5.9普通倍数

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  普通倍数

  

  [Figure 1]

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  Charlie is playing a video game. He has to grab the magic token when the guard turns his back. He notices that the magic token appears every 4 seconds and the guard turns his back every 3 seconds. How can Charlie use this information to get the timing right so he can grab the magic token?
  ::查理在玩电玩游戏。 当卫兵转过身来时,他必须抓住魔兆。 他注意到魔兆每四秒钟就出现一次,卫兵每三秒钟就转过身来。 Charlie如何利用这个信息来把握时机,以便他能抓住魔兆?

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  In this concept, you will learn to identify multiples and find common multiples for pairs of numbers.
  ::在此概念中,您将学会识别多个数,并找到对数字的常见多个数。

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  Finding Common Multiples
  ::查找共同的多重

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  A  multiple  is the product of a quantity and a whole number. Here are some multiples for the quantity of 3, multiplied by different  whole numbers .
  ::倍数是数量和整数的产物。 这是数量为 3 的一些倍数, 乘以不同的整数 。

  $\begin{array}{r}3\times 1=3,3\times 2=6,3\times 3=9,3\times 4=12,3\times 5=15,3\times 6=18\end{array}$

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  Listing out these products is the same as listing out multiples.
  ::列出这些产品与列出多重产品相同。

  3, 6, 9, 12, 15, 18...

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  You can see that this is also the same as counting by threes. The dots at the end mean that these multiples can go on and on and on. Every number has an  infinite  number of multiples.
  ::你可以看到,这也和以三计是一样的。最后的点意味着这些倍数可以持续、持续、持续。每个数字都有无限的倍数。

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  List six multiples for 4.
  ::列出 4 的 6 个倍数 。

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  To do this, think of taking the quantity 4 and multiplying it by 1, 2, 3, 4, 5...
  ::要做到这一点,考虑用数量4 乘以1,2,3,3,4,5... 乘以1,2,3,4,5...

  $\begin{array}{r}4\times 1=4,4\times 2=8,4\times 3=12,4\times 4=16,4\times 5=20\end{array}$

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  Our answer is 4, 8, 12, 16, 20, 24...
  ::我们的答案是4,8,12,16,20,24...

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  A  common multiple  is a multiple that two or more numbers have in common. List the multiples of the numbers to find the common multiples.
  ::常见多个是两个或两个以上数字共有的多个。列出数字的多个以查找常见多个。

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  Find common multiples for 3 and 4.
  ::查找 3 和 4 的常见倍数。

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  First, write out the first few multiples for the numbers and then identify the multiples the two numbers have in common.
  ::首先,写出数字的前几个数数,然后确定这两个数字共有的数个数。

  3, 6, 9,  12 , 15, 18, 21,  24 , 27, 30, 33,  36

  4, 8,  12 , 16, 20,  24 , 28, 32,  36 , 40, 44, 48

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  Some of the common multiples of 3 and 4 are 12, 24, and 36.
  ::3号和4号的常见乘数中有些是12号、24号和36号。

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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 Charlie and his video game.
  ::早些时候,你得到一个问题 关于查理和他的电子游戏。

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  Charlie has to grab the magic token that appears every 4 seconds when the guard turns his back, which is every 3 seconds. Find the common multiples of 3 and 4 to find out when both will occur at the same time.
  ::Charlie必须抓住每4秒就出现一次的魔法标记, 当警卫转过身来时, 也就是每3秒就出现一次。 找到3和4的公用倍数, 以找出两者何时同时发生 。

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  First, list the first few multiples of 3 and 4.
  ::首先,列出3和4的前几个数倍数。

  3, 6, 9, 12, 15, 18, 21, 24, 27

  4, 8, 12, 16, 20, 24, 28, 32, 36

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  Then, identify the common multiples.
  ::然后,找出共同的多重。

  3, 6, 9,  12 , 15, 18, 21,  24 , 27

  4, 8,  12 , 16, 20,  24 , 28, 32, 36

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  Some common multiples of 3 and 4 are 12 and 24. Charlie can grab the magic token 12 or 24 seconds after he enter that stage. Note that 12 and 24 are multiples of 12. Charlie will get a chance to grab the magic token every 12 seconds.
  ::3 和 4 中的一些常见的乘数是 12 和 24 。 Charlie 可以在进入那个阶段12 或 24 秒后抓住魔法牌。 请注意, 12 和 24 是 12 乘数是 12 。 Charlie 每 12 秒就会有机会抓住魔法牌 。

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  Example 2
  ::例2

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  What are common multiples of 3 and 7?
  ::3和7的常见乘数是多少?

