4.5使用绝对值的整数和

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  使用绝对值的整数和

  

  [Figure 1]

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  The weather has been very cold this winter in North Dakota where Lauren lives! This morning the meteorologist said that the temperature was  $\begin{array}{r}-{12}^{\circ }F\end{array}$ . Lauren was hoping to go for a ride on her horse on Saturday and luckily for Lauren, it is supposed to warm up a bit by the weekend. The meteorologist said the temperature will be  $\begin{array}{r}{23}^{\circ }F\end{array}$  higher on Saturday. How could Lauren use absolute value to help her to add the two integers in  order  to figure out what the temperature will be on Saturday?
  ::罗伦住的北达科他州冬季天气非常寒冷!今天上午,气象学家说气温是—12°F。劳伦本来希望在星期六骑她的马,

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  In this concept, you will learn how to find the  sum  of integers using absolute value.
  ::在此概念中,您将学会如何用绝对值来找到整数的总和。

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  Adding Integers Using Absolute Value
  ::使用绝对值添加整数

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  Integers  are the set of  whole numbers  and their opposites.
  ::整组是整组数字和反面数字的组合。

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  There are many different strategies for adding integers. One strategy for adding involves absolute value. The  absolute value  of a number is its distance from  zero  on the  number line . Remember that the symbol for absolute value is | |. The absolute value of an integer will always be  positive  (or zero).
  ::添加整数有多种不同的策略。 添加一个策略涉及绝对值。 数字的绝对值是数字行与零的距离。 记住绝对值的符号是\\\\\\\\\\\。 一个整数的绝对值总是正( 或零) 。

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  To add two integers using the absolute value strategy first look at the signs of the two integers.
  ::要使用绝对值策略添加两个整数,请先查看两个整数的符号。

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  • If the two integers have the same sign:
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    1. Add their absolute values.
       ::加上他们的绝对值
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    2. Give the answer the same sign as the two original integers.
       ::给答案给出与两个原始整数相同的符号。
    
    ::如果两个整数有相同的符号: 添加其绝对值。 给答案的符号与两个原始整数相同。
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  • If the two integers have different signs:
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    1. Subtract the lesser absolute value from the greater absolute value.
       ::将较低绝对值从较大绝对值中减去。
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    2. Give the answer the same sign as the integer with the greater absolute value.
       ::给答案给出与绝对值较大的整数相同的符号。
    
    ::如果两个整数有不同的符号:从更大的绝对值中减去较小绝对值的绝对值。给答案的符号与整数的符号相同,绝对值则更大。

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  Let's look at an example.
  ::让我们举个例子。

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  Find the sum of  $\begin{array}{r}-13+(-12)\end{array}$ .
  ::查找- 13+(- 12)之和。

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  First, look at the signs of the integers. Both integers have the same sign, a negative sign.
  ::首先, 看看整数的符号。 两个整数都有相同的符号, 一个负符号 。

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  Step 1 is to add their absolute values.  $\begin{array}{r}|-13|=13\end{array}$  and  $\begin{array}{r}|-12|=12\end{array}$ , so you have
  ::第一步是增加它们的绝对值。 = 13 = 13 = 13 和 = 12 = 12,所以你已经有了。

  $\begin{array}{r}13+12=25\end{array}$

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  Step 2 is to give the answer the same sign as the original two integers. In this case, that is a negative sign. So the 25 becomes -25.
  ::第二步是给答案与原来的两个整数一样的符号。 在这种情况下, 这是一个负符号 。 因此, 25 变成 - 25 。

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  The answer is -25. So  $\begin{array}{r}-13+(-12)=-25\end{array}$ .
  ::答案是 -25。所以 - 13+ ( - 12) = - 25。

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  Let's look at another example.
  ::让我们再举一个例子。

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  Find the sum of  $\begin{array}{r}13+(-12)\end{array}$ .
  ::查找总和为13+ (- 12) 。

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  First, look at the signs of the integers. This time the integers have different signs, one negative and one positive.
  ::首先, 看看整数的符号。 这一次整数有不同的符号, 一个是负的, 一个是正的 。

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  Step 1 is to subtract the lesser absolute value from the greater absolute value.  $\begin{array}{r}|13|=13\end{array}$  and  $\begin{array}{r}|-12|=12\end{array}$ , so the lesser absolute value is 12 and the greater absolute value is 13. So you have
  ::步骤1是从更大的绝对值中减去较低的绝对值。 13 = 13 = 13 和 = 12 = 12 = 12, 所以较低的绝对值是 12 , 更大的绝对值是 13。 所以, 您的绝对值是 13 。

  $\begin{array}{r}13-12=1\end{array}$

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  Step 2 is to give the answer the same sign as the integer with the greater absolute value. 13 had the greater absolute value and it is a positive integer. So your final answer is positive.
  ::第二步是给答案与整数的符号相同,绝对值更大。 13 的绝对值更大,是正整数。 所以最后答案是正。

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  The answer is 1. So  $\begin{array}{r}13+(-12)=1\end{array}$ .
  ::答案是 1. 所以13+ ( - 12) = 1。

