5.18小数作为带数

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  小数作为带数

  

  [Figure 1]

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  Henry is working on building a dog house. He needs to get lumber that is 6 inches wide and 1.5 inches thick. He goes to the hardware store and sees that they have 6 by  $\begin{array}{r}1\frac{1}{4}\end{array}$ , 6 by  $\begin{array}{r}1\frac{1}{2}\end{array}$ , and 6 by  $\begin{array}{r}\frac{3}{4}\end{array}$ . Which one does Henry need?
  ::Henry正在建造一条狗屋。他需要的是6英寸宽和1.5英寸厚的木材。他去了五金店,看到五金店有6乘14,6乘12,6乘3乘4。亨利需要哪个?

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  In this concept, you will learn to convert decimals to mixed numbers.
  ::在此概念中,您将学会将小数点转换为混合数字。

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  Converting Decimals to Mixed Numbers
  ::将十进制转换为混合数字

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  Some decimal numbers represent both a part and a whole. These decimal numbers can be written as  mixed numbers . The decimal number must have both a whole and a part to be written as a  mixed number . The mixed number and the decimal are equal because they both have the same value.
  ::某些小数数代表一个部分和一个整体。这些小数数可以混合数写入。小数数必须同时包含一个整体和一个部分,以混合数写入。混合数和小数数是相等的,因为它们都有相同的值。

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  Here is a decimal number.
  ::这是十进制数字。

  $\begin{array}{r}4.5\end{array}$

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  Let’s write this decimal in a  place value  chart.
  ::让我们将这个小数点写进一个地点值图表。

  Tens	Ones	Decimal Point	Tenths	Hundredths	Thousandths	Ten-Thousandths
  	4	.	5

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  This decimal number has 4 ones and 5 tenths. The 4 represents the wholes. The 5 tenths represents the fraction.  The five is the  numerator  and the tenths is the  denominator .
  ::这个小数位数为 4 和 5 十分之和。 4 表示整体。 5 表示分数。 5 表示分数。 5 是分子, 10 是分母。

  $$\begin{array}{r}4.5=4\frac{5}{10}\end{array}$$

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  Next, check and see if the fraction can be simplified. In this case, five-tenths can be simplified to one-half.
  ::下一步, 检查和检查分数是否可以简化 。 在此情况下, 十分之五可以简化为 一半 。

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

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  $\begin{array}{r}4.5\end{array}$  can be written as  $\begin{array}{r}4\frac{1}{2}\end{array}$ .
  ::4.5可写为4,1,2。

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  A decimal value can only be expressed one way. However, many fractions can be written to express the same value.
  ::小数点值只能用一种方式表示。但是,许多分数可以写来表示相同的值。

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  $\begin{array}{r}0.75\end{array}$  can be written as  $\begin{array}{r}\frac{75}{100}\end{array}$ . You can make an equivalent fraction that has the same value.
  ::0.75 可以写为 75 100。您可以做一个等值的分数,其值相同。

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  Simplify   $\begin{array}{r}\frac{75}{100}\end{array}$ .
  ::简化75 100

  $$\begin{array}{r}\frac{75}{100}=\frac{3}{4}\end{array}$$

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  You can keep on creating   that have the same value as  $\begin{array}{r}0.75\end{array}$ .
  ::您可以继续创建与 0.75 相同的值。

  $$\begin{array}{r}\frac{75}{100}=\frac{3}{4}=\frac{6}{8}=\frac{9}{12}\end{array}$$

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  Finding equivalent fractions for mixed numbers is similar.  The whole number stays the same, but the fraction can vary.
  ::查找混合数字的等效分数是相似的。 整数保持不变, 但分数可以变化 。

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  Here is a decimal number.
  ::这是十进制数字。

  $\begin{array}{r}4.56\end{array}$

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  Convert the decimal number to a mixed number and find equivalent fractions.
  ::将小数数转换为混合数并找到相等的分数。

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  First, convert the decimal to a mixed number.  $\begin{array}{r}4.56\end{array}$  is read as four and fifty-six hundredths, the four is the whole number, the fifty-six is the numerator, and the denominator is the hundredths.
  ::首先,将小数点转换为混合数。 4.56 读为四五六六百, 四是整数, 五十六是分子, 分母是百分数。

  $$\begin{array}{r}4\frac{56}{100}\end{array}$$

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  Then, simplify the fraction part of this mixed number to get another mixed number that is equivalent to the one above. The   of 56 and 100 is 4.
  ::然后,简化这一混合数字的分数部分,以获得与上述数字相同的另一个混合数字。56和100是4。

  $$\begin{array}{r}4\frac{56}{100}=4\frac{14}{25}\end{array}$$

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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 Henry building a dog house.
  ::之前,你被问及 亨利建造狗屋的问题

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  He needs lumber that is 6 inches wide and  $\begin{array}{r}1.5\end{array}$  inches thick. Convert  $\begin{array}{r}1.5\end{array}$  inches into a fraction to find the lumber he needs.
  ::他需要6英寸宽和1.5英寸厚的木材。 将1.5英寸的木材转换成一个小块, 以寻找他需要的木材。

