7.7反比分数的识别与书写

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• 选择节反比分数的识别与书写

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  反比分数的识别与书写

  
  

  

  [Figure 1]

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  Lily says she has an unbeatable math trick. She bets the class that she can guess everyone's final number at the end of the trick. She says, "Pick any whole number. Add 3. Multiply the  sum  by 5. Then, subtract 10. Multiply that number by the  reciprocal . I bet I can guess your final number." Why is Lily so sure she will always guess correctly?
  ::Lily说,她有一个无法战胜的数学把戏。她打赌班级里她可以猜出每个人最后的数。她说,“把一个整数都挑出来,加3,乘以5乘以5。然后,减去10。再乘以10。我敢打赌,我可以猜出你最后的数。”为什么Lily总是猜对了?

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  In this concept, you will learn how to write and identify reciprocal fractions.
  ::在此概念中,您将学会如何写作和识别对等分数。

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  Identifying and Writing Reciprocal Fractions
  ::确定和编写对等分数

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  Before you dive into the mechanics of dividing fractions, let’s think about some division facts. Division is the opposite of multiplication. Multiplication and division are  inverse operations . The word “inverse” means opposite. Addition and subtraction are also inverse operations. 
  ::在你潜入分裂分数的机制之前,让我们想想一些分裂的事实。 分裂与乘法相反。 乘法和除法是反向的。 “ 反向”一词的意思是相反的。 增减也是反向的。

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  When dividing with fractions, the rule is to multiply by the reciprocal of the  divisor .
  ::当用分数分隔时, 规则是乘以断层的对等 。

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  A  reciprocal  is the inverse or opposite form of a fraction. You find the reciprocal of any number by flipping the  numerator  and the  denominator . 
  ::互惠是分数的反反反反形式。您可以通过翻转分子和分母找到任何数字的对等形式。

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  Here is an example.
  ::举一个例子。

  $$\begin{array}{r}\frac{4}{5}\stackrel{\to }{}\frac{5}{4}\end{array}$$

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  Flip the numerator and the denominator. The reciprocal of four-fifths is five-fourths.
  ::翻转分子和分母,五分之四对等为五分之四

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  Here is another example. 
  ::下面是另一个例子。

  $$\begin{array}{r}\frac{1}{2}\stackrel{\to }{}\frac{2}{1}\end{array}$$

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  Look what happens when you multiply a fraction by its reciprocal.
  ::看看当你乘以一个分数乘以其对等值时会发生什么。

  $$\begin{array}{r}\frac{1}{2}\times \frac{2}{1}=\frac{2}{2}=1\end{array}$$

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  The product of any number and its reciprocal is always 1. 
  ::任何数字的产物及其对等性始终为1。

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  Identifying the reciprocal of a fraction is important to learning how to  divide  fractions. 
  ::分数的对等性对于学习如何分分数很重要。

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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 Lily's riddle.
  ::之前你对Lily的谜题有疑问

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  Lily bets the class that she can guess everyone's final number at the end of her riddle: "Pick any whole number. Add 3. Multiply the sum by 5. Then, subtract 10. Multiply that number by the reciprocal. I bet I can guess your final number." Look at the last part of the riddle, "multiply that number by the reciprocal." By now you know that any number multiplied by its reciprocal will always be 1. 
  ::Lily打赌,她可以猜出每个人在谜语结尾处的最终数字: “把整个数字都找出来,加3,乘以3,再乘以5。然后,减10。再乘以10。我敢打赌,我能猜出你的最后数字。” 看看谜语的最后部分,“把那个数字乘以对等数字。”现在你知道,任何数字乘以对等数字都会是1。

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  Here is an example. If you start with the number 5, The number after subtracting 10 will be 30.
  ::以下是一个例子。如果你从数字5开始,减去10后的数字将是30。

    $\begin{array}{r}5+3=8\times 5=40-10=30\end{array}$

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  The reciprocal of 30 is  $\begin{array}{r}\frac{1}{30}\end{array}$ . Multiply 30 by the reciprocal.
  ::30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以互惠乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30乘以30

  $\begin{array}{r}30\times \frac{1}{30}=1\end{array}$

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  Lily is sure because no matter the starting number, the last number will always be 1. 
  ::Lily是肯定的 因为不管开始的号码是多少 最后的号码总是1

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  Example 2
  ::例2

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  Write a reciprocal for the fraction  $\begin{array}{r}\frac{5}{7}\end{array}$ .
  ::对分数 5 7 写一个对等 。

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  To write a reciprocal, "flip" the fraction so that the denominator becomes the numerator and the numerator becomes the denominator.
  ::写一个对等的,“翻转”分数,使分母成为分子,使分子成为分母。

    $\begin{array}{r}\frac{5}{7}\stackrel{\to }{}\frac{7}{5}\end{array}$

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  The reciprocal is  $\begin{array}{r}\frac{7}{5}\end{array}$ .
  ::互惠为7 5。

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  Example 3
  ::例3

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  Identify the reciprocal of  $\begin{array}{r}\frac{1}{4}\end{array}$ .
  ::确定1 4之对等。

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  Flip the numerator and the denominator.
  ::翻转分子和分母。

    $\begin{array}{r}\frac{1}{4}\stackrel{\to }{}\frac{4}{1}\end{array}$

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  The reciprocal is  $\begin{array}{r}\frac{4}{1}\end{array}$ .
  ::互惠为4 1。

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  Example 4
  ::例4

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  Identify the reciprocal of  $\begin{array}{r}\frac{4}{7}\end{array}$ .
  ::确定对等4 7。

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  Flip the numerator and the denominator.
  ::翻转分子和分母。

    $\begin{array}{r}\frac{4}{7}\stackrel{\to }{}\frac{7}{4}\end{array}$

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  The reciprocal is  $\begin{array}{r}\frac{7}{4}\end{array}$ .
  ::互惠为7 4。

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  Example 5
  ::例5

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  Identify the reciprocal of  $\begin{array}{r}\frac{2}{5}\end{array}$ .
  ::确定对等2 5。

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  Flip the numerator and the denominator.
  ::翻转分子和分母。

    $\begin{array}{r}\frac{2}{5}\stackrel{\to }{}\frac{5}{2}\end{array}$

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  The reciprocal is  $\begin{array}{r}\frac{5}{2}\end{array}$ .
  ::互惠为5 2。

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  Review
  ::回顾

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  Identify the reciprocals. You don't need to simplify or convert into a mixed number.
  ::识别对等数据。 您不需要简化或转换成混合数字 。

  1. $\begin{array}{r}\frac{1}{2}\end{array}$
  2. $\begin{array}{r}\frac{2}{3}\end{array}$
  3. $\begin{array}{r}\frac{4}{5}\end{array}$
  4. $\begin{array}{r}\frac{11}{12}\end{array}$
  5. $\begin{array}{r}\frac{8}{9}\end{array}$
  6. $\begin{array}{r}\frac{9}{10}\end{array}$
  7. $\begin{array}{r}\frac{12}{13}\end{array}$
  8. $\begin{array}{r}\frac{11}{2}\end{array}$
  9. $\begin{array}{r}\frac{14}{6}\end{array}$
  10. $\begin{array}{r}\frac{8}{3}\end{array}$
  11. $\begin{array}{r}\frac{9}{4}\end{array}$
  12. $\begin{array}{r}\frac{11}{7}\end{array}$
  13. $\begin{array}{r}\frac{15}{4}\end{array}$
  14. $\begin{array}{r}\frac{18}{7}\end{array}$
  15. $\begin{array}{r}\frac{21}{8}\end{array}$

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  Review (Answers) 
  ::回顾(答复)