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  First, write out the first few multiples for the numbers.
  ::首先,写出数字的前几个数。

  3, 6, 9, 12, 15, 18, 21, 24, 27, 30

  7, 14, 21, 28, 35, 42, 49, 56, 63, 70

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  Then, identify the multiples the two numbers have in common.
  ::然后,找出这两个数字共有的倍数。

  3, 6, 9, 12, 15, 18,  21 , 24, 27, 30

  7, 14,  21 , 28, 35, 42, 49, 56, 63, 70

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  A common multiple of 3 and 7 is 21.
  ::3和7的共同乘数为21。

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  In this list, the only common multiple between 3 and 7 is 21. You could find more multiples by increasing the length of the list of multiples for 3 and 7 or finding a multiple of the common multiple.
  ::在此列表中, 3到7之间唯一常见的多个数是 21 。 您可以通过增加 3 和 7 的多个数列表的长度, 或找到 共多个数的多个数来找到更多多个数 。

  $\begin{array}{r}21\times 2=42\end{array}$

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  42 is a multiple of both 3 and 7.
  ::42是3和7的倍数。

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  Example 3
  ::例3

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  List eight multiples of 6.
  ::列出6的8倍数

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  First, multiply 6 by 1 through 8.
  ::第一,乘以6乘以1乘以8乘以6乘以1乘以8

  $\begin{array}{r}6\times 1=6,6\times 2=12,6\times 3=18,6\times 4=24,6\times 5=30,6\times 6=36,6\times 7=42,6\times 8=48\end{array}$

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  The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, and 48.
  ::6的乘数为6,6,12,18,24,30,36,42和48。

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  Example 4
  ::例4

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  List six multiples of 8.
  ::列出8的六倍数

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  First, multiply 8 by 1 through 6.
  ::第一,乘以8乘以1乘以6乘以8乘以1乘以6

  $\begin{array}{r}8\times 1=8,8\times 2=16,8\times 3=24,8\times 4=32,8\times 5=40,8\times 6=48\end{array}$  

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  Six multiples of 8 are 8, 16, 24, 32, 40, and 48.
  ::8的六倍数为8、16、24、32、40和48。

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  Example 5
  ::例5

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  What are the first two common multiples of 6 and 8?
  ::头两个6和8的常见倍数是多少?

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  First, list the first few multiples of 6 and 8.
  ::首先,列出6号和8号的前几个数倍数。

  6, 12, 18, 24, 30, 36, 42, 48 ...

  8, 16, 24, 32, 40, 48, ...

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  Then, identify the common multiples.
  ::然后,找出共同的多重。

  6, 12, 18,  24 , 30, 36, 42,  48  ...

  8, 16,  24 , 32, 40,  48  ...

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  Two common multiples of 6 and 8 are 24 and 48.
  ::6和8的2个共同倍数分别为24和48。

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  Review
  ::回顾

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  List the first five multiples for each of the following numbers.
  ::列出下列数字中每个数字的前五个乘数。

  1. 3
  2. 5
  3. 6
  4. 7
  5. 8

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  Find two common multiples of each pair of numbers.
  ::找到每对数字的两个常见倍数。

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  6. 3 and 5
     ::3和5
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  7. 2 and 3
     ::2和3
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  8. 3 and 4
     ::第3和4条和第3和4条
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  9. 2 and 6
     ::2和6
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  10. 3 and 9
      ::3和9
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  11. 5 and 7
      ::5和7
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  12. 4 and 12
      ::第四条和第十二条
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  13. 5 and 6
      ::第五条和第六条
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  14. 10 and 12
      ::第10和12条
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  15. 5 and 8
      ::第5和8条

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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