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  First, convert the decimal to a fraction.  $\begin{array}{r}1.5\end{array}$  is 1 and 5 tenths.
  ::首先,将小数点转换为分数。 1. 5是 1 和 5 十分。

  $$\begin{array}{r}1.5=1\frac{5}{10}\end{array}$$

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  Then, write the fraction in  simplest form . The GCF of 5 and 10 is 5.
  ::然后,以最简单的形式写下分数。5和10的GEF是5。

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

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  Henry needs to by the 6 by  $\begin{array}{r}1\frac{1}{2}\end{array}$  inch pieces of wood.
  ::亨利需要6乘12英寸的木头

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  Example 2
  ::例2

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  Convert the following decimal to a mixed number in simplest form.
  ::以最简单的形式将以下小数点转换为混合数。

  $\begin{array}{r}6.55\end{array}$

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  First, convert the decimal to a mixed number.  $\begin{array}{r}6.55\end{array}$  is read as six and fifty-five hundredths. 6 is the whole number, 55 is the numerator, and 100 is the denominator.
  ::首先,将小数点转换为混合数。 6.55读为六五五五五五百。 6是整数,55是分子,100是分母。

  $$\begin{array}{r}6.55=6\frac{55}{100}\end{array}$$

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  Then, write the fraction in simplest form. The GCF of 55 and 100 is 5.
  ::然后,以最简单的形式写下分数。全球合作框架为55和100是5。

  $$\begin{array}{r}6\frac{55}{100}=6\frac{11}{20}\end{array}$$

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  $\begin{array}{r}6.55\end{array}$  is written as  $\begin{array}{r}6\frac{11}{20}\end{array}$  in simplest form.
  ::6.55以最简单的形式写成6 11 20。

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  Example 3
  ::例3

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  Convert the decimal to a mixed number in simplest form.
  ::以最简单的形式将小数点转换为混合数。

  $\begin{array}{r}7.8\end{array}$

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  First, convert the decimal to a mixed number.  $\begin{array}{r}7.8\end{array}$  is 7 and 8 tenths.
  ::首先,将小数点转换为混合数。 7.8是7和8十分。

  $$\begin{array}{r}7.8=7\frac{8}{10}\end{array}$$

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  Then, write the fraction in simplest form. The GCF of 8 and 10 is 2.
  ::然后,以最简单的形式写下分数。8和10的绿色气候基金是2。

  $$\begin{array}{r}7\frac{8}{10}=7\frac{4}{5}\end{array}$$

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  $\begin{array}{r}7.8\end{array}$  is written as  $\begin{array}{r}7\frac{4}{5}\end{array}$  in simplest form.
  ::7.8以最简单的形式写成7 4 5。

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  Example 4
  ::例4

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  Convert the decimal to a mixed number in simplest form.
  ::以最简单的形式将小数点转换为混合数。

  $\begin{array}{r}4.45\end{array}$

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  First, convert the decimal to a mixed number.  $\begin{array}{r}4.45\end{array}$  is 4 and 45 hundredths.
  ::首先,将小数点转换为混合数。 4.45是4和45万分之一。

  $$\begin{array}{r}4.45=4\frac{45}{100}\end{array}$$

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  Then, write the fraction in simplest form. The GCF of 45 and 100 is 5.
  ::然后,以最简单的形式写下分数。全球合作框架45和100是5。

  $$\begin{array}{r}4\frac{45}{100}=4\frac{9}{20}\end{array}$$

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  $\begin{array}{r}4.45\end{array}$  is written as  $\begin{array}{r}4\frac{9}{20}\end{array}$  in simplest form.
  ::4.45以最简单的形式写成4 9 20。

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  Example 5
  ::例5

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  Convert the decimal to a mixed number in simplest form.
  ::以最简单的形式将小数点转换为混合数。

  $\begin{array}{r}2.25\end{array}$

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  First, convert the decimal to a mixed number.  $\begin{array}{r}2.25\end{array}$  is 2 and 25 hundredths.
  ::首先,将小数点转换为混合数字。 2.25是2-2500。

  $$\begin{array}{r}2.25=2\frac{25}{100}\end{array}$$

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  Then, write the fraction in simplest form. The GCF of 25 and 100 is 25.
  ::然后,以最简单的形式写下分数。全球合作框架25和100是25。

  $$\begin{array}{r}2\frac{25}{100}=2\frac{1}{4}\end{array}$$

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  $\begin{array}{r}2.25\end{array}$  is written as  $\begin{array}{r}2\frac{1}{4}\end{array}$  in simplest form.
  ::2.25以最简单的形式写成2,14。

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  Review
  ::回顾

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  Convert each decimal to a mixed number in simplest form.
  ::以最简单的形式将每个小数点转换为混合数。

  1. 3.5
  2. 2.4
  3. 13.2
  4. 25.6
  5. 3.45
  6. 7.17
  7. 18.18
  8. 9.20
  9. 7.65
  10. 13.11
  11.  7.25
  12. 9.75
  13. 10.10
  14. 4.33
  15. 8.22

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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