5.2寻找因子的可整除性规则

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  寻找因子的可整除性规则

  

  [Figure 1]

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  Lisa, Mark, and Stacy are meeting up for lunch. Their total comes out to $28.87. They decide they want to split the bill between the three of them. Will they be able to split the check equally? And how much will each of them pay?
  ::丽莎,马克,斯泰西正在开会吃午饭。他们总共拿出28.87美元。他们决定把帐单分成三个人。他们能平分支票吗?他们每人要付多少钱?

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  In this concept, you will learn and apply the divisibility rules to find  factors  of given numbers.
  ::在此概念中,您将学习并应用可分数规则来查找给定数字的因素。

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  Finding Factors by Using Divisibility Rules
  ::使用《可区分规则》确定因素

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  There are some quick tests you can use to see if a large number is divisible by another number.
  ::有一些快速的测试, 您可以使用这些测试来查看一个大的数字是否被另一个数字分割 。

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  Divisibility rules  help determine if a number is divisible by let’s say 2 or 3 or 4. This can help us to identify the factors of a number. Here is a chart that shows all of the basic divisibility rules.
  ::可见性规则有助于确定一个数字是否可以通过2或3或4来区分。 这可以帮助我们确定数字的因数。 这是一张显示所有基本可分性规则的图表。

  Characteristic of number	Number divisible by	Example
  Last digit is even	2	208
  The  sum  of all digits is divisible by 3	3	114 $\begin{array}{r}1+1+4=6\end{array}$
  The last two digits are divisible by 4	4	288
  The last digit is 0 or 5	5	75
  The number is divisible by 2 and 3	6	2,154
  Double the last digit, subtract it from the rest of the number. Is your answer divisible by 7?	7	574 $\begin{array}{r}4\times 2=8,57-8=49,49÷7=7\end{array}$
  The last three digits are divisible by 8	8	1,888
  The sum of the digits are divisible by 9	9	342
  The number ends in 0	10	2,060
  The number is divisible by both 3 and 4	12	3,024

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  Some of these rules will be more useful than others, but this chart will help you.
  ::其中一些规则将比其他规则更有用,但本图表将对你们有所帮助。

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  Find a factor of 1,346 using the divisibility rules. Go through each rule and see if it applies.
  ::使用可变规则查找1,346因数。 检查每个规则, 看看是否适用 。

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  1. The last digit is even-this number is divisible by 2.
     ::最后一位数是偶数 -- 这个数字可以除以 2 。
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  2. The sum of all the digits is 14-this number is not divisible by 3.
     ::所有数字的总和是14 这个数字不能除以3
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  3. The last two digits are not divisible by 4-this number is not divisible by 4.
     ::最后两个位数不能用 4 来变换, 这个数字不能用 4 来变换。
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  4. The last digit is not  zero  or five-this number is not divisible by 5.
     ::最后一个数字不是0或5,这个数字不能除以5。
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  5. $\begin{array}{r}1,346-12=1,334\end{array}$  - this number is not divisible by 7.
     ::1, 346 - 12 = 1, 334 - 这个数字不能除以 7 。
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  6. The last three numbers are not divisible by 8.
     ::最后三个数字不能除以 8。
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  7. The sum of the digits is 14-this number is not divisible by 9
     ::数字总和是14 这个数字不能除以 9
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  8. The number does not end in zero-this number is not divisible by 10
     ::数字不会以零结束结束, 此数字不能除以 10 。
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  9. The number is not divisible by 3 and 4
     ::数字不能除以 3 和 4
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  10. The number 1,346 is divisible by 2.
      ::1 346号数字除以 2。

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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 Lisa and her friends having lunch.
  ::早些时候,你得到一个问题 丽莎和她的朋友吃午饭。

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  They want to split a bill of $28.87 equally between the three of them. Check the divisibility rule and  divide  to see how much each of them will pay.
  ::他们想将28.87美元的帐单平分给三个人。