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  You can use the same strategy to find the sum of more than two integers. Start by adding the first pair of integers. Then, add the next integer to the sum of the first pair. Continue in this way until you have added all of the integers.
  ::您可以使用相同的策略来查找超过两个整数的总和。 从添加第一对整数开始。 然后, 在第一对整数的总和中添加下一个整数。 继续这样直到您添加了全部整数为止 。

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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 Lauren and her cold winter in North Dakota.
  ::早些时候,你得到一个问题 关于劳伦和她的寒冬 在北达科他州。

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  It is currently  $\begin{array}{r}-{12}^{\circ }F\end{array}$ , but it is supposed to warm up by  $\begin{array}{r}{23}^{\circ }F\end{array}$  on Saturday when Lauren is hoping to go for a ride on her horse. Lauren wanted to figure out what the temperature will be on Saturday.
  ::劳伦想弄清楚周六的温度会如何。

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  In order to figure out what the temperature will be on Saturday, Lauren would need to add  $\begin{array}{r}-12+23\end{array}$ .
  ::为了弄清楚星期六的温度, Lauren需要加上12+23。

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  First, look at the signs of the integers. The integers have different signs, one negative and one positive.
  ::首先,看看整数的符号。整数有不同的符号,一个是负的,一个是正的。

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  Step 1 is to subtract the lesser absolute value from the greater absolute value.  $\begin{array}{r}|-12|=12\end{array}$  and  $\begin{array}{r}|23|=23\end{array}$ , so the lesser absolute value is 12 and the greater absolute value is 23. So you have
  ::步骤1是从更大的绝对值中减去较低的绝对值。 = 12 = 12 = 23 = 23 = 23, 所以较低的绝对值是 12, 更大的绝对值是 23。

  $\begin{array}{r}23-12=11\end{array}$

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  Step 2 is to give the answer the same sign as the integer with the greater absolute value. 23 had the greater absolute value and it is a positive integer. So your answer is positive.
  ::第二步是给答案的符号与整数相同,绝对值较大。 23的绝对值较大, 整数为正数。 因此, 您的回答是正数 。

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  The answer is 11. So  $\begin{array}{r}-12+23=11\end{array}$ .
  ::答案是11,所以 - 12 + 23 = 11。

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  Lauren can expect that it will be  $\begin{array}{r}{11}^{\circ }F\end{array}$  on Saturday.
  ::Lauren预计星期六会是11点F

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  Example 2
  ::例2

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  Find the sum of  $\begin{array}{r}-12+(-18)\end{array}$ .
  ::查找 - 12+( - 18)之和。

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  First, look at the signs of the integers. Both integers have the same sign, a negative sign.
  ::首先, 看看整数的符号。 两个整数都有相同的符号, 一个负符号 。

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  Step 1 is to add their absolute values.  $\begin{array}{r}|-12|=12\end{array}$  and  $\begin{array}{r}|-18|=18\end{array}$ , so you have
  ::第一步是增加它们的绝对值。 = 12 = 12 = 12 和 = 18 = 18 = 18, 因此你已经有了。 = = 12 = 12 = 12 = 12 = 12 和 = 18 = 18 = 18 = 18

  $\begin{array}{r}12+18=30\end{array}$

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  Step 2 is to give the answer the same sign as the original two integers. In this case, that is a negative sign. So the 30 becomes -30.
  ::第二步是给答案与原来的两个整数一样的符号。 在这种情况下, 这是一个负的符号。 因此, 30 变成 - 30 。

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  The answer is -30. So  $\begin{array}{r}-12+(-18)=-30\end{array}$ .
  ::答案是-30。所以 - 12 + ( - 18) =- 30。

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  Example 3
  ::例3

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  Find the sum of  $\begin{array}{r}-12+8\end{array}$ .
  ::查找 - 12+8的总和。

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  First, look at the signs of the integers. The integers have different signs, one negative and one positive.
  ::首先,看看整数的符号。整数有不同的符号,一个是负的,一个是正的。

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  Step 1 is to subtract the lesser absolute value from the greater absolute value.  $\begin{array}{r}|-12|=12\end{array}$  and  $\begin{array}{r}|8|=8\end{array}$ , so the lesser absolute value is 8 and the greater absolute value is 12. So you have
  ::步骤1是从更大的绝对值中减去较低的绝对值。 = 12 = 12 = 和 8 = 8 = 8, 因此, 较低的绝对值是 8, 更大的绝对值是 12。 因此, 您的绝对值是 12 。

    $\begin{array}{r}12-8=4\end{array}$

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  Step 2 is to give the answer the same sign as the integer with the greater absolute value. 12 had the greater absolute value and it is a negative integer. So your answer is negative and the 4 becomes a -4.
  ::第二步是给答案的符号与整数相同,绝对值更大。 12 的绝对值较大, 是负整数。 所以答案是负的, 4 变成 A - 4 。

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  The answer is -4. So  $\begin{array}{r}-12+8=-4\end{array}$ .
  ::答案是 -4. 那么 - 12+8 = - 4。

