1.5整数加减法的估计

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• 选择节整数加减法的估计

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  整数加减法的估计

  

  [Figure 1]

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  Eduardo has 67 apps on his phone. His older brother Rocco has 79 apps, and their younger sister, Jemima, has just 22 apps. Eduardo’s father asks him how many apps the kids have in total. Eduardo starts to get out his pen and paper to make the calculation, but his dad stops him and asks him to just estimate. How can Eduardo quickly come up with an approximate answer?
  ::Eduardo的哥哥Rocco有79个应用程序,他们的妹妹Jemima只有22个应用程序。 Eduardo的父亲问他孩子总共有多少应用程序。 Eduardo的父亲开始拿出笔和纸来进行计算,但他的爸爸却阻止了他,要求他只是估计。 爱德华多怎么能够很快找到大致答案呢?

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  In this concept, learn how to estimate sums and differences of  whole numbers  using  rounding .
  ::在这一概念中,学习如何使用四舍五入法估计整个数字的总数和差异。

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  Estimating Adding and Subtracting Whole Numbers
  ::估计增加和减减整数

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  To  estimate  means to find an answer that is close to the exact answer. The key with  estimation  is to only use it in instances that don’t require an exact answer. Estimation means to find an answer that makes sense and works with the problem, but is not necessarily exact.
  ::估算意味着找到一个接近准确答案的答案。 估算的关键在于仅仅在不需要准确答案的情况下使用它。 估算意味着找到一个合理且能解决问题的答案,但不一定准确。

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  You can estimate  sums  (the answers to addition problems), and  differences  (the answers to subtraction problems). The first step in estimating a  sum  or a  difference  is to  round  the numbers, by changing them to the nearest power of ten, hundred, thousand, etc. Round the numbers first, then use mental math to estimate an answer.
  ::您可以估算总和(对附加问题的答案)和差异(对减法问题的答案) 。 估算总和或差数的第一步是四舍五入数字,将其修改为最接近的十万,等等。 先将数字四舍五入,然后使用心理数学来估算答案。

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  When rounding, follow these rounding rules:
  ::当四舍五入时,请遵守这些四舍五入的规则:

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  1. If the number being rounded is less than 5, round down.
     ::如果四舍五入的数值小于5,则四舍五入。
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  2. If the number being rounded is 5 or greater, round up.
     ::如果四舍五入的数值为5或5以上,则分组。

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  For example, to round the number 69 to the nearest ten:
  ::例如,将数字乘以69到最接近的10:

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  First, to round to the tens place, look at the digit to the right (in this case, the 9).
  ::首先,从十位数到十位数,看看右边的位数(在本案中,是九位数)。

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  Next, see that 9 is greater than 5, so round the tens digit up. The 6 becomes a 7.
  ::接下来,看9比5大于5, 左右数十位数上升。 6变成7。

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  Finally, to round to the nearest ten, make the ones digit a  zero . The answer is 70.
  ::最后,要四舍五入到最接近的十点,请将数字数为零。答案是70。

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  As another example, round the number 130 to the nearest hundred:
  ::例如,将数字130乘以最接近的100:

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  First, to round to the hundreds place, consider the value in the tens.
  ::首先,到数百个地方,考虑一下几十个的价值。

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  Next, notice that 3 is less than 5, so round down (keep the hundreds digit the same).
  ::接下来,请注意3小于5,请四舍五入(将数百位数保持不变)。

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  Finally, replace the tens and ones digits with zeroes. The rounded value is 100.
  ::最后,将十位数和十位数替换为零。四舍五入值为100。

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  To see how rounding can help with estimating, consider this problem:
  ::为了了解四舍五入如何有助于估算,请考虑这一问题:

  $$\begin{array}{r}58+22=\underset{\_}{}\end{array}$$

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  To estimate this answer, first round both numbers to the nearest ten.
  ::为估计这一答案,第一轮两个数字均为最接近的十。

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  58 rounds up to 60.
  ::58轮以上至60轮。

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  22 rounds down to 20.
  ::22发,20发

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  Then sum the rounded values: 60 + 20 = 80
  ::然后将四舍五入值: 60+ 20= 80之和

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  The estimated answer is 80.
  ::估计答案是80。

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  Some key things to think about when estimating:
  ::估计时需要考虑的一些关键事项:

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  1. The estimate must make sense for the problem.
     ::估计必须能解决问题。
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  2. The estimate must be reasonable.
     ::估计数必须合理。
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  3. The estimate must be close to the exact answer.
     ::估计必须接近准确答案。
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  4. If none of the above fit the estimate,  use exact math for the problem.
     ::如果上述情况不符合估计,请使用精确的数学来解决问题。

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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 Eduardo and his application approximation.
  ::早些时候,你得到一个问题 关于Eduardo和他的申请近似。

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  Eduardo needs to estimate the sum of 67, 79 and 22.
  ::Eduardo需要估算67、79和22的总数。

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  First, round the numbers.
  ::首先,用数字来圆。

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  67 rounds up to 70
  ::67发至70发

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  79 rounds up to 80
  ::79发,至多80发

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  22 rounds down to 20
  ::22发,20发

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  Next, use mental math.
  ::下一位,用心理数学

  70 + 80 + 20

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  The estimation is 170.
  ::估计是170

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  Eduardo can tell his dad that the kids have approximately 170 apps between them.
  ::Eduardo可以告诉他爸爸 孩子们之间大约有170个应用程序

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  Example 2
  ::例2

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  Estimate the sum.
  ::估计总和。

  $$\begin{array}{r}387+293=\underset{\_}{}\end{array}$$

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  First, to estimate this answer, since these numbers are a little bigger than the last problem, round to the nearest hundred.
  ::首先,要估计这个答案, 因为这些数字比上一个问题大一点, 圆到最近的100。

