6.5比例查找百分比，p

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  比例查找百分比，p

  

  [Figure 1]

   

  Max went berry picking. He picked both raspberries and blackberries, but he had only one pail. Max counts 24 raspberries and 11 blackberries in the scoop he takes from the pail. What percent of Max’s is raspberries and what percent is blackberries?

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  In this concept, you will learn to use proportions to find the percent,  $\begin{array}{r}p\end{array}$ .
  ::在这一概念中,你将学会使用比例来找到百分比,p.。

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  Using Proportions to Find the Percent, p
  ::使用比例来查找百分比,p

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  A  percent  is a part of a whole out of 100.
  ::百分之一是整个100的一部分

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  You can write a percent as a  fraction  with a denominator of 100. You can use a  proportion  to figure out a percent.
  ::您可以以100分母作为分数写百分之一。您可以用比例来算出百分之一。

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  Look at this proportion:  $\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$ .
  ::看看这个比例:a b = p 100。

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  You can say that “ $\begin{array}{r}a\end{array}$  is the amount to the base,  $\begin{array}{r}b\end{array}$ , and  $\begin{array}{r}p\end{array}$  is the percent out of 100.”
  ::你可以说,“a是基数,b和p是100的百分率。”

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  Since percent statements always involve three numbers, given any two of these numbers, you can find the third number using the proportion.
  ::由于百分数的报表总是包含三个数字,如果有其中两个数字,则使用该比例可以找到第三个数字。

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  Let’s look at an example.
  ::让我们举个例子。

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  What percent of 40 is 6?
  ::40比6是多少?

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  First, notice that you are looking for the percent. So the  $\begin{array}{r}p\end{array}$  over 100 is going to stay the same in the proportion.
  ::首先,请注意您正在寻找百分比。 所以百分位数在比例上会保持不变 。

  $$\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$$

  You need to fill in the  $\begin{array}{r}a\end{array}$  and the  $\begin{array}{r}b\end{array}$  so you can solve for  $\begin{array}{r}p\end{array}$ , the percent. The words “of 40” let you know that 40 is the base and 6 is the amount out of that base.

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  Here is your proportion to solve.
  ::这是你们要解决的比例

  $$\begin{array}{r}\frac{6}{40}=\frac{p}{100}\end{array}$$

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  Now you can use cross products and solve.
  ::现在,您可以使用交叉产品和解决方案。

  $$\begin{array}{r}\begin{array}{rcl}40p& =& 600\\ p& =& 15\end{array}\end{array}$$

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  The answer is 6 is 15% of 40.
  ::答案是6是40分的15%。

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  Let’s look at another example.
  ::让我们再看看另一个例子。

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  What percent of 300 is 40?
  ::三百分之四是多少?

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  First, use the following percent proportion.
  ::首先,使用以下百分比比例。

  $$\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$$

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  Next, fill in the given information.
  ::下一步填入给定信息。

  $$\begin{array}{r}\frac{40}{300}=\frac{p}{100}\end{array}$$

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  Then, cross-multiply and divide.
  ::然后,交叉倍增和分裂。

  $$\begin{array}{r}\begin{array}{rcl}300p& =& 4,000\\ p& =& 13.3\mathrm{\%}\end{array}\end{array}$$

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  The answer is 40 is 13.3% of 300.
  ::答案是40是300的13.3%。

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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 Max and his berries.
  ::之前,你得到一个问题 关于麦克斯和他的浆果。

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  24 of his scoop were raspberries and 11 were blackberries. What percent of the scoop were raspberries and what percent were blackberries?
  ::其中24个是草莓,11个是黑莓。

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  First, the total number of berries in Max’s handful is 24 + 11 = 35.
  ::首先,马克斯的草莓总数为24+11=35。

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  Next, let’s figure out the percents.
  ::接下来,让我们来计算一下百分比。

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  You can start with the raspberries. There are 24 raspberries out of 35 berries in Max’s hand. There is your first proportion.
  ::你可以从草莓开始。在马克斯手里的35个浆果中,有24个草莓。这是你的第一个比例。

  $$\begin{array}{r}\frac{24}{35}=\frac{p}{100}\end{array}$$

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  Now you need to find the percent. You can do so by cross-multiplying and then dividing.
  ::现在,你需要找到百分比。你可以通过交叉倍增来做到这一点,然后进行分割。

  $$\begin{array}{r}\begin{array}{rcl}35p& =& 2,400\\ p& =& 68.57\mathrm{\%}\end{array}\end{array}$$

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  The answer is 68.57% of Max’s handful berries is raspberries.
  ::答案是马克斯(Max)62.57%的小浆果是草莓。

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  Next, let’s look at the blackberries. 11 out of 35 berries are blackberries.
  ::下面让我们看看黑莓。 35个浆果中有11个是黑莓。

  $$\begin{array}{r}\begin{array}{rcl}\frac{11}{35}& =& \frac{p}{100}\\ 35p& =& 1,100\\ p& =& 31.43\mathrm{\%}\end{array}\end{array}$$

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  The answer is 31.43% of Max’s handful of berries is blackberries.
  ::答案是麦斯一小撮浆果的31.43%是黑莓。

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  Example 2
  ::例2

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  Jeremy has 25 marbles and 12 of them are cat’s eye marbles. What percent of his marbles are cat’s eye marbles?
  ::Jeremy有25颗大理石,其中12颗是猫眼大理石。 猫眼大理石占猫眼大理石的多大比例?