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  Example 4
  ::例4

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  Find the sum of  $\begin{array}{r}-9+(-12)\end{array}$ .
  ::查找- 9+ (- 12) 之和。

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  First, look at the signs of the integers. Both integers have the same sign, a negative sign.
  ::首先, 看看整数的符号。 两个整数都有相同的符号, 一个负符号 。

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  Step 1 is to add their absolute values.  $\begin{array}{r}|-9|=9\end{array}$  and  $\begin{array}{r}|-12|=12\end{array}$ , so you have
  ::步骤1是增加它们的绝对值。=--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

  $\begin{array}{r}9+12=21\end{array}$

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  Step 2 is to give the answer the same sign as the original two integers. In this case, that is a negative sign. So the 21 becomes -21.
  ::第二步是给答案与原来的两个整数一样的符号。 在这种情况下, 这是一个负符号 。 因此, 21 变成 - 21 。

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  The answer is -21. So  $\begin{array}{r}-9+(-12)=-21\end{array}$ .
  ::答案是-21。所以- 9+( - 12) =- 21。

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  Example 5
  ::例5

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  Find the sum of  $\begin{array}{r}7+(-2)+(-10)\end{array}$ .
  ::查找7+(-2)+(-10)的总和。

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  First, add the first two integers,  $\begin{array}{r}7+(-2)\end{array}$ . These two integers have different signs, one negative and one positive.
  ::首先,添加前两个整数,即7+(-2)。这两个整数有不同的符号,一个是负的,另一个是正的。

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  Step 1 is to subtract the lesser absolute value from the greater absolute value.  $\begin{array}{r}|7|=7\end{array}$  and  $\begin{array}{r}|-2|=2\end{array}$ , so the lesser absolute value is 2 and the greater absolute value is 7. So you have
  ::步骤1是从更大的绝对值中减去较低的绝对值。 7 = 7 和 = 2 = 2 = 2, 因此, 较低的绝对值是 2, 更大的绝对值是 7。

  $\begin{array}{r}7-2=5\end{array}$

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  Step 2 is to give the answer the same sign as the integer with the greater absolute value. 7 had the greater absolute value and it is a positive integer. So your result is positive.
  ::第二步是给答案的符号与整数相同,绝对值较大。7的绝对值较大,是正整数。所以结果为正数。

    $\begin{array}{r}7+(-2)=5\end{array}$

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  Next, take your result of 5 and add the third integer from the original sum, (-10). These two integers also have different signs, one negative and one positive.
  ::接下来,将结果取5, 从原始总和(- 10) 中加上第三个整数, (- 10) 。 这两个整数也有不同的符号, 一个是负的, 一个是正的。

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  Again, Step 1 is to subtract the lesser absolute value from the greater absolute value.  $\begin{array}{r}|5|=5\end{array}$  and  $\begin{array}{r}|-10|=10\end{array}$ , so the lesser absolute value is 5 and the greater absolute value is 10. So you have
  ::步骤1是从更大的绝对值中减去较低的绝对值。 5 = 5 = 5 和 10 = 10, 所以较低的绝对值是 5, 更大的绝对值是 10。

  $\begin{array}{r}10-5=5\end{array}$

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  Again, Step 2 is to give the answer the same sign as the integer with the greater absolute value. -10 had the greater absolute value and it is a negative integer. So your result becomes negative.
  ::第二步是给答案的符号与整数相同,绝对值较大。 -10的绝对值较大,是负整数。所以结果为负。

  $\begin{array}{r}5+(-10)=-5\end{array}$

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  The final answer is -5. So  $\begin{array}{r}7+(-2)+(-10)=-5\end{array}$ .
  ::最后一个答案是 -5. 所以7+(-2)+(-10)=-5。

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  Review
  ::回顾

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  Use absolute values to find each sum.
  ::使用绝对值来找到每一总和。

  1.   $\begin{array}{r}20+(-9)\end{array}$
  2.   $\begin{array}{r}-6+(-9)\end{array}$
  3. $\begin{array}{r}4+(-9)\end{array}$
  4.   $\begin{array}{r}-12+(-19)\end{array}$
  5. $\begin{array}{r}-2+(-5)\end{array}$
  6.   $\begin{array}{r}-11+(-13)\end{array}$
  7. $\begin{array}{r}-30+(-40)\end{array}$
  8. $\begin{array}{r}-8+3+(-9)\end{array}$  
  9. $\begin{array}{r}6+1+(-9)\end{array}$
  10. $\begin{array}{r}(-8)+-20\end{array}$
  11. $\begin{array}{r}(-6)+8+(-4)\end{array}$
  12. $\begin{array}{r}(2)+8+(-12)\end{array}$
  13. $\begin{array}{r}5+7+(-15)\end{array}$
  14. $\begin{array}{r}-5+-7+(-15)\end{array}$  
  15. $\begin{array}{r}-15+-17+(12)\end{array}$

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  Review (Answers)
  ::回顾(答复)