8.14分数作为百分比

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• 选择节分数作为百分比

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  分数作为百分比

  

  [Figure 1]

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  Sam is on his way to the Grand Canyon. He calculates that the Grand Canyon is about 500 miles from his house. He takes a break at a rest stop and checks the odometer in his car. So far he has traveled 325 miles. What percent of the total trip to the Grand Canyon has Sam traveled so far?
  ::Sam正在前往大峡谷的路上。 他计算出大峡谷离家约500英里。 他在休息站休息一阵,检查车里的气压计。 到目前为止,他已经行驶了325英里。 到大峡谷的总行程中,萨姆旅行了多少比例?

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  In this concept, you will learn to convert fractions to percents.
  ::在此概念中, 您将学习将分数转换为百分比 。

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  Writing Fractions as Percents
  ::以百分比写入分数

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  A  percent  is part of a whole where the whole is 100. Percents can be written as fractions by removing the percent symbol and writing the number over the  denominator  of 100.
  ::1%是整体的一部分,其整体为100。 百分数可以通过去除百分数符号和在100分母上写出数字,作为分数来写成。

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  To write 14% as a fraction, take the number and write it as the quantity over a fraction with the denominator 100.
  ::将14%作为一个分数来写, 将数字作为分数, 以分数100作为分数, 以分数比分数100。

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  14% is  $\begin{array}{r}\frac{14}{100}\end{array}$ .
  ::14%是14 100

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  Fractions with a denominator of 100 can also be written as a percent by doing the reverse.
  ::分数为100分数的分数也可以通过倒数写成百分比。

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  Write  $\begin{array}{r}\frac{47}{100}\end{array}$  as a percent.
  ::写47百一百成百上百的百分率。

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  Remove the fraction bar and denominator and add the percent symbol.
  ::删除分数栏和分母,并添加百分比符号。

  $$\begin{array}{r}47\mathrm{\%}\end{array}$$

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  $\begin{array}{r}\frac{47}{100}\end{array}$  is written as 47%.
  ::47 100 以47%的写法写成。

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  Fractions with a denominator other than 100 can still be written as a percent. A fraction can be rewritten with a denominator of 100 using  . The equivalent fraction can then be converted to a percent.
  ::分母不大于 100 的分数仍然可以以百分比写成。 分数可以用分母100 来重新写。 等分数可以转换成百分比 。

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  Let’s write  $\begin{array}{r}\frac{2}{5}\end{array}$  as a percent.
  ::让我们以百分之二十五的比例写下。

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  First, write a  proportion  to find the equivalent fraction of  $\begin{array}{r}\frac{2}{5}\end{array}$  with the denominator of 100.
  ::首先,写一个比例 找到等值分数 2 5 和 分母 100。

  $$\begin{array}{r}\frac{2}{5}=\frac{}{100}\end{array}$$

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  Next, cross-multiply or use mental math to find the unknown  numerator .
  ::下一个,交叉乘法或使用心理数学 找到未知的分子。

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  Think, “100 divided by 5 is 2. I can multiply 2 by 20 to get the equivalent numerator.”
  ::想想,“100除以5是2,我可以乘以2乘以20,以获得相等的分子。”

  $$\begin{array}{r}\begin{array}{rcl}2\times 20& =& 40\\ \frac{2}{5}& =& \frac{40}{100}\end{array}\end{array}$$

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  Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.
  ::然后,使用相等的分数来找到百分比。删除分数栏和分母,并添加百分比符号。

  $$\begin{array}{r}40\mathrm{\%}\end{array}$$

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  $\begin{array}{r}\frac{2}{5}\end{array}$  is written as 40%.
  ::2 5 书写为40%。

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  One special fraction remember is  $\begin{array}{r}\frac{1}{3}\end{array}$ .
  ::记住一个特殊的分数是13。

  $$\begin{array}{r}\frac{1}{3}=\frac{}{100}\end{array}$$

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  Converting  $\begin{array}{r}\frac{1}{3}\end{array}$  to a percent is a little tricky because 3 does not  divide  evenly into 100. The result is a  repeating decimal .
  ::将13%转换为1%是一个小问题, 因为 3 不均匀地分为100, 结果是重复十进制 。

  $$\begin{array}{r}100÷3=0.3333333\dots \end{array}$$

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  Instead, remember that  $\begin{array}{r}\frac{1}{3}\end{array}$  is written as  $\begin{array}{r}33\frac{1}{3}\mathrm{\%}\end{array}$ , read as “thirty three and one-third percent.”
  ::但请记住,1,3,3的写法是33,1,3%,读法是“百分之三十三,1/3”。

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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 Sam on his way to the Grand Canyon.
  ::早些时候,你在萨姆去大峡谷的路上 遇到一个问题

