6.11不重命名混和数的区别

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• 选择节不重命名混和数的区别

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  不重命名混和数的区别

  

  [Figure 1]

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  Matt is making a dress for his sister. He has  $\begin{array}{r}7\frac{2}{3}\end{array}$  yards of fabric. He needs  $\begin{array}{r}2\frac{1}{3}\end{array}$   yards to make the dress. How much fabric will Matt have after he makes her dress?
  ::马特为妹妹做衣服 他有723码的布料 他需要23码的布料

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  In this concept, you will learn how to subtract mixed numbers. 
  ::在这个概念中,你会学会如何减去混合数字。

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  Subtracting Mixed Numbers without Renaming
  ::不重命名的混合数字减法

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  A  mixed number  is a whole number with a fraction. Just as you can add mixed numbers, you can also subtract mixed numbers in the same way. Subtract the fractions first and then the  whole numbers .
  ::混合数字是一个包含一个分数的整数。正如您可以添加混合数字一样,您也可以以同样的方式减去混合数字。先减去分数,然后减去整数。

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  Here is a subtraction problem. 
  ::这是一个减法问题。

  $$\begin{array}{rl}& 6\frac{3}{8}\\ & \underset{\_}{-4\frac{1}{8}}\end{array}$$

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  Start by subtracting the fractions. These fractions have the same  denominator  so you can simply subtract the numerators. 
  ::以减去分数开始。这些分数具有相同的分母,这样您就可以简单地减去分子。

  $$\begin{array}{rl}& 6\frac{3}{8}\\ & \underset{\_}{-4\frac{1}{8}}\\ & \frac{2}{8}\end{array}$$

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  Next, subtract the whole numbers.
  ::接下来,减去全部数字。

  $$\begin{array}{rl}& 6\frac{3}{8}\\ & \underset{\_}{-4\frac{1}{8}}\\ & 2\frac{2}{8}\end{array}$$

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  Finally,  simplify  the fraction in   $\begin{array}{r}2\frac{2}{8}\end{array}$ . 
  ::最后,将分数简化为 2 2 8 。

  $$\begin{array}{r}2\frac{2}{8}=2\frac{1}{4}\end{array}$$

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  The final answer is  $\begin{array}{r}2\frac{1}{4}\end{array}$ .
  ::最后一个答案是2 14。

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  If the subtraction problem involves mixed numbers with different denominators, rewrite the fractions of the mixed numbers so they have a  common denominator  before subtracting.
  ::如果减法问题涉及具有不同分母的混合数字,请重写混合数字的分数,以便在减法前有一个共同分母。

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  Here is another subtraction problem. 
  ::这是另一个减法问题。

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

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  First, rewrite the fractions with a common denominator. The common denominator is 12. 
  ::首先,用共同分母重写分母。 共同分母为 12 。

  $$\begin{array}{r}\frac{3}{4}=\frac{9}{12}\frac{1}{6}=\frac{2}{12}\end{array}$$

  $$\begin{array}{rl}& 6\frac{9}{12}\\ & \underset{\_}{-3\frac{2}{12}}\end{array}$$

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  Then, subtract the fractions. 
  ::然后,扣除分数。

  $$\begin{array}{rl}& 6\frac{9}{12}\\ & \underset{\_}{-3\frac{2}{12}}\\ & \frac{7}{12}\end{array}$$

   Next, subtract the whole numbers. 

  $$\begin{array}{rl}& 6\frac{9}{12}\\ & \underset{\_}{-3\frac{2}{12}}\\ & 3\frac{7}{12}\end{array}$$

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  The  difference  is  $\begin{array}{r}3\frac{7}{12}\end{array}$ .
  ::差数是3 7 12

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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 Matt making a dress for his sister.
  ::之前有人给你一个问题 马特为他妹妹做衣服

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  Matt has  $\begin{array}{r}7\frac{2}{3}\end{array}$  yards of fabric and uses  $\begin{array}{r}2\frac{1}{3}\end{array}$   yards to make his sister a dress. Subtract the  amount  of fabric he used from the original amount to find how much fabric he has left. 
  ::马特有7,2,3码的布料,用2,13码的布料 给他妹妹做一件衣服。减去他用在原来数量的布料 来找出他剩下多少布料。

    $\begin{array}{r}7\frac{2}{3}-2\frac{1}{3}=\underset{\_}{}\end{array}$

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  First, subtract the fractions.
  ::首先,减去分数。

