6.13 需要重命名的带分数减法

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  需要重命名的带分数减法

  

  [Figure 1]

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  Terry is  $\begin{array}{r}6\frac{1}{4}\end{array}$  feet tall. Five years ago, she was  $\begin{array}{r}1\frac{1}{3}\end{array}$  feet shorter. How tall was Terry five years ago?
  ::5年前,她矮了13英尺 5年前泰瑞有多高?

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  In this concept, you will learn how to subtract  mixed number  by borrowing and renaming.
  ::在此概念中,您将学会如何通过借贷和重新命名来减去混合数字。

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  Subtracting Mixed Numbers with Renaming
  ::以重命名方式减去混合数字

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  To  rename  a fraction means to take the fractions and write an equivalent fraction. Here is an example.
  ::要重命名一个分数, 意味着要取取分数并写入一个等效分数。 这里举一个例子 。

  $$\begin{array}{r}\frac{1}{3}=\frac{3}{9}\end{array}$$

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  Sometimes when you subtract mixed numbers, you must rename the mixed numbers in a different way. Here is an example.
  ::有时当减去混合数字时,必须用不同的方式重命名混合数字。这里举一个例子。

  $$\begin{array}{rl}& 6\\ & \underset{\_}{-4\frac{5}{6}}\end{array}$$

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  To subtract a fraction from a whole number, rename the whole number to a mixed number. It is similar to borrowing when subtracting. Remember that 1 can be written as a fraction.
  ::要从整数中减去一个分数,请将整数重命名为混合数。它与减去时的借款相似。要记住, 1 可以写成一个分数 。

  $$\begin{array}{r}1=\frac{2}{2}\text{or}\frac{3}{3}\text{or}\frac{4}{4}\text{. . .}\end{array}$$

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  Rename 6 into a mixed number. Borrow 1 from the whole number and rename it into a fraction with a  denominator  of 6.
  ::将 6 重命名为混合数字。 从整个数字中借入 1 , 将其重新命名为分数, 分母为 6 。

  $$\begin{array}{r}6=5\frac{6}{6}\end{array}$$

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  Now rewrite the problem with 6 as a mixed number.
  ::现在将问题重写为 6 , 混为一谈。

  $$\begin{array}{rl}& 5\frac{6}{6}\\ & \underset{\_}{-4\frac{5}{6}}\end{array}$$

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  Then, subtract the mixed numbers.
  ::然后,减去混合数字。

  $$\begin{array}{rl}& 5\frac{6}{6}\\ & \underset{\_}{-4\frac{5}{6}}\\ & 1\frac{1}{6}\end{array}$$

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  The  difference  is  $\begin{array}{r}1\frac{1}{6}\end{array}$ .
  ::差别是11.6

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  Sometimes you will also have to rename a mixed number if the fraction being subtracted is larger than the first fraction. Here is a subtraction problem with mixed numbers. 
  ::有时,如果所减去的分数大于第一个分数,您也必须重命名混合数字。这里是混合数字的减法问题。

  $$\begin{array}{rl}& 6\frac{1}{9}\\ & \underset{\_}{-3\frac{4}{9}}\end{array}$$

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  This problem involves subtracting a larger fraction, four-ninths, from a smaller fraction, one-ninths. To make this work, rename the first mixed number by borrowing from the whole number. Remember to add the fraction to the renamed mixed number. 
  ::这个问题涉及到从小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小大小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小小

  $$\begin{array}{rl}6& =5\frac{9}{9}\\ 5\frac{9}{9}+\frac{1}{9}& =5\frac{10}{9}\end{array}$$

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  Rewrite the problem with the new mixed number.
  ::用新的混合数字重写问题。

  $$\begin{array}{rl}& 5\frac{10}{9}\\ & \underset{\_}{-3\frac{4}{9}}\end{array}$$

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  Then, subtract the mixed numbers.
  ::然后,减去混合数字。

  $$\begin{array}{rl}& 5\frac{10}{9}\\ & \underset{\_}{-3\frac{4}{9}}\\ & 2\frac{6}{9}\end{array}$$

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  Next,  simplify  the fraction.
  ::接下来,简化分数。

  $$\begin{array}{r}2\frac{6}{9}=2\frac{2}{3}\end{array}$$

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   The difference is  $\begin{array}{r}2\frac{2}{3}\end{array}$ .
  ::差别是2 2 3

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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 Terry five years ago.
  ::之前,五年前,你遇到一个 Terry 的问题。

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  Terry is  $\begin{array}{r}6\frac{1}{4}\end{array}$  feet tall, but was  $\begin{array}{r}1\frac{1}{3}\end{array}$  feet shorter five years ago. Subtract to find Terry's height five years ago. 
  ::泰瑞是614英尺高,但五年前是133英尺短。

  $$\begin{array}{r}6\frac{1}{4}-1\frac{1}{3}=\underset{\_}{}\end{array}$$

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  First, rename the fractions so they have a  common denominator . 
  ::首先,重命名分数,让它们有一个共同的分母。

  $$\begin{array}{r}6\frac{1}{4}-1\frac{1}{3}=6\frac{3}{12}-1\frac{4}{12}\end{array}$$

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  Then, rename  $\begin{array}{r}6\frac{3}{12}\end{array}$ . Borrow 1 from 6 and add it to the fraction.
  ::然后重命名 6 3 12 . 从 6 借款 1 并添加到分数中 。

  $$\begin{array}{r}6\frac{3}{12}=5\frac{15}{12}\end{array}$$

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  Next, subtract the mixed numbers.
  ::接下来,减去混合数字。

  $$\begin{array}{r}5\frac{15}{12}-1\frac{4}{12}=4\frac{11}{12}\end{array}$$

    