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  Sam has traveled 325 miles on a 500 mile journey to the Grand Canyon. To find the percent he has traveled so far, Sam can write the ratio of the miles traveled to the total miles as a percent.
  ::萨姆在前往大峡谷500英里的旅程中行驶了325英里。 为了发现他迄今所旅行的百分率,萨姆可以将行驶的里程与总里程的比率以百分率表示。

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  First, write a proportion to find the equivalent fraction of  $\begin{array}{r}\frac{325}{500}\end{array}$  with the denominator of 100.
  ::首先,写一个比例,找到相当于325500分位数的分母,分母为100分位数。

  $$\begin{array}{r}\frac{325}{500}=\frac{}{100}\end{array}$$

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  Next, solve the proportion to find the unknown quantity. Divide the numerator and denominator by 5.
  ::下一步, 解析比例以找到未知数量。 分子和分母除以 5 。

  $$\begin{array}{r}\begin{array}{rcl}500÷5& =& 100\\ 325÷5& =& 65\\ \frac{325}{500}& =& \frac{65}{100}\end{array}\end{array}$$

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  Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.
  ::然后,使用相等的分数来找到百分比。删除分数栏和分母,并添加百分比符号。

  $$\begin{array}{r}65\mathrm{\%}\end{array}$$

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  Sam has traveled 65% of the total trip.
  ::萨姆已经旅行了 65%的总行程。

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  Example 2
  ::例2

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  Write the fraction as a percent.
  ::将分数写成百分比 。

  $$\begin{array}{r}\frac{23}{50}\end{array}$$

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  First, write a proportion to find the equivalent fraction of  $\begin{array}{r}\frac{23}{50}\end{array}$  with the denominator of 100.
  ::首先,写一个比例来找到 23 50的等值分数, 分母为100。

  $$\begin{array}{r}\frac{23}{50}=\frac{}{100}\end{array}$$

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  Then, find the unknown numerator.
  ::然后找到未知的分子

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  Think, “50 is half of 100. 23 is half of 46.”
  ::想想,“50是100的一半,23是46的一半。”

  $$\begin{array}{r}\frac{23}{50}=\frac{46}{100}\end{array}$$

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  Then, use the equivalent fraction to find the percent. Remove the fraction bar and denominator and add the percent symbol.
  ::然后,使用相等的分数来找到百分比。删除分数栏和分母,并添加百分比符号。

  $$\begin{array}{r}46\mathrm{\%}\end{array}$$

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  $\begin{array}{r}\frac{23}{50}\end{array}$  is written as 46%.
  ::23 50是46%的写法。

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  Example 3
  ::例3

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  Write the fraction as a percent.
  ::将分数写成百分比 。

  $$\begin{array}{r}\frac{48}{100}\end{array}$$

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  Remove the fraction bar and denominator and add the percent symbol.
  ::删除分数栏和分母,并添加百分比符号。

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  The answer is  $\begin{array}{r}\frac{48}{100}\end{array}$  is 48%.
  ::答案是48 100是48%

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  Example 4
  ::例4

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  Write the fraction as a percent.
  ::将分数写成百分比 。

  $$\begin{array}{r}\frac{82}{100}\end{array}$$

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  Remove the fraction bar and denominator and add the percent symbol.
  ::删除分数栏和分母,并添加百分比符号。

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  The answer is  $\begin{array}{r}\frac{82}{100}\end{array}$  is 82%.
  ::答案是82 100是82%

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  Example 5
  ::例5

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  Write the fraction as a percent.
  ::将分数写成百分比 。

  $$\begin{array}{r}\frac{91}{100}\end{array}$$

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  Remove the fraction bar and denominator and add the percent symbol.
  ::删除分数栏和分母,并添加百分比符号。

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  The answer is  $\begin{array}{r}\frac{91}{100}\end{array}$  is 91%.
  
  ::答案是91100是91%

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  Review
  ::回顾

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  Write each fraction as a percent.
  ::将每一分数写成百分比。

  1. $\begin{array}{r}\frac{4}{100}\end{array}$
  2. $\begin{array}{r}\frac{24}{100}\end{array}$
  3. $\begin{array}{r}\frac{20}{100}\end{array}$
  4. $\begin{array}{r}\frac{76}{100}\end{array}$
  5. $\begin{array}{r}\frac{61}{100}\end{array}$
  6. $\begin{array}{r}\frac{1}{4}\end{array}$
  7. $\begin{array}{r}\frac{3}{4}\end{array}$
  8. $\begin{array}{r}\frac{3}{6}\end{array}$
  9. $\begin{array}{r}\frac{2}{5}\end{array}$
  10. $\begin{array}{r}\frac{4}{5}\end{array}$
  11. $\begin{array}{r}\frac{8}{10}\end{array}$
  12. $\begin{array}{r}\frac{6}{10}\end{array}$
  13. $\begin{array}{r}\frac{6}{50}\end{array}$
  14. $\begin{array}{r}\frac{3}{25}\end{array}$  
  15. $\begin{array}{r}\frac{20}{50}\end{array}$

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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
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