6.8不同分母分数的区别

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  不同分母分数的区别

  

  [Figure 1]

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  Cindy is painting her room. She has  $\begin{array}{r}\frac{6}{8}\end{array}$  of a gallon of paint at the start. She used  $\begin{array}{r}\frac{1}{2}\end{array}$  of a gallon to paint one wall. How much paint does Cindy have left? Will she have enough to paint another wall? 
  ::Cindy在画她的房间。她一开始有68加仑的油漆。她用12加仑的油漆画一堵墙。Cindy还剩下多少油漆?她有足够的油漆墙吗?

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  In this concept, you will learn how to subtract fractions with different denominators.
  ::在这个概念中,你会学习如何减去分数,分母不同。

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  Subtracting Fractions with Different Denominators
  ::以不同的分数计减分数

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  You can   by rewriting the fractions with a  common denominator  before adding. The same step is taken to subtract fractions with different denominators. 
  ::您可以在添加前用共同分母重写分数。同一步骤是用不同的分母来减分数。

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  To find the  difference  of two fractions with different denominators, rewrite the fractions with a common denominator before subtracting. 
  ::要找到两个分数的差数, 不同分母的差数, 请在减法前用一个共同分母重写分数 。

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

  $$\begin{array}{r}\frac{6}{8}-\frac{1}{4}=\underset{\_}{}\end{array}$$

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  The fractions in this problem have different denominators, 8 and 4. 
  ::这一问题中的分数有不同的分母,即8分和4分母。

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  Rewrite the fractions so they share a common denominator. The  least common denominator  (LCD) is the  lowest  common multiple  (LCM) of 8 and 4.
  ::重写分数, 以便它们共享一个共同分母。 最小的公分母( LCD) 是8 和 4 的最小公分母( LCM ) 。

  8:  8 , 16, 24 . . .

  4: 4,  8 , 12, 16 . . .

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  The  LCM  is 8. Find the equivalent of each fraction with the  denominator  8.  $\begin{array}{r}\frac{6}{8}\end{array}$  is already in terms of eighths. Multiply the  numerator  and denominator of  $\begin{array}{r}\frac{1}{4}\end{array}$  by 2.
  ::LCM为 8 。 查找分母 8 、 6 8 和 分母 8 的 等同 。 乘以 14 乘以 4 乘以 2 的 分子 和 分母 1 4 乘以 2 。

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

  $$\begin{array}{r}\frac{6}{8}-\frac{1}{4}=\frac{6}{8}-\frac{2}{8}\end{array}$$

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  Now you can subtract the fractions with the common denominator. Subtract the numerators over the common denominator.
  ::现在,您可以用共同分母来减去分数。将分子从共同分母中减去。

  $$\begin{array}{r}\frac{6}{8}-\frac{2}{8}=\frac{4}{8}\end{array}$$

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  Finally,  simplify  the fraction by dividing the numerator and the denominator by the   (GCF). The GCF of 4 and 8 is 4.  Divide  the numerator and the denominator by 4.
  ::最后,通过将分子和分母除以(GCF)来简化分数。全球合作框架4和8是4. 分子和分母除以4。

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

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  The difference is  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::差别是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 Cindy and her paint project.
  ::早些时候,你得到一个问题 关于辛迪和她的油漆项目。

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  Cindy had  $\begin{array}{r}\frac{6}{8}\end{array}$  of a gallon of paint and used  $\begin{array}{r}\frac{1}{2}\end{array}$  gallon to paint one wall. Subtract the  amount  used from the original amount to find the amount of paint Cindy has left.
  ::Cindy有6,8加仑的油漆,用12加仑来油漆一堵墙。减去原来的数额,找到Cindy留下的油漆数量。

  $\begin{array}{r}\frac{6}{8}-\frac{1}{2}=\underset{\_}{}\end{array}$

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  First, find the LCM of 8 and 2. The LCM is 8.
  ::第一,找到8和2的LCM,LCM是8。

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  Then, rewrite the fractions with the common denominator 8.
  ::然后用共同分母8重写分数。

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

    $\begin{array}{r}\frac{6}{8}-\frac{1}{2}=\frac{6}{8}-\frac{4}{8}\end{array}$

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  Next, subtract the fractions.
  ::接下来,减去分数。

  $\begin{array}{r}\frac{6}{8}-\frac{4}{8}=\frac{2}{8}\end{array}$

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  Finally, simplify the fraction.
  ::最后,简化分数。

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

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  Cindy has  $\begin{array}{r}\frac{1}{4}\end{array}$  of a gallon left over. She will not have enough to paint another wall.
  ::Cindy只剩14加仑了 她没有钱再刷一堵墙

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  Example 2
  ::例2

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  Find the difference:  $\begin{array}{r}\frac{3}{4}-\frac{6}{12}=\underset{\_}{}\end{array}$ . Answer in  simplest form .
  ::查找差异: 3 4 - 6 12 = _. 回答最简单。

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  The fractions do not have a common denominator. The denominators are 4 and 12. 
  ::分数没有共同的分母,分母为4和12。

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  First, find the LCM of 4 and 12. The LCM is 12. 
  ::首先,找到4和12的LCM,LCM是12。

  4: 4, 8,  12 , . . .

