1.6整数乘除估计

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  整数乘除估计

  

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  Craig placed an  order  for 1700 highlighters for a special event hosted by his company. However, instead of placing a single order, he accidentally subscribed to receive 1700 highlighters every month for a year. As the purchase was non-refundable, Craig needs to know how many highlighters to expect so that he can pitch to his boss other ways to use them.  He is running into a meeting and doesn’t have time to make a calculation. How can Craig estimate the number of highlighters the company will receive over the course of the year?
  ::克雷格为其公司主办的特别活动下了一个1700个亮点的订单。 但是,他没有发出单张,而是不小心在一年中每个月接到1700个亮点。 由于购买是无法偿还的,克雷格需要知道有多少亮点,以便他能向老板投出其他使用方式。 他正在开会,没有时间进行计算。 克雷格如何估计公司在一年中将会收到1700个亮点的数量?

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  In this concept, you will learn how to estimate products and quotients of  whole numbers  using  rounding .
  ::在这个概念中,你将学会如何使用四舍五入来估计产品和整个数字的商数。

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  Estimating Multiplying and Dividing Whole Numbers
  ::估计乘数和拆分整数

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  Just as you can estimate sums and differences, you can also estimate  products  and  quotients .
  ::您也可以估算产品和商数。您也可以估算产品和商数。您也可以估算产品和商数。您也可以估算产品和商数。您也可以估算产品和商数。您也可以估算产品和商数。您也可以估算产品和商数。

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  Remember, a  product  is the answer to a multiplication problem. A  quotient  is the answer to a division problem.To estimate products and quotients, first  round  according to the following rules:
  ::记住, 产品是乘法问题的答案。 商数是除法问题的答案。 要估计产品和商数, 首轮根据以下规则 :

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  1. If the number to the right of the digit you are rounding is less than 5, round down (keep the number being rounded as it is).
     ::如果您四舍五入的位数右侧的数小于5, 则四舍五入( 保持整数的四舍五入 ) 。
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  2. If the number to the right of the digit you are rounding is greater than 5, round up.
     ::如果您正在四舍五入的位数右侧的数大于 5 , 则整数整数 。

  Let's look at this problem.

  $$\begin{array}{r}12\times 19=\underset{\_}{}\end{array}$$

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  First, round the first number to the nearest ten. Since the number in the ones place is less than 5, round down (the digit in the tens place is left as-is). 12 rounds to 10.
  ::首先,将第一个数字圆到最接近的十个数字。因为第一个数字小于5,然后四舍五入(十位数字左转)。 12轮到10轮。

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  Next, round the second number to the nearest ten. Since the number in the ones place is a 9, which is more than 5, round the 1 from the tens place up to a 2. 19 rounds to 20.
  ::下一回合是第二回合到最接近的十位数。 因为一个地方的数字是9, 超过5, 圆1, 从几十个地方到2, 19个回合到20个回合。

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  Finally, multiply the rounded numbers by each other:
  ::最后,将四舍五入数乘以四舍五入数:

  $$\begin{array}{r}10\times 20=200\end{array}$$

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  The estimate of the product is 200.
  ::该产品的估计值为200。

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  Here is an example of a division problem. Estimate the quotient.
  ::这是分裂问题的一个例子。 估计商数 。

  $$\begin{array}{r}32÷11\end{array}$$

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  First, round each number to the nearest ten. 32 rounds down to 30, since the number in the ones place is smaller than 5. 11 rounds down to 10, since the number in the ones place is smaller than 5.
  ::首先,将每个数字轮到最接近的十点。 32轮下到30,因为那些地方的人数小于5,11轮下到10,因为那些地方的人数小于5。

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  Next find the quotient of the estimated values:
  ::下一步找到估计值的商数 :

  $$\begin{array}{r}30÷10=3\end{array}$$

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  The estimated quotient is 3.
  ::估计商数为3。

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  Sometimes, when working with division, you need to find a  compatible number  instead of a rounded number. A  compatible number  is one that is easily divisible.
  ::有时,在与分部合作时,您需要找到一个兼容的编号,而不是四舍五入的编号。一个兼容的编号是一个容易分辨的数字。

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  Let’s look at estimating a problem that needs a compatible number.
  ::让我们来估计一个需要兼容数字的问题。

  $$\begin{array}{r}2321÷8=\underset{\_}{}\end{array}$$

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  Normally, you would round 2321 down to 2300, but 2300 is not easily divisible by 8. The nearest hundred easily divisible by 8 is 2400, because 24 divided by 8 is 3. This makes 2400 a compatible number.
  ::通常情况下,2321回合下到2300,2300是不容易分辨的,但是2300是8,8是不容易分辨的 最接近的百分百乘8是2400, 因为24除8是3, 这使得24000是一个兼容的号码。

  $$\begin{array}{r}2400÷8=300\end{array}$$

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  The estimate is 300.
  ::估计数为300。

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  Remember to keep the following things in mind when estimating:
  ::在估算时,铭记要铭记以下各点:

