5.12最小公分母分数排序

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  最小公分母分数排序

   

  

  [Figure 1]

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  Sam surveyed his classmates for a class assignment. He asked his classmates about some of their interests and hobbies. The results of the survey were:
  ::Sam调查了同学的课堂任务,并向同学们询问了他们的一些兴趣和爱好。

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  $\begin{array}{r}\frac{7}{8}\end{array}$  watched TV
  ::7 8次观看电视

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  $\begin{array}{r}\frac{1}{4}\end{array}$  rode bikes
  ::1 4辆骑自行车

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  $\begin{array}{r}\frac{5}{8}\end{array}$  read books
  ::5 8本读书5 8本

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  $\begin{array}{r}\frac{3}{4}\end{array}$  played sports
  ::3 4场运动

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  $\begin{array}{r}\frac{3}{8}\end{array}$  played an instrument or sang
  ::3 8 弹奏乐器或歌唱

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  Sam is using this information to make a presentation. What is the  order  of activities if Sam were to rank them from the most popular to least?
  ::Sam利用这些信息进行演示。 如果Sam把他们从最受欢迎的人排到最少,那么活动顺序是什么?

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  In this concept, you will learn to order fractions using lowest common denominators.
  ::在此概念中,您将学会使用最低公分母来排序分数。

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  Using the Least Common Denominator to Order Fractions
  ::使用最小常见分数来排序分数

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  Sometimes, you will need to write fractions in  order  from least to greatest or from greatest to least. This becomes very simple if the fractions have the same  denominator .
  ::有时,您需要从最小到最大或者从最大到最小写分数。如果分数具有相同的分母,这变得非常简单。

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  Write in order from least to greatest.
  ::从最少到最伟大的写作顺序。

  $$\begin{array}{r}\frac{4}{9},\frac{2}{9},\frac{8}{9},\frac{3}{9},\frac{6}{9}\end{array}$$

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  Since all of these fractions have a  common denominator , use the numerators and arrange them in order from the smallest  numerator  to the largest numerator.
  ::由于所有这些分数都有共同的分母,请使用分子,并按从最小的分子到最大的分子顺序排列。

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  The answer is  $\begin{array}{r}\frac{2}{9},\frac{3}{9},\frac{4}{9},\frac{6}{9},\frac{8}{9}\end{array}$
  ::答案是2 9,3 9,4 9,6 9,8 9

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  To order fractions that do not have a common denominator, rewrite all of the fractions using the  lowest common denominator  (LCD).
  ::要订购没有共同分母的分数,请使用最低共同分母(LCD)重写所有分数。

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  Order these fractions from least to greatest.
  ::将这些分数从最小排序到最大排序 。

  $$\begin{array}{r}\frac{2}{3},\frac{1}{4},\frac{1}{2},\frac{5}{6}\end{array}$$

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  First, find the  LCD . The lowest  common multiple  of 3, 4, 2, and 6 is 12. Remember, if you cannot figure out the LCD in your head, list the multiples to find the  least common multiple  (LCM).
  ::首先,找到LCD。3、4、2和6的最低公分数是12。记住,如果你在脑中无法找到LCD,请列出多个来找到最小公分数(LCM)。

  $$\begin{array}{r}3-3,6,9,124-4,8,122-2,4,6,8,10,126-6,12\end{array}$$

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  Then, rewrite each fraction with the denominator 12.
  ::然后,用分母12重写每一分数。

  $$\begin{array}{r}\begin{array}{rcl}\frac{2}{3}& =& \frac{8}{12}\\ \frac{1}{4}& =& \frac{3}{12}\\ \frac{1}{2}& =& \frac{6}{12}\\ \frac{5}{6}& =& \frac{10}{12}\end{array}\end{array}$$

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  Next, order the fractions from least to greatest.
  ::接下来,将分数从最小排序到最大排序。

  $$\begin{array}{r}\frac{1}{4},\frac{1}{2},\frac{2}{3},\frac{5}{6}\end{array}$$

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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 Sam’s survey.
  ::更早之前,

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  Sam wants to find the order of activities from most popular to least popular. Compare the fractions and list them from greatest to least.
  ::Sam想要从最受欢迎到最不受欢迎的活动顺序。 比较分数,从最大到最小列出它们。

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  $\begin{array}{r}\frac{7}{8}\end{array}$  watched TV
  ::7 8次观看电视

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  $\begin{array}{r}\frac{1}{4}\end{array}$  rode bikes
  ::1 4辆骑自行车

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  $\begin{array}{r}\frac{5}{8}\end{array}$  read books
  ::5 8本读书5 8本

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  $\begin{array}{r}\frac{3}{4}\end{array}$  played sports
  ::3 4场运动

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  $\begin{array}{r}\frac{3}{8}\end{array}$  played an instrument or sang
  ::3 8 弹奏乐器或歌唱

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  First, find the LCD. The LCD of 4 and 8 is 8.
  ::首先找到LCD 4和8的LCD是8

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  Then, rewrite each fraction with the denominator of 8. Three of the fractions already have denominators of 8. Find the equivalent fraction for  $\begin{array}{r}\frac{1}{4}\end{array}$  and  $\begin{array}{r}\frac{3}{4}\end{array}$ .
  ::然后,用8分母重写每分分分母。 3分分分母中已有8分分母。 找到14分和3分分分母。

