5.20作为小数的混合数

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 作为小数的混合数

  Collapse Expand

  作为小数的混合数

  

  [Figure 1]

  播放段落

  Kara is making curtains for her room. She has a total of  $\begin{array}{r}6\frac{4}{5}\end{array}$  yards of fabric to work with. Each curtain needs to be 3.45 yards and she is making 2 curtains. Will she have enough fabric for both?
  ::卡拉正在为她的房间做窗帘。 她有总共6455码的织物要一起工作。 每个窗帘需要3.45码,她正在做两个窗帘。 她有足够的布料可以两边都用吗?

  播放段落

  In this concept, you will learn to  .
  ::在这个概念中,你会学会。

  播放段落

  Converting Mixed Numbers to Decimals
  ::将混合数字转换为十进制

  播放段落

  You can convert fractions to decimals using two methods. One method involves using fractions with base ten denominators and place values. Another method involves division. These methods can also be use to convert mixed numbers to decimal numbers.
  ::您可以使用两种方法将分数转换为小数。 一种方法是使用带有基本 10 分母和位置值的分数。 另一种方法是分割。 这些方法也可以用来将混合数字转换为小数。

  播放段落

  Here is a  mixed number .
  ::这是混合数字。

  $$\begin{array}{r}5\frac{3}{10}\end{array}$$

  播放段落

  You can also think of a mixed number as the  sum  of a whole number and a fraction.
  ::您也可以将混合数字视为整个数字和分数的总和。

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

  播放段落

  To find the decimal value of a mixed number, convert the fraction to a decimal number and add the whole number to the decimal value of the fraction. Remember that the whole number in a fraction has the same value as a whole number in a decimal number.  Whole numbers  are placed on the left side of the  decimal point .
  ::要找到混合数的十进制值, 请将分数转换为十进制数, 并将整数添加到分数的十进制值。 记住, 分数中的整数与十进制数中的整数具有相同的值。 整数被放在小数点左侧 。

  播放段落

  The fraction  $\begin{array}{r}\frac{3}{10}\end{array}$  is 3 tenths. Place the whole number, 5, to the left of the decimal point and the 3 in the tenths place.  
  ::分数 3 10 是 3 十分。 将整数, 5 放在小数点左边, 3 放在 十 位。

  $$\begin{array}{r}5\frac{3}{10}=5.3\end{array}$$

  播放段落

  Here is another mixed number.
  ::这是另一个混合数字。

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

  播放段落

  First, find the decimal value of  $\begin{array}{r}\frac{1}{5}\end{array}$ .  Divide  1 by 5 to get the decimal part of the number.
  ::首先,找到小数点值为 15。除以 1 乘 5 以获得数字的小数点部分 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.2}{5\overline{)1.0}}\\ & & \underset{\_}{-1.0}\\ & & 0\end{array}\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}8\frac{1}{5}=8.2\end{array}$$

  播放段落

  The decimal value of  $\begin{array}{r}8\frac{1}{5}\end{array}$  is  $\begin{array}{r}8.2\end{array}$ .
  ::小数点为8,1,5,小数点为8.2。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Kara and her curtains.
  ::早些时候,有人给了你卡拉和她的窗帘的问题。

  播放段落

  Kara wants to make 2 curtains that are 3.45 yards each and has  $\begin{array}{r}6\frac{4}{5}\end{array}$  yards of fabric. Convert the mixed number to see if she will have enough.
  ::Kara想要做两扇窗帘,每扇窗帘3.45码,有6、4、5码的织物。转换混合数,看她是否有足够的。

  播放段落

  First, convert the fraction part into a decimal.
  ::首先,将分数部分转换为小数点。

  $$\begin{array}{r}\frac{4}{5}=0.8\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}6\frac{4}{5}=6.8\end{array}$$

  播放段落

  Next, find the total  amount  she needs.
  ::接下来,找出她需要的总额

  $$\begin{array}{r}3.45\times 2=6.9\end{array}$$

  播放段落

  Kara will not have enough fabric and will be short 0.1 yards of fabric.
  ::卡拉将没有足够的布料 并且将是短0.1码的布料。