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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 to find the solution.
     ::如果上述情况不符合估计,请使用精确的数学来找到解决办法。

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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 Craig and his non-refundable highlighters.
  ::早些时候,你得到一个问题 关于克雷格和他的 不可退还的亮点。

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  Craig needs to estimate the total of 1700 highlighters every month for 12 months.
  ::克雷格需要估计 12个月每月总共1700个亮点

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  First, round the numbers:
  ::首先,将数字四舍五入:

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  1700 rounds up to 2000
  ::至2000年1700发子弹

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  12 rounds down to 10
  ::12发,下至10发

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

  $\begin{array}{r}2,000\times 10=20,000\end{array}$

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  The  estimation  is 20,000.
  ::估计是20,000。

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  Craig can report in the meeting that he has a plan to make use of approximately 20,000 highlighters this year.
  ::克雷格可以在会上报告,他计划在今年利用大约20,000个亮点。

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  Example 2
  ::例2

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  Estimate the quotient.
  ::估计商数。

  $$\begin{array}{r}869÷321=\underset{\_}{}\end{array}$$

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  First, round each number to the nearest hundred.
  ::首先,每个数字的四舍五入到最接近的100。

  $$\begin{array}{r}869\text{ rounds to }900\\ 321\text{ rounds to }300\end{array}$$

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  Then, estimate.
  ::然后,估计。

  $$\begin{array}{r}900÷300=3\end{array}$$

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  The estimated quotient is 3.
  ::估计商数为3。

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  Example 3
  ::例3

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}34\times 18=\underset{\_}{}\end{array}$$

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  First round 34 to the nearest ten. Since the number in the ones place is less than 5, round down (keep the 3 in the tens place). 34 rounds to 30.
  ::第一回合34至最接近的十轮。 由于在第一回合中的人数少于5, 则四舍五入( 将三舍五入到十舍十)。 34发到三十舍三十。

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  Next round 18 to the nearest ten. Since the number in the ones place is greater than 5, round up. 18 rounds to 20.
  ::下一轮18至最接近的10个。由于在那些地方的人数超过5个,所以分组18至20个。

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  Finally, multiply the rounded values:
  ::最后,乘以四舍五入值:

  $$\begin{array}{r}30\\ \underset{\_}{\times 20}& \\ 00& \\ \underset{\_}{+600}& \\ 600& \end{array}$$

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  The estimated product is 600.
  ::估计产品为600。

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  Example 4
  ::例4

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  Estimate the product.
  ::估计产品。

  $$\begin{array}{r}187\times 11=\underset{\_}{}\end{array}$$

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  First, round 187 to the nearest hundred. Since the number in the tens place is greater than 5, round up. 187 rounds to 200.
  ::第一,第187回合到最近的100回合。因为在几十个地方的数字超过5个。 187回合到200回合。 187回合到200回合。

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  Next, round 11 to the nearest 10. Since the number in the ones place is less than 5, round down. 11 rounds to 10.
  ::下一轮,第11轮到最近的10轮,因为那些地方的人数不到5人,然后进行11轮到10轮的回合。

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  Finally, multiply the rounded values:
  ::最后,乘以四舍五入值:

  $$\begin{array}{rl}200& \\ \underset{\_}{\times 10}& \\ 000& \\ \underset{\_}{+2000}& \\ 2000& \end{array}$$

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  The estimated product is 2000.
  ::估计产品为2000年。

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  Example 5
  ::例5

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  Estimate the quotient.
  ::估计商数。

  $$\begin{array}{r}120÷11=\underset{\_}{}\end{array}$$

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  First, note that 120 will  divide  evenly by 10, so just round the second number, leaving 120 as it is.
  ::第一,注意120将平均除以10,所以仅次于第二个数字,留下120个。

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  Next, since the number in the ones place of the second number is less than 5, round down. 11 rounds to 10.
  ::其次,由于第二位数字中的数字不到5,因此四舍五入。 11轮到10轮。

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  Finally, use mental math to divide 120 by 10.
  ::最后,用心理数学来将120除以10。

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  The estimated quotient is 12.
  ::估计商数为12。

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  Review
  ::回顾

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  Estimate the following products and quotients.
  ::估计以下产品和商数。

  1. $\begin{array}{r}17\times 12=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}22\times 18=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}9\times 18=\underset{\_}{}\end{array}$
  4. $\begin{array}{r}7\times 23=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}36\times 40=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}13\times 31=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}9\times 27=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}11\times 32=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}19\times 33=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}22\times 50=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}43÷6=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}19÷10=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}44÷8=\underset{\_}{}\end{array}$
  14. $\begin{array}{r}72÷7=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}17÷8=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}43÷9=\underset{\_}{}\end{array}$
  17. $\begin{array}{r}62÷8=\underset{\_}{}\end{array}$
  18. $\begin{array}{r}102÷18=\underset{\_}{}\end{array}$
  19. $\begin{array}{r}395÷11=\underset{\_}{}\end{array}$
  20. $\begin{array}{r}778÷22=\underset{\_}{}\end{array}$

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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