  $\begin{array}{r}\frac{1}{4}=\frac{4}{8}\end{array}$

  $\begin{array}{r}\frac{3}{4}=\frac{6}{8}\end{array}$

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  Next, order the fractions from greatest to least.
  ::接下来,将分数从最大到最小排序。

  $$\begin{array}{r}\frac{7}{8},\frac{6}{8},\frac{5}{8},\frac{4}{8},\frac{3}{8}\end{array}$$

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  Sam should list the activities as:
  ::Sam应列出下列活动:

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  Most Popular to Least Popular Activity
  ::最受欢迎的活动

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  1. Watch TV
     ::观察电视电视
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  2. Play sports
     ::游戏运动运动
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  3. Read books
     ::阅读书籍
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  4. Ride bike
     ::骑自行车
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  5. Play instrument or sing
     ::播放乐器或唱歌

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  Example 2
  ::例2

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  Write the following fractions in order from least to greatest.
  ::写下以下的分数, 以从最小到最大顺序排列 。

  $$\begin{array}{r}\frac{4}{7},\frac{2}{3},\frac{5}{7}\end{array}$$

   

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  First, find the lowest common denominator. The lowest common multiple of 3 and 7 is 21.
  ::首先,找到最低公分母,最低公分数为3和7,最低公分数为21。

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  Then, rewrite each fraction with the denominator 12.
  ::然后,用分母12重写每一分数。

  $$\begin{array}{r}\begin{array}{rcl}\frac{4}{7}& =& \frac{12}{21}\\ \frac{2}{3}& =& \frac{14}{21}\\ \frac{5}{7}& =& \frac{15}{21}\end{array}\end{array}$$

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  Next, order the fractions from least to greatest.
  ::接下来,将分数从最小排序到最大排序。

  $$\begin{array}{r}\frac{4}{7},\frac{2}{3},\frac{5}{7}\end{array}$$

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  Notice that the original order was in order from least to greatest.
  ::注意原始订单从最低到最高顺序的顺序。

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  Example 3
  ::例3

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  What would be the LCD for fractions with the denominators of 3, 5, and 6?
  ::分母为3、5和6的分母的液晶体会是什么?

  $$\begin{array}{r}3-3,6,9,12,15,18,21,24,27,305-5,10,15,20,25,306-6,12,18,24,30\end{array}$$

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  The LCD would be 30.
  ::液晶显示器为30岁。

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  Example 4
  ::例4

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  Rewrite the fractions with a common denominator.
  ::以共同分母重写分数 。

  $$\begin{array}{r}\frac{4}{5},\frac{1}{5},\frac{2}{3}\end{array}$$

  $$\begin{array}{r}\frac{24}{60},\frac{6}{30},\frac{20}{30}\end{array}$$

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  The LCD is 15.
  ::LCD是15岁。

  $$\begin{array}{r}\begin{array}{rcl}\frac{4}{5}& =& \frac{12}{15}\\ \frac{1}{5}& =& \frac{3}{15}\\ \frac{2}{3}& =& \frac{10}{15}\end{array}\end{array}$$

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  Example 5
  ::例5

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  Write the fractions above in order from greatest to least.
  ::写入上面的分数, 从最大到最小顺序 。

  $$\begin{array}{r}\frac{4}{5},\frac{2}{3},\frac{1}{5}\end{array}$$

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  Review
  ::回顾

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  Write each series in order from least to greatest.
  ::每一系列都按从最少到最大的顺序排列。

  1. $\begin{array}{r}\frac{5}{6},\frac{1}{3},\frac{4}{9}\end{array}$
  2. $\begin{array}{r}\frac{6}{7},\frac{1}{4},\frac{2}{3}\end{array}$
  3. $\begin{array}{r}\frac{6}{6},\frac{4}{5},\frac{2}{3}\end{array}$
  4. $\begin{array}{r}\frac{1}{2},\frac{3}{5},\frac{2}{3}\end{array}$
  5. $\begin{array}{r}\frac{2}{7},\frac{1}{4},\frac{3}{6}\end{array}$
  6. $\begin{array}{r}\frac{1}{6},\frac{2}{9},\frac{2}{5}\end{array}$
  7. $\begin{array}{r}\frac{4}{16},\frac{4}{5},\frac{3}{7}\end{array}$
  8. $\begin{array}{r}\frac{9}{10},\frac{4}{5},\frac{3}{4}\end{array}$
  9. $\begin{array}{r}\frac{4}{5},\frac{1}{2},\frac{2}{3}\end{array}$
  10. $\begin{array}{r}\frac{9}{11},\frac{2}{3},\frac{3}{4}\end{array}$
  11. $\begin{array}{r}\frac{4}{7},\frac{1}{5},\frac{3}{8}\end{array}$
  12. $\begin{array}{r}\frac{6}{7},\frac{1}{3},\frac{2}{5}\end{array}$
  13. $\begin{array}{r}\frac{7}{8},\frac{4}{5},\frac{1}{3}\end{array}$
  14. $\begin{array}{r}\frac{1}{6},\frac{4}{5},\frac{2}{4}\end{array}$
  15. $\begin{array}{r}\frac{1}{9},\frac{4}{7},\frac{2}{9},\frac{7}{8}\end{array}$

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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