  播放段落

  Example 2
  ::例2

  播放段落

  Write the following mixed number as a decimal.
  ::将以下混合数字写为小数。

  $$\begin{array}{r}16\frac{3}{4}\end{array}$$

  播放段落

  First, convert the fraction part into a decimal. Divide or find an equivalent fraction with the  denominator  as a base ten value.
  ::首先,将分数部分转换为小数点。除以或找到一个等值分数,分母为基十值。

  $$\begin{array}{r}\frac{3}{4}=\frac{75}{100}=0.75\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}16\frac{3}{4}=16.75\end{array}$$

  播放段落

  The decimal value of  $\begin{array}{r}16\frac{3}{4}\end{array}$  is  $\begin{array}{r}16.75\end{array}$ .
  ::小数点为16 3 4,小数点为16.75。

  播放段落

  Example 3
  ::例3

  播放段落

  Write the mixed number as a decimal.
  ::混合数字写为小数。

  $$\begin{array}{r}6\frac{13}{100}\end{array}$$

  播放段落

  First, convert the fraction part into a decimal.  $\begin{array}{r}\frac{13}{100}\end{array}$  is 13 hundredths.
  ::首先,将分数部分转换为小数点。 13 100是1 300。

  $$\begin{array}{r}\frac{13}{100}=0.13\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}6\frac{13}{100}=6.13\end{array}$$

  播放段落

  The decimal value of  $\begin{array}{r}6\frac{13}{100}\end{array}$  is  $\begin{array}{r}6.13\end{array}$ .
  ::小数点后6 13 100是6.13。

  播放段落

  Example 4
  ::例4

  播放段落

  Write the mixed number as a decimal.
  ::混合数字写为小数。

  $$\begin{array}{r}15\frac{9}{10}\end{array}$$

  播放段落

  First, convert the fraction part into a decimal.  $\begin{array}{r}\frac{9}{10}\end{array}$  is 9 tenths.
  ::首先,将分数部分转换为小数点。 9 10是十分之九。

  $$\begin{array}{r}\frac{9}{10}=0.9\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  播放段落

  The decimal value of  $\begin{array}{r}15\frac{9}{10}\end{array}$  is  $\begin{array}{r}15.9\end{array}$ .
  ::小数点后15 9 10是15.9。

  播放段落

  Example 5
  ::例5

  播放段落

  Write the mixed number as a decimal.
  ::混合数字写为小数。

  $$\begin{array}{r}6\frac{1}{4}\end{array}$$

  播放段落

  First, convert the fraction part into a decimal.
  ::首先,将分数部分转换为小数点。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{0.25}{4\overline{)1.00}}\\ & & \underset{\_}{-8}\\ & & 20\\ & & \underset{\_}{-20}\\ & & 0\end{array}\end{array}$$

  播放段落

  Then, place the whole number to the left of the decimal point.
  ::然后将整个数字放在小数点左边。

  $$\begin{array}{r}6\frac{1}{4}=6.25\end{array}$$

  播放段落

  The decimal value of  $\begin{array}{r}6\frac{1}{4}\end{array}$  is  $\begin{array}{r}6.25\end{array}$ .
  ::小数点为6,14,小数点为6.25。

  播放段落

  Review
  ::回顾

  播放段落

  Write each mixed number as a decimal.
  ::每个混合数以小数表示。

  1. $\begin{array}{r}4\frac{1}{10}\end{array}$   
  2. $\begin{array}{r}6\frac{8}{10}\end{array}$
  3. $\begin{array}{r}14\frac{6}{100}\end{array}$
  4. $\begin{array}{r}7\frac{18}{100}\end{array}$
  5. $\begin{array}{r}12\frac{9}{10}\end{array}$
  6. $\begin{array}{r}24\frac{11}{100}\end{array}$
  7. $\begin{array}{r}8\frac{19}{100}\end{array}$
  8. $\begin{array}{r}5\frac{10}{20}\end{array}$
  9. $\begin{array}{r}4\frac{1}{2}\end{array}$
  10. $\begin{array}{r}7\frac{1}{3}\end{array}$
  11. $\begin{array}{r}5\frac{2}{10}\end{array}$
  12. $\begin{array}{r}9\frac{1}{8}\end{array}$
  13. $\begin{array}{r}10\frac{2}{100}\end{array}$
  14. $\begin{array}{r}46\frac{1}{4}\end{array}$  
  15. $\begin{array}{r}65\frac{4}{5}\end{array}$

  播放段落

  Review (Answers) 
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源