    $\begin{array}{r}\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\end{array}$

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  Then, subtract the whole numbers.
  ::然后,减去全部数字。

    $\begin{array}{rl}& 7-2=5\\ \\ & 7\frac{2}{3}-2\frac{1}{3}=5\frac{1}{3}\end{array}$

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  Matt will have  $\begin{array}{r}5\frac{1}{3}\end{array}$  yards of fabric left over. 
  ::马特还有513码的布料

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  Example 2
  ::例2

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  Subtract the fractions. Answer in  simplest form .
  ::减去分数。 回答最简单。

  $\begin{array}{r}12\frac{46}{49}-10\frac{39}{49}=\underset{\_}{}\end{array}$

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  The fractions have a common denominator.
  ::分数有一个共同的分母。

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  First, subtract the fractions. 
  ::首先,减去分数。

   

  $$\begin{array}{r}\frac{46}{49}-\frac{39}{49}=\frac{7}{49}\end{array}$$

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  Then, subtract the whole numbers.
  ::然后,减去全部数字。

   

  $$\begin{array}{rl}12-10& =2\\ \\ 12\frac{46}{49}-10\frac{39}{49}& =2\frac{7}{49}\end{array}$$

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  Next, simplify the fraction part of the mixed number.
  ::接下来,简化混合数字的分数部分。

  $$\begin{array}{r}2\frac{7}{49}=2\frac{1}{7}\end{array}$$

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  The difference is  $\begin{array}{r}2\frac{1}{7}\end{array}$ .
  ::差数是2 17

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  Example 3
  ::例3

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  Subtract the fractions:  $\begin{array}{r}4\frac{4}{5}-3\frac{1}{5}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::减去分数: 4 4 5 - 3 1 5 = _. 回答最简单。

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  First, subtract the fractions.
  ::首先,减去分数。

   

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

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  Then, subtract the whole numbers.
  ::然后,减去全部数字。

  $$\begin{array}{rl}4-3& =1\\ \\ 4\frac{4}{5}-3\frac{1}{5}& =1\frac{3}{5}\end{array}$$

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  The difference is  $\begin{array}{r}1\frac{3}{5}\end{array}$ .
  ::差别是13 5。

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  Example 4
  ::例4

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  Subtract the fractions:  $\begin{array}{r}6\frac{4}{6}-1\frac{2}{6}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::减去分数: 6 4 6 - 1 2 6 = _. 回答最简单。

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  First, subtract the fractions.
  ::首先,减去分数。

   

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

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  Then, subtract the whole numbers.
  ::然后,减去全部数字。

   

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

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  Next, simplify the fraction part of the mixed number.
  ::接下来,简化混合数字的分数部分。

   

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

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  The difference is  $\begin{array}{r}5\frac{1}{3}\end{array}$ .
  ::差别是513

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  Example 5
  ::例5

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  Subtract the fractions:  $\begin{array}{r}7\frac{8}{9}-4\frac{4}{6}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::减去分数: 7 8 9 - 4 4 6 = _. 回答最简单。

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  First, rewrite the fractions with a common denominator of 18. 
  ::首先,重写分数,共同分母为18。

   

  $$\begin{array}{rl}& \frac{8}{9}=\frac{16}{18}\frac{4}{6}=\frac{12}{18}\\ \\ & 7\frac{16}{18}-4\frac{12}{18}=\underset{\_}{}\end{array}$$

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  Then, subtract the fractions.
  ::然后,扣除分数。

   

  $$\begin{array}{r}\frac{16}{18}-\frac{12}{18}=\frac{4}{18}\end{array}$$

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  Next, subtract the whole numbers.
  ::接下来,减去全部数字。

   

  $$\begin{array}{rl}7-4& =3\\ \\ 7\frac{16}{18}-4\frac{12}{18}& =3\frac{4}{18}\end{array}$$

  Finally, simplify the fraction.

   

  $$\begin{array}{r}3\frac{4}{18}=3\frac{2}{9}\end{array}$$

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  The difference is  $\begin{array}{r}3\frac{2}{9}\end{array}$ .
  
  ::差别是3 2 9

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  Review
  ::回顾

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  Subtract the following mixed numbers. Answer in simplest form.
  ::减去下列混合数字。回答最简单。

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

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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