1.2整数减法

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  整数减法

  

  [Figure 1]

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  Tiffany is driving a truckload of hay bales to one of her customers at a nearby farm. On the way, Tiffany pulls into a weigh station - her truck weighs 24,380 pounds. After delivering the hay, she pulls back into the same weigh station, and learns that her truck now weighs 23,120 pounds. How can Tiffany use this information to figure out the weight of the hay she delivered?
  ::Tiffany在附近农场开着一卡车干草包给一个顾客。在路上,Tiffany拉进一个称重站,她的卡车重24,380磅。在交付干草后,她又拉回同一个称重站,得知她的卡车现在重23,120磅。Tiffany如何利用这个信息来计算她交付的干草的重量?

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  In this concept, you will learn how to subtract  whole numbers .
  ::在这个概念中,你会学会如何减去整个数字。

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  Subtracting Whole Numbers
  ::减减整数

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  Subtraction is the opposite of addition.This means that if you add two numbers and get a total, then you can subtract one of the original numbers from the total and end up with the other original number. When you add two numbers you get the  sum , when you subtract two numbers, you get the  difference .
  ::减法与加法截然相反。 这意味着, 如果您添加两个数字并获得一个总数字, 那么您就可以从总数字中减去一个原始数字, 并最终与另一个原始数字相提并论。 当您添加两个数字时, 当减去两个数字时, 您可以得到两个数字, 差数 。

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

  $$\begin{array}{r}15-9=\underset{\_}{}\end{array}$$

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  First, rewrite the problem vertically. Remember to line up the digits according to  place value .
  ::首先, 垂直重写问题 。 记住要按照位置值排列数字 。

  $$\begin{array}{r}15\\ \underset{\_}{-9}\\ 6\end{array}$$

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  The difference is 6.
  ::差额是6。

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  Let's look at an example with more digits.
  ::让我们用更多数字来举个例子。

  $$\begin{array}{r}12,456-237=\underset{\_}{}\end{array}$$

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  The first step is to line up these digits according to place value. Let’s look at this in a place value chart.
  ::第一步是根据地点值排列这些数字。 让我们用一个地点值图表来看待这一点。

  Place Value Chart for the Numbers 12,456 and 237

  Ten Thousands	Thousands	Hundreds	Tens	Ones
  1	2	4	5	6
  		2	3	7

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  This is what the problem looks like when written vertically.
  ::这就是垂直书写时的问题。

  $$\begin{array}{r}12,456\\ \underset{\_}{-237}\end{array}$$

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  To successfully subtract these two values, you are going to need to  regroup . Regrouping is when you borrow from the next place value column to make subtraction easier.
  ::要成功减去这两个值, 您需要重新组合。 重新组合是当您从下一个位置值列中借入后一个位置值列以方便减法时 。

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  Look at the ones column of the example. You can’t take 7 from 6, so you borrow from the next number. The next number is in the tens column, so you borrow a 10. When you take the 10, you  reduce  the 5 in that column to a 4 (you had 5 tens, you gave 1 ten away). You then turn your 6 into 16 with your borrowed 10. 
  ::查看示例中的列。 您不能从 6 中取 7 。 因此您可以借用下一个数字 。 下一个数字在 10 列中, 您可以借用 10 。 当你拿 10 时, 您将该列中的 5 减为 4 ( 您有 5 10 个, 您给了 110 个 ) 。 然后, 您将您的 6 转换为 16 个 。 您又借 10 个 。

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  Let’s put that into action.
  ::让我们把这一点付诸行动。

  

  [Figure 2]

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  Be sure you subtract according to place value. 
  ::请确定您根据位置值减去。

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  The answer is 12,219.
  ::答案是12 219美元。

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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 Tiffany and her heavy hay.
  ::早些时候,你得到一个问题 关于蒂芬妮和她的重干草。

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  Tiffany’s truck weighed 24,380 pounds with the hay, and 23,120 pounds without it.
  ::Tiffany的卡车有干草24,380磅, 没有干草23,120磅。

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  The difference between those two weights is the weight of the hay. To figure out the difference, Tiffany can subtract the smaller number from the larger number.
  ::这两个重量之间的差别是干草的重量。为了找出差别,Tiffany可以从较大的数字中减去较小数字。

  $$\begin{array}{r}24380-23120\end{array}$$

  
  

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  First, write the problem vertically.
  ::首先,垂直写出问题。

  $$\begin{array}{r}24380\\ \underset{\_}{-23120}\end{array}$$

  
  

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  Next, subtract, regrouping if necessary.
  ::下一步,减去,必要时重新组合。

   

  $$\begin{array}{rl}24380& \\ \underset{\_}{-23120}& \\ 1260\end{array}$$

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  The difference is 1,260.
  ::差额是1 260美元。

