6.10混合数和

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  混合数和

  

  [Figure 1]

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  Ben wants to build a tire swing. He has a rope that is  $\begin{array}{r}10\frac{5}{6}\end{array}$  feet long. He ties it to the tree branch but realizes that the rope is  $\begin{array}{r}2\frac{1}{2}\end{array}$  feet short. How much rope does Ben need to make a tire swing?
  ::Ben想造一个轮胎摆动。他的绳子长10,5,6英尺。他把绳子绑在树枝上,但意识到绳子短了212英尺。Ben需要多少绳子来摆动轮胎摆动?

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  In this concept, you will learn how to add mixed numbers. 
  ::在这个概念中,你们将学会如何增加混合数字。

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  Adding Mixed Numbers
  ::添加混合数字

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  A  mixed number  is a whole number with a fraction. 
  ::混合数字是一个带有分数的整数。

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  $\begin{array}{r}9\frac{4}{5}\end{array}$  is a mixed number. It has nine wholes and four-fifths of another whole.
  ::9 4 5是一个混合数字,有9个整数和5个整数的五分之四。

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  You have already learned how to add fractions. Now you are going to learn how to add mixed numbers.
  ::您已经学会了如何添加分数。 现在您要学习如何添加混合数字 。

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  Adding mixed numbers is a lot like adding fractions, the key is that you have to add the fractions first. In some cases, the  sum  of two fractions can make a whole number. If that happens, you can add the  whole numbers  all at once after you have added the fractions.
  ::添加混合数字非常像添加分数, 关键是您必须先添加分数。 在某些情况下, 两个分数的总和可以形成一个整数。 如果发生这种情况, 您可以在添加分数后同时添加全部数字 。

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  Here is an addition problem.
  ::还有一个附加问题。

  $$\begin{array}{r}5\frac{2}{5}+3\frac{3}{5}=\underset{\_}{}\end{array}$$

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  First, add the fractions. The fractions have  like denominators  so the sum is the sum of the numerators over the  common denominator .
  ::首先,添加分数。分数具有相似的分母,所以总和是共同分母上的分子总和。

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

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  Then, add the whole numbers to the sum of the fraction. Remember that  $\begin{array}{r}\frac{5}{5}\end{array}$  is also equal to one whole.
  ::然后将整数加到分数的总和中。 记住, 5 5 等于一个整数 。

  $$\begin{array}{r}5+3+1=9\end{array}$$

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  The sum is 9.
  ::总和是9。

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  Here is another addition problem.
  ::还有一个附加问题。

  $$\begin{array}{r}6\frac{1}{4}+3\frac{2}{4}=\underset{\_}{}\end{array}$$

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  First, add the fractions.
  ::首先,添加分数。

  $$\begin{array}{r}\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\end{array}$$

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  Then, add the whole numbers to the fraction.
  ::然后,将整数加到分数中。

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

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  The sum is  $\begin{array}{r}9\frac{3}{4}\end{array}$ .
  ::金额是9 3 4。

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  Some addition problems will involve mixed numbers with different denominators. To add mixed numbers with different denominators, rewrite the fractions of the mixed numbers so they have a common denominator before adding.
  ::某些添加问题涉及不同分母的混合数字。 要添加不同分母的混合数字,请重写混合数字的分数,以便在添加前有一个共同分母。

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  Here is another addition problem.
  ::还有一个附加问题。

   

  $$\begin{array}{r}6\frac{7}{8}+4\frac{2}{4}=\underset{\_}{}\end{array}$$

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  First, rewrite the fractions with a common denominator. The common denominator is 8.
  ::首先,用共同的分母重写分母。 共同的分母是 8 。

   

  $$\begin{array}{r}6\frac{7}{8}+4\frac{2}{4}=6\frac{7}{8}+4\frac{4}{8}\end{array}$$

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  Then, add the fractions. Convert the  improper fraction  to a mixed number
  ::然后添加分数。 将不适当的分数转换成混合数

  $$\begin{array}{r}5+2+1\frac{3}{10}=8\frac{3}{10}\end{array}$$

   

  $$\begin{array}{r}\frac{11}{8}=1\frac{3}{8}\end{array}$$

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  Next, add the whole numbers to sum of the fraction.
  ::下一步,将整数添加到分数的总和中。

  $$\begin{array}{r}6+4+1\frac{3}{8}=11\frac{3}{8}\end{array}$$

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  The sum is  $\begin{array}{r}11\frac{3}{8}\end{array}$ .
  ::总共是11 3 8。

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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 Ben and the tire swing.
  ::早些时候,有人给了你一个问题 关于本和轮胎摆动。

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  Ben had a rope that was  $\begin{array}{r}10\frac{5}{6}\end{array}$  feet long, but was short  $\begin{array}{r}2\frac{1}{2}\end{array}$  feet. Add the mixed numbers to find the length of the rope Ben needs to build his tire swing.
  ::Ben的绳子长10,5,6英尺,但短2,12英尺。 加上混合数字,找到Ben的绳子长度,Ben需要制造他的轮胎摆动。

  $$\begin{array}{r}10\frac{5}{6}+2\frac{1}{2}=\underset{\_}{}\end{array}$$

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  The fractions in these mixed numbers have different denominators.
  ::这些混合数字中的分数有不同的分母。