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  387 rounds up to 400.
  ::387发至多400发子弹。

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  293 rounds up to 300.
  ::293发,最多300发

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  Then sum the estimated values. 400 + 300 = 700
  ::然后计算估计值。 400+300=700

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  The estimate is 700.
  ::估计数为700。

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  Example 3
  ::例3

  $\begin{array}{r}17+27=\underset{\_}{}\end{array}$

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  First, to round the 17 to the tens place, look at the digit to the right of the tens place.
  ::首先,把17到 10 个地方,看数字 到 10 个地方的右侧。

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  Next, since the number in the ones place is a 7, which is larger than 5, round the 1 in the tens place up to 2. The first number rounds to 20.
  ::其次,由于一个地方的数字是7, 大于5, 将一个在几十个地方, 圆1到2, 第一个数到20。

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  Then, to round the 27 to the tens place, look at the digit to the right of the tens place.
  ::然后,在27到 10 个地方的周围, 看看数字到 10 个地方的右侧。

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  Then, since the number in the ones place is a 7, which is larger than 5, round the 2 in the tens place up to a 3. The second number rounds to 30.
  ::然后,由于在那些地方的数字是7, 大于5, 圆2, 圆10, 圆10, 圆3, 第二回合为30。

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  Finally, sum the estimated values. 20 + 30 = 50
  ::最后,总和估计值。 20+30=50

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  The solution is 50.
  ::解决办法是50。

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  Example 4
  ::例4

  $\begin{array}{r}290+510=\underset{\_}{}\end{array}$

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  First, to round the 290 to the nearest hundred, look at the digit to the right of the hundreds place, which would be the tens.
  ::首先,在290到最近的100之间, 看看数百个地方右侧的位数, 也就是几十个。

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  Next, since the number in the tens place is a 9, which is larger than 5, round the 2 in the hundreds place up to 3. The first number rounds to 300.
  ::其次,由于在几十个地方的数字是9个,大于5个,在数百个地方的2个圆2个圆,到3个圆3个圆,第一个圆到300个圆。

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  Next, to round the 510 to the hundreds place, look at the digit in the tens place.
  ::接下来,从510到数百个地方, 看看几十个地方的数字。

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  Then, since the number in the tens place is a 1, which is smaller than 5, keep the 5 in the hundreds place. The second number rounds to 500.
  ::然后,由于在 10 位的数字是 1 , 小于 5 , 使 5 位保持在 数百 位。 第二回合为 500 。

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  Finally, sum the estimated values. 300 + 500 = 800
  ::最后,加之估计值300+500=800

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  The answer is 800.
  ::答案是800

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  Example 5
  ::例5

  $\begin{array}{r}592-411=\underset{\_}{}\end{array}$

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  First, to round the 592 to the hundreds place, look at the digit in the tens place.
  ::首先,从592到数百个地方, 看看几十个地方的数字。

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  Next, since the number in the tens place is a 9, which is larger than 5, round the hundreds place up to 6. The first number rounds to 600.
  ::其次,由于在几十个地方的数字是9个,大于5个,数百个地方四舍五入,最高达6个,第一组数字为600个。

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  Then, to round the 411 to the hundreds place, look at the digit to the right of the hundreds place.
  ::然后,绕411到数百个地方, 看看数百个地方右边的位数。

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  Then, since the number in the tens place is a 1, which is smaller than 5, keep the 4 in the hundreds place. The second number rounds to 400.
  ::然后,由于在 10 位的数字是 1 , 小于 5 , 保持 4 在 数百 位。 第二回合为 400 。

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  Finally, subtract the estimated values. 600 - 400 = 200
  ::最后,减去估计值。 600- 400=200

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  The answer is 200.
  ::答案是200

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  Review
  ::回顾

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  Estimate the following sums and differences.
  ::估计以下数额和差额。

  1. $\begin{array}{r}45+62=\underset{\_}{}\end{array}$  
  2. $\begin{array}{r}32+45=\underset{\_}{}\end{array}$  
  3. $\begin{array}{r}21+54=\underset{\_}{}\end{array}$  
  4. $\begin{array}{r}103+87=\underset{\_}{}\end{array}$  
  5. $\begin{array}{r}101+92=\underset{\_}{}\end{array}$  
  6. $\begin{array}{r}342+509=\underset{\_}{}\end{array}$  
  7. $\begin{array}{r}502+307=\underset{\_}{}\end{array}$  
  8. $\begin{array}{r}672+430=\underset{\_}{}\end{array}$  
  9. $\begin{array}{r}201+303=\underset{\_}{}\end{array}$  
  10. $\begin{array}{r}678+407=\underset{\_}{}\end{array}$  
  11. $\begin{array}{r}23-9=\underset{\_}{}\end{array}$  
  12. $\begin{array}{r}46-8=\underset{\_}{}\end{array}$  
  13. $\begin{array}{r}58-12=\underset{\_}{}\end{array}$  
  14. $\begin{array}{r}76-9=\underset{\_}{}\end{array}$  
  15. $\begin{array}{r}204-112=\underset{\_}{}\end{array}$  
  16. $\begin{array}{r}87-65=\underset{\_}{}\end{array}$  
  17. $\begin{array}{r}98-33=\underset{\_}{}\end{array}$  
  18. $\begin{array}{r}354-102=\underset{\_}{}\end{array}$  
  19. $\begin{array}{r}562-112=\underset{\_}{}\end{array}$  
  20. $\begin{array}{r}789-99=\underset{\_}{}\end{array}$   

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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