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  First, check to see if the sum of all the digits is divisible by 3.
  ::首先,检查一下,看看所有数字的总和 是否除以 3 。

  $$\begin{array}{r}2+8+8+7=25\to \text{no}\end{array}$$

   

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  Then, divide the total by 3.
  ::然后,将总数除以3。

  $$\begin{array}{r}\mathrm{\$}28.87÷3=9.623333\dots 3\end{array}$$

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  $28.87 is not divisible by 3. Two people will pay $9.62 and one person will pay $9.63.
  ::28.87美元不能除以3。 两人将支付9.62美元,一人支付9.63美元。

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  Example 2
  ::例2

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  Test if 918 divisible by 9. Why or why not?
  ::测试如果918除以9. 为什么或为什么?

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  To figure this out, use the divisibility rules. Check to see if the sum of the digits is divisible by 9.
  ::要弄清楚这一点, 请使用可变规则。 检查数字的总和是否除以 9 。

  $$\begin{array}{r}9+1+8=18\end{array}$$

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  18 is divisible by 9, therefore 918 is also divisible by 9.
  ::18可除以9,因此918也可除以9。

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  Example 3
  ::例3

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  Use the divisibility rules to answer the following question.
  ::使用可分性规则回答下列问题。

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  Is 3,450 divisible by 10?
  ::三千四百五十除以十吗?

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  First, check to see if the number ends in 0.
  ::首先,检查数字是否以 0 结尾。

  $$\begin{array}{r}3,45\underset{\_}{0}\to \text{yes}\end{array}$$

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  3,450 is divisible by 0.
  ::3,450分之0是可分辨的

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  Example 4
  ::例4

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  Use the divisibility rules to answer the following question.
  ::使用可分性规则回答下列问题。

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  Is 1,298 divisible by 3?
  ::1,298能除以3吗?

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  First, check if the sum of all digits is divisible by 3.
  ::首先,检查所有位数的总和是否除以 3 。

  $$\begin{array}{r}1+2+9+8=20\to \text{no}\end{array}$$

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  1,298 is not divisible by 3.
  ::1,298不能被3除以。

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  Example 5
  ::例5

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  Use the divisibility rules to answer the following question.
  ::使用可分性规则回答下列问题。

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  Is 3,678 divisible by 2?
  ::3,678分之2是3,678分之2吗?

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  First, check if the last digit is even.
  ::首先,检查最后一位数是否相等。

  $$\begin{array}{r}3,67\underset{\_}{8}\to \text{yes}\end{array}$$

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  3,678 is divisible by 2.
  ::3,678可除以 2。

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  Review
  ::回顾

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  Use the divisibility rules to answer the following questions. Explain your reasoning.
  ::使用可分性规则回答下列问题。 请解释您的推理 。

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  1. Is 18 divisible by 3?
     ::18分可以3分吗?
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  2. Is 22 divisible by 2?
     ::22分2分吗?
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  3. Is 44 divisible by 6?
     ::四十四分除六分吗?
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  4. Is 112 divisible by 2 and 3?
     ::2和3分112分吗?
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  5. Is 27 divisible by 9 and 3?
     ::27分可以分9分3分3吗?
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  6. Is 219 divisible by 9?
     ::219分9分吗?
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  7. Is 612 divisible by 2 and 3?
     ::612可以分2和3吗?
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  8. Is 884 divisible by 4?
     ::884可以4分吗?
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  9. Is 240 divisible by 5?
     ::240分5分吗?
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  10. Is 782 divisible by 7?
      ::782可以除以7吗?
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  11. Is 212 divisible by 4 and 6?
      ::212分4和6分吗?
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  12. Is 456 divisible by 6 and 3?
      ::456可以除以6和3吗?
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  13. Is 1848 divisible by 8 and 4?
      ::1848年是8和4分之差吗?
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  14. Is 246 divisible by 2?
      ::246分之2可以变吗?
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  15. Is 393 divisible by 3?
      ::393可以3分吗?
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  16. Is 7450 divisible by 10?
      ::7450可以除以10吗?

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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