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  The total weight of the hay delivered was 1,260 pounds.
  ::交付的干草总重量为1 260磅。

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  Example 2
  ::例2

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  Find the difference.
  ::找出差别

  $$\begin{array}{r}567-391=\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\mathrm{\_}\end{array}$$

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  To subtract these values, first line up the values according to place value.
  ::要减去这些数值,请根据地点值将数值排列第一行。

  $$\begin{array}{r}567\\ \underset{\_}{-391}\end{array}$$

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  Then, go ahead and subtract, regrouping (borrowing) if necessary.
  ::然后,继续减去,必要时重新组合(借款)。

  $$\begin{array}{rl}{}_4& \\ {\cancel{5}}^{1}67& \\ \underset{\_}{-391}& \\ 176& \end{array}$$

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  The answer is 176.
  ::答案是176个

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  Example 3
  ::例3

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  Find the difference.
  ::找出差别

  $\begin{array}{r}674-59=\underset{\_}{}\end{array}$

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  First, rewrite the problem vertically, lining up the numbers according to place value. 
  ::首先,垂直重写问题,根据地点值排列数字。

  $$\begin{array}{rl}674& \\ \underset{\_}{-59}& \end{array}$$

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  Then subtract each column right to left, borrowing as necessary.
  ::然后将每一栏从右到左减去,必要时借用。

   

  $$\begin{array}{rl}{}_6& \\ 6\cancel{7}{}^{1}4& \\ \underset{\_}{-59}& \\ 615& \end{array}$$

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  The answer is 615.
  ::答案是615

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  Example 4
  ::例4

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  Find the difference.
  ::找出差别

  $\begin{array}{r}15,987-492=\underset{\_}{}\end{array}$

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  First, rewrite the problem vertically, lining up the numbers according to place value. 
  ::首先,垂直重写问题,根据地点值排列数字。

  $$\begin{array}{rl}15987& \\ \underset{\_}{-492}& \end{array}$$

  Then subtract each column right to left, borrowing as necessary. 

  $$\begin{array}{rl}{}_8& \\ 15{\cancel{9}}^{1}87& \\ \underset{\_}{-492}& \\ 15495& \end{array}$$

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  The answer is 15,495.
  ::答案是15 495

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  Example 5
  ::例5

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  Find the difference.
  ::找出差别

  $\begin{array}{r}22,456-18,297=\underset{\_}{}\end{array}$

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  First, rewrite the problem vertically, lining up the numbers according to place value. 
  ::首先,垂直重写问题,根据地点值排列数字。

  $$\begin{array}{rl}22456& \\ \underset{\_}{-18297}& \end{array}$$

  Then subtract each column right to left, borrowing as necessary. 

  $$\begin{array}{rl}{}_1{}_3{}_{{}^{1}4}& \\ {\cancel{2}}^{1}2\cancel{4}{\cancel{5}}^{1}6& \\ \underset{\_}{-18297}& \\ 4159& \end{array}$$

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  The answer is 4,159.
  ::答案是4 159

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  Review
  ::回顾

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  Find the difference.
  ::找出差别

  1. $\begin{array}{r}56-21=\underset{\_}{}\end{array}$  
  2. $\begin{array}{r}50-23=\underset{\_}{}\end{array}$  
  3. $\begin{array}{r}267-19=\underset{\_}{}\end{array}$  
  4. $\begin{array}{r}345-127=\underset{\_}{}\end{array}$  
  5. $\begin{array}{r}560-233=\underset{\_}{}\end{array}$  
  6. $\begin{array}{r}1,600-289=\underset{\_}{}\end{array}$  
  7.   $\begin{array}{r}5,400-2,334=\underset{\_}{}\end{array}$  
  8.   $\begin{array}{r}8,990-7,865=\underset{\_}{}\end{array}$  
  9. $\begin{array}{r}12,340-3,456=\underset{\_}{}\end{array}$  
  10. $\begin{array}{r}23,410-19,807=\underset{\_}{}\end{array}$  
  11. $\begin{array}{r}35,611-9,037=\underset{\_}{}\end{array}$  
  12. $\begin{array}{r}22,410-11,807=\underset{\_}{}\end{array}$  
  13. $\begin{array}{r}54,600-21,807=\underset{\_}{}\end{array}$  
  14. $\begin{array}{r}88,419-32,817=\underset{\_}{}\end{array}$  
  15. $\begin{array}{r}93,415-10,007=\underset{\_}{}\end{array}$  
  16. $\begin{array}{r}67,419-39,807=\underset{\_}{}\end{array}$  
  17. $\begin{array}{r}123,410-119,807=\underset{\_}{}\end{array}$  
  18. $\begin{array}{r}334,410-219,807=\underset{\_}{}\end{array}$  

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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