  12:  12 , 24 . . .

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  Then, rewrite the fractions with the common denominator of 12. 
  ::然后,用12的公分母重写分数。

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

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

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  Next, subtract the fractions. Subtract the numerators over the common denominator. 
  ::接下来,减去分数。在共同分母上减去分子。

  $\begin{array}{r}\frac{9}{12}-\frac{6}{12}=\frac{3}{12}\end{array}$

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  Finally, simplify the fraction.
  ::最后,简化分数。

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

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  The difference is  $\begin{array}{r}\frac{1}{4}\end{array}$ .
  ::差别是14。

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  Example 3
  ::例3

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  Find the difference:  $\begin{array}{r}\frac{5}{6}-\frac{1}{3}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找差异: 5 6 - 1 3 = _. 回答最简单。

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  First, find the LCM of 6 and 3. The LCM is 6.
  ::第一,找到6和3的LCM,LCM是6。

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  Then, rewrite the fractions with a common denominator. 
  ::然后用共同的分母重写分数。

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

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

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  Next, subtract the fractions. 
  ::接下来,减去分数。

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

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  Finally, simplify the fraction.
  ::最后,简化分数。

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

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  The difference is  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::差别是12。

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  Example 4
  ::例4

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  Find the difference:  $\begin{array}{r}\frac{1}{2}-\frac{4}{9}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找差异: 1 2 - 4 9 = _. 回答最简单。

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  First, find the LCM of 2 and 9. The LCM is 18.
  ::第一,找到2和9的LCM,LCM是18。

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  Then, rewrite the fractions with a common denominator. 
  ::然后用共同的分母重写分数。

    $\begin{array}{rl}\frac{1}{2}& =\frac{9}{18}\\ \frac{4}{9}& =\frac{8}{18}\end{array}$

    $\begin{array}{r}\frac{1}{2}-\frac{4}{9}=\frac{9}{18}-\frac{8}{18}\end{array}$

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  Next, subtract the fractions. 
  ::接下来,减去分数。

    $\begin{array}{r}\frac{9}{18}-\frac{8}{18}=\frac{1}{18}\end{array}$

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  The fraction is in simplest form.
  ::分数以最简单的形式出现。

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  The difference is  $\begin{array}{r}\frac{1}{18}\end{array}$ .
  ::差别是1 18。

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  Example 5
  ::例5

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  Find the difference:  $\begin{array}{r}\frac{4}{5}-\frac{1}{4}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找差异: 4 5 - 1 4 = _. 回答最简单。

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  First, find the LCM of 5 and 4. The LCM is 20.
  ::第一,找到5和4的LCM,LCM是20。

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  Then, rewrite the fractions with a common denominator. 
  ::然后用共同的分母重写分数。

    $\begin{array}{rl}\frac{4}{5}& =\frac{16}{20}\\ \frac{1}{4}& =\frac{5}{20}\end{array}$

    $\begin{array}{r}\frac{4}{5}-\frac{1}{4}=\frac{16}{20}-\frac{5}{20}\end{array}$

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  Next, subtract the fractions. 
  ::接下来,减去分数。

    $\begin{array}{r}\frac{16}{20}-\frac{5}{20}=\frac{11}{20}\end{array}$

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  The fraction is in simplest form.
  ::分数以最简单的形式出现。

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  The difference is  $\begin{array}{r}\frac{11}{20}\end{array}$ .
  ::差别是11 20

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  Review
  ::回顾

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  Subtract the following fractions. Answer in simplest form.
  ::减去下列分数。回答最简单。

  1. $\begin{array}{r}\frac{4}{8}-\frac{1}{8}=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}\frac{9}{10}-\frac{1}{2}=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}\frac{10}{10}-\frac{1}{3}=\underset{\_}{}\end{array}$  
  4. $\begin{array}{r}\frac{15}{16}-\frac{2}{8}=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}\frac{9}{10}-\frac{1}{3}=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}\frac{3}{5}-\frac{1}{3}=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}\frac{9}{10}-\frac{1}{4}=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}\frac{20}{30}-\frac{1}{5}=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}\frac{18}{19}-\frac{2}{19}=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}\frac{4}{6}-\frac{1}{8}=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}\frac{7}{8}-\frac{4}{9}=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}\frac{1}{2}-\frac{1}{3}=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}\frac{4}{5}-\frac{1}{3}=\underset{\_}{}\end{array}$
  14. $\begin{array}{r}\frac{7}{9}-\frac{2}{5}=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}\frac{11}{12}-\frac{2}{3}=\underset{\_}{}\end{array}$
  16. $\begin{array}{r}\frac{6}{7}-\frac{4}{5}=\underset{\_}{}\end{array}$

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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