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  Five years ago, Terry was  $\begin{array}{r}4\frac{11}{12}\end{array}$  feet tall. 
  ::五年前 泰瑞身高41112英尺

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  Example 2
  ::例2

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  Subtract the mixed numbers.
  ::减去混合数字。

  $\begin{array}{r}8\frac{1}{3}-2\frac{3}{4}=\underset{\_}{}\end{array}$

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  First, rename the fractions so they they have a common denominator of 12.
  ::首先,重命名分数,这样它们就有12个共同分母。

   

  $$\begin{array}{r}8\frac{4}{12}-2\frac{9}{12}=7\frac{16}{12}-2\frac{9}{12}\end{array}$$

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  Then, rename  $\begin{array}{r}8\frac{4}{12}\end{array}$ . You cannot subtract  $\begin{array}{r}\frac{9}{12}\end{array}$  from  $\begin{array}{r}\frac{4}{12}\end{array}$ . Borrow 1 from the whole number 8 and rename the mixed number.
  ::然后重命名 8 4 12 。 您不能从 4 12 中减去 9 12 。 从整个 8 中借款 1 并重命名混合编号 。

   

  $$\begin{array}{r}8\frac{4}{12}=7\frac{12}{12}+\frac{4}{12}=7\frac{16}{12}\end{array}$$

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  Next, rewrite the problem and subtract the mixed numbers.
  ::接下来,重写问题,减去混合数字。

  $$\begin{array}{r}7\frac{16}{12}-2\frac{9}{12}=5\frac{7}{12}\end{array}$$

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  The difference is  $\begin{array}{r}5\frac{7}{12}\end{array}$ .
  ::差异是5 7 12。

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  Example 3
  ::例3

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  Subtract the mixed numbers:  $\begin{array}{r}7-2\frac{1}{5}=\underset{\_}{}\end{array}$ . Answer in  simplest form .
  ::减去混合数字:7-2 1 5 =_。回答最简单。

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  First, rename the whole number as a mixed number with a denominator of 5.  
  ::首先,将整个数字改名为混合数字,分母为5。

  $$\begin{array}{r}7=6\frac{5}{5}\end{array}$$

  $$\begin{array}{r}7-2\frac{1}{5}=6\frac{5}{5}-2\frac{1}{5}\end{array}$$

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  Then, subtract the mixed numbers.
  ::然后,减去混合数字。

   

  $$\begin{array}{r}6\frac{5}{5}-2\frac{1}{5}=4\frac{4}{5}\end{array}$$

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  The difference is  $\begin{array}{r}4\frac{4}{5}\end{array}$ .
  ::差别是4 4 5。

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  Example 4
  ::例4

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  Rename 8 as an equivalent mixed number.
  ::8 重命名为等同混合数。

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  Borrow one from the whole number and rename it into a fraction.
  ::从整个数字中借一个,然后重新命名成一个分数。

   

  $$\begin{array}{r}8=7\frac{8}{8}\end{array}$$

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  8 is equivalent to  $\begin{array}{r}7\frac{8}{8}\end{array}$ .
  ::8等于7 8 8 。

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  Example 5
  ::例5

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  Subtract the mixed numbers:  $\begin{array}{r}9\frac{1}{4}-3\frac{3}{4}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::减去混合数字:9 1 4 - 3 3 4 = _。回答最简单。

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  First, rename  $\begin{array}{r}9\frac{1}{4}\end{array}$ . Borrow 1 from 9 and add it to the fraction.
  ::首先,重命名为914。从9借1,再加到分数中。

  $$\begin{array}{r}9\frac{1}{4}=8\frac{5}{4}\end{array}$$

  $$\begin{array}{r}9\frac{1}{4}-3\frac{3}{4}=8\frac{5}{4}-3\frac{3}{4}\end{array}$$

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  Then, subtract the mixed numbers. 
  ::然后,减去混合数字。

  $$\begin{array}{r}8\frac{5}{4}-3\frac{3}{4}=5\frac{2}{4}\end{array}$$

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  Next, simplify the fraction.
  ::接下来,简化分数。

   

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

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  The difference is  $\begin{array}{r}5\frac{1}{2}\end{array}$ .
  
  ::差数是512

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  Review
  ::回顾

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  Rename each whole number as a mixed number with a fraction terms of sixths.
  ::将每个整数重命名为混合数, 分数为六分之一 。

  1. 4
  2. 5
  3. 6
  4. 10
  5. 9
  6. 12

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  Find each difference. Rename mixed numbers as needed. Answer in simplest form.
  ::查找每个差异。 需要时重命名混合数字, 以最简单的形式回答 。

  7. $\begin{array}{r}3-2\frac{1}{4}=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}7-2\frac{2}{6}=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}10-4\frac{1}{5}=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}8-2\frac{4}{9}=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}14-6\frac{2}{3}=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}15-6\frac{2}{10}=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}11-4\frac{1}{7}=\underset{\_}{}\end{array}$
  14. $\begin{array}{r}18-16\frac{1}{5}=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}20-15\frac{2}{6}=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}7\frac{1}{6}-4\frac{3}{6}=\underset{\_}{}\end{array}$
  17. $\begin{array}{r}9\frac{1}{5}-3\frac{4}{5}=\underset{\_}{}\end{array}$
  18. $\begin{array}{r}10\frac{1}{8}-4\frac{3}{8}=\underset{\_}{}\end{array}$
  19. $\begin{array}{r}15\frac{1}{9}-8\frac{4}{9}=\underset{\_}{}\end{array}$
  20. $\begin{array}{r}17\frac{4}{7}-9\frac{6}{7}=\underset{\_}{}\end{array}$

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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