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  First, rewrite the fractions to have a common denominator.
  ::首先,重写分数以便有一个共同的分母。

   

  $$\begin{array}{r}10\frac{5}{6}+2\frac{1}{2}=10\frac{5}{6}+2\frac{3}{6}\end{array}$$

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  Then, add the fractions. Convert the improper fraction to a mixed number.
  ::然后添加分数。 将不适当的分数转换成混合数 。

    

  $$\begin{array}{r}\frac{5}{6}+\frac{3}{6}=\frac{8}{6}\end{array}$$

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

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  Next, add the whole numbers to the sum of the fractions.
  ::下一步,在分数的总和中添加整数。

   

  $$\begin{array}{r}10+2+1\frac{2}{6}=13\frac{2}{6}\end{array}$$

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

   

  $$\begin{array}{r}13\frac{2}{6}=13\frac{1}{3}\end{array}$$

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  Ben needs a rope that is  $\begin{array}{r}13\frac{1}{3}\end{array}$  feet long.
  ::本需要一条长1313英尺长的绳子

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  Example 2
  ::例2

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  Find the sum:  $\begin{array}{r}5\frac{4}{5}+2\frac{1}{2}=\underset{\_}{}\end{array}$ . Answer in  simplest form .
  ::查找总和: 5 4 5 + 2 1 2 = _. 回答最简单。

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  First, rewrite the fractions with a common denominator. The common denominator is 10.
  ::首先,用共同的分母重写分数。 共同的分母是 10 。

  $$\begin{array}{r}5\frac{4}{5}+2\frac{1}{2}=5\frac{8}{10}+2\frac{5}{10}\end{array}$$

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  Then, add the fractions. Convert the improper fraction to a mixed number.
  ::然后添加分数。 将不适当的分数转换成混合数 。

   

  $$\begin{array}{r}\frac{8}{10}+\frac{5}{10}=\frac{13}{10}\end{array}$$

  $$\begin{array}{r}\frac{13}{10}=1\frac{3}{10}\end{array}$$

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  Next, add the whole numbers to the sum of the fractions.
  ::下一步,在分数的总和中添加整数。

   

  $$\begin{array}{r}5+2+1\frac{3}{10}=8\frac{3}{10}\end{array}$$

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  The sum is  $\begin{array}{r}8\frac{3}{10}\end{array}$ .
  ::金额是8 3 10。

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  Example 3
  ::例3

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  Find the sum:  $\begin{array}{r}12\frac{1}{4}+6\frac{1}{4}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找总和: 12 1 4+ 6 1 4 = _. 回答最简单。

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  First, add the fractions. 
  ::首先,添加分数。

   

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

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  Then, add the whole numbers to the sum of the fractions.
  ::然后,将整数加到分数的总和中。

   

  $$\begin{array}{r}12+6+\frac{2}{4}=18\frac{2}{4}\end{array}$$

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  Next, simply the fraction.
  ::接下来,简单的分数。

   

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

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  The sum is  $\begin{array}{r}18\frac{1}{2}\end{array}$ .
  ::金额是1812。

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  Example 4
  ::例4

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  Find the sum:  $\begin{array}{r}6\frac{1}{3}+4\frac{2}{3}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找总和:6,1,3+4,2,3=_。回答最简单。

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  First, add the fractions.
  ::首先,添加分数。

   

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

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  Then, add the whole numbers to the sum of the fractions.
  ::然后,将整数加到分数的总和中。

   

  $$\begin{array}{r}6+4+1=11\end{array}$$

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  The sum is 11. 
  ::总数为11。

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  Example 5
  ::例5

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  Find the sum:  $\begin{array}{r}3\frac{1}{2}+2\frac{2}{5}=\underset{\_}{}\end{array}$ . Answer in simplest form.
  ::查找总和: 3, 1, 2 + 2, 2 5 = _. 回答最简单。

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  First, rewrite the fractions with a common denominator of 10.
  ::首先,重写分数,共同分母为10。

  $$\begin{array}{r}3\frac{1}{2}+2\frac{2}{5}=3\frac{5}{10}+2\frac{4}{10}\end{array}$$

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  Then, add the fractions.
  ::然后,你应当增加分数。

   

  $$\begin{array}{r}\frac{5}{10}+\frac{4}{10}=\frac{9}{10}\end{array}$$

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  Next, add the whole numbers to the sum of the fractions.
  ::下一步,在分数的总和中添加整数。

   

  $$\begin{array}{r}3+2+\frac{9}{10}=5\frac{9}{10}\end{array}$$

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  The sum is  $\begin{array}{r}5\frac{9}{10}\end{array}$ .
  
  ::金额是5 -9 -10

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  Review
  ::回顾

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  Find the sum. Answer in simplest form.
  ::找到金额,回答最简单

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

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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