begin{array}{r}6-3=\end{array}$$

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  Then, take the difference.
  ::那么,采取区别。

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  The difference between 6 and 3 is 3.
  ::6和3之间的差值是3。

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  Finally, notice whether the bigger integer was first or second.
  ::最后,注意较大的整数是第一个还是第二个。

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  In this case, it was first, so the answer is positive.
  ::在这种情况下,这是第一个问题,因此答案是肯定的。

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  The answer is 3.
  ::答案是3

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Candace and her jump rope vendetta.
  ::之前,你得到一个问题 关于坎迪斯和她跳绳的仇杀。

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  She wants to beat her friend's jump rope high score of 487. Her own high score is 324. How many more jumps will she have to do this year without missing?
  ::她想击败她朋友的跳绳高分487。她自己的高分是324。今年她还要跳多少次而不失踪?

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  To figure this out, first she sets up a subtraction problem between two integers of the same sign.
  ::首先,她在同一符号的两个整数之间设置了一个减法问题。

  $$\begin{array}{r}487-324\end{array}$$

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  Next, she takes the smaller number from the bigger.
  ::接下来,她从大号取小号数

  $$\begin{array}{r}487-324=153\end{array}$$

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  Then, she decides which number was bigger. 
  ::然后,她决定哪个数字更大。

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  In this case, Lauren had more jumps, so Candace knows that she has to make at least 153 more jumps herself to beat Lauren.
  ::在这个案例中 Lauren跳得更多 所以Candace知道 她至少得再跳153跳 才能打败Lauren

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  Example 2
  ::例2

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  Joaquin made fifteen sugar cookies. He wanted to give one to everyone in his class of 25. How many more does he need to make?
  ::Joaquin做了15个糖饼干 他想给25年级的每个人一个 他还要做多少?

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  First, write the situation as a mathematical expression.
  ::首先,将情况写成数学表达式。

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  He starts with 15 cookies and wants to give away 25.
  ::他从15个饼干开始 想要放弃25个饼干

  $$\begin{array}{r}15-25\end{array}$$

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  Next, take the smaller number from the larger number. 
  ::接下来,从较大的数字中选取较小的数字。

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  25 less 15 is 10.
  ::25减15是10。

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  Then, check to see which number is bigger.
  ::然后,检查看看哪个数字更大。

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  In this case, the second is bigger, so the answer is negative.
  ::在这种情况下,第二个是更大的,所以答案是否定的。

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  The answer is -10. This means that Juaquin is 10 cookies shy of his goal. He will need to make ten more to give everyone in his class one.
  ::答案是 - 10。 这意味着 Juaquin 距离他的目标差10个饼干。 他需要再多做10个饼干, 才能给他班级的每个人一个。

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  Example 3
  ::例3

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  Find the difference.
  ::找出差别

  5 – 10 = ____

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  First, take the smaller number from the bigger.
  ::首先,从更大的数字中取一个较小的数字。

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  10 less 5 is 5.
  ::10减5是5。

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  Next, see which number in the original problem was bigger.
  ::接下来,看看在最初的问题中哪个数字更大。

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  In this case, it was the second so the answer is negative.
  ::在这种情况下,这是第二个问题,因此答案是否定的。

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  The answer is -5.
  ::答案是 -5

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  Example 4
  ::例4

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  Find the difference.
  ::找出差别

  14 – 7 = ____

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  First, take the smaller number from the bigger.
  ::首先,从更大的数字中取一个较小的数字。

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  14 less 7 is 7.
  ::14减7是7。

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  Next, see which number in the original problem was bigger.
  ::接下来,看看在最初的问题中哪个数字更大。

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  In this case, it was the first so the answer is positive.
  ::在这种情况下,这是第一个,因此答案是肯定的。

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  The answer is 7.
  ::答案是7个

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  Example 5
  ::例5

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  Find the difference.
  ::找出差别

  -4 – -8 = ____

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  First, re-write the problem as an addition.
  ::首先,重写问题作为补充。

  -4 + 8

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  Next, re-write the problem as the difference between two positive numbers.
  ::接下来,将问题重写为两个正数之间的差别。

  8 - 4

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  Then, take the smaller number from the larger.
  ::然后,从较大的数字中取出较小的数字。

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  8 less 4 is 4.
  ::8减4是4。

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  Finally, decide which number was bigger.
  ::最后,决定哪个数字更大。

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  In this case, the 8 was bigger, which was the first. So the answer is positive.
  ::在这个例子中,8是更大的,这是第一个。所以答案是肯定的。

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  The answer is 4.
  
  ::答案是4。

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  Review
  ::回顾

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  In the following problems, subtract each pair of integers.
  ::在下面的问题中,请减去每对整数。

  1. $\begin{array}{r}14-19\end{array}$
  2. $\begin{array}{r}24-19\end{array}$
  3. $\begin{array}{r}-1-7\end{array}$
  4. $\begin{array}{r}-4-12\end{array}$
  5. $\begin{array}{r}-14-29\end{array}$
  6. $\begin{array}{r}-24-(-19)\end{array}$
  7. $\begin{array}{r}9-11\end{array}$
  8. $\begin{array}{r}13-(-1)\end{array}$
  9. $\begin{array}{r}23-19\end{array}$
  10. $\begin{array}{r}-31-15\end{array}$
  11. $\begin{array}{r}-18-(-19)\end{array}$
  12. $\begin{array}{r}-14-6\end{array}$
  13. $\begin{array}{r}-74-39\end{array}$
  14. $\begin{array}{r}54-(-29)\end{array}$
  15. $\begin{array}{r}64-99\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源