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  You can think of this problem as “What percent of 25 is 12?”
  ::你可以认为这个问题是“25 %是12 %?”

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  12 is the amount  $\begin{array}{r}(a)\end{array}$  and 25 is the base  $\begin{array}{r}(b)\end{array}$ . You need to find the percent  $\begin{array}{r}(p)\end{array}$ .
  ::12 是数额 (a) , 25 是基数 (b) 。 您需要找到百分比 (p) 。

  $$\begin{array}{r}\begin{array}{rcl}\frac{a}{b}& =& \frac{p}{100}\\ \frac{12}{25}& =& \frac{p}{100}\\ 25p& =& 1,200\\ \frac{25p}{25}& =& \frac{1,200}{25}\\ p& =& 48\end{array}\end{array}$$

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  Since  $\begin{array}{r}p=48\end{array}$ , the fraction you are looking for is  $\begin{array}{r}\frac{48}{100}\end{array}$ , which is 48%.
  ::由于p=48, 你要找的分数是48 100, 也就是48%。

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  The answer is that 48% of Jeremy’s marbles are cat’s eye marbles.
  ::答案是,杰里米48%的弹珠是猫眼珠。

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  Example 3
  ::例3

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  What percent of 20 is 2?
  ::20分之2是多少?

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  First, you can use the following percent proportion.
  ::首先,你可以使用以下百分比比例。

  $$\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$$

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  Next, you can fill in the given information.
  ::接下来,您可以填写给定信息 。

  $$\begin{array}{r}\frac{2}{20}=\frac{p}{100}\end{array}$$

  Now you can cross multiply and divide.

  $$\begin{array}{r}\begin{array}{rcl}20p& =& 200\\ p& =& 10\mathrm{\%}\end{array}\end{array}$$

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  The answer is 2 is 10% of 20.
  ::答案是 2 等于 20 的 10% 。

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  Example 4
  ::例4

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  What percent of 30 is 6?
  ::30是6是多少?

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  First, you can use the following percent proportion.
  ::首先,你可以使用以下百分比比例。

  $$\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$$

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  Next, you can fill in the given information.
  ::接下来,您可以填写给定信息 。

  $$\begin{array}{r}\frac{6}{30}=\frac{p}{100}\end{array}$$

   
  Now you can cross multiply and divide.

  $$\begin{array}{r}\begin{array}{rcl}30p& =& 600\\ P& =& 20\mathrm{\%}\end{array}\end{array}$$

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  The answer is 6 is 20% of 30.
  ::答案是6是30分的20%

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  Example 5
  ::例5

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  What percent of 45 is 15?
  ::45分的百分之十五是15分呢?

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  First, you can use the following percent proportion.
  ::首先,你可以使用以下百分比比例。

  $$\begin{array}{r}\frac{a}{b}=\frac{p}{100}\end{array}$$

  Next, you can fill in the given information.

  $$\begin{array}{r}\frac{15}{45}=\frac{p}{100}\end{array}$$

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  Now you can cross multiply and divide.
  ::现在,你可以跨越乘数和分裂。

  $$\begin{array}{r}\begin{array}{rcl}45p& =& 1,500\\ p& =& 33.3\mathrm{\%}\end{array}\end{array}$$

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  The answer is 15 is 33.3% of 45.
  ::答案是15,占45分的33.3%。

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  Review
  ::回顾

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  Find each percent using a proportion. Round your percent to the nearest tenths place when needed.
  ::使用比例来查找每一百分比。 需要时, 将您的百分率四舍五入到最近的十分之一 。

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  1. What percent of 18 is 9?
     ::十八分之九是多少?
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  2. What percent of 20 is 4?
     ::20分之四是多少?
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  3. What percent of 28 is 7?
     ::28分中7分是多少?
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  4. What percent of 30 is 6?
     ::30是6是多少?
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  5. What percent of 9 is 3?
     ::百分之九还是百分之三?
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  6. What percent of 36 is 18?
     ::36分中哪分是18分?
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  7. What percent of 40 is 8?
     ::40分的百分之八是多少?
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  8. What percent of 48 is 12?
     ::四十八分之十二是多少?
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  9. What percent of 50 is 30?
     ::50分中多少是30分?
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  10. What percent of 80 is 60?
      ::80是60是多少?
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  11. What percent of 90 is 12?
      ::百分之九十是百分之十二? 百分之九十是百分之十二?
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  12. What percent of 75 is 25?
      ::75是25是多少?
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  13. What percent of 60 is 12?
      ::60分中哪分是12分?
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  14. What percent of 50 is 40?
      ::50分中多少是40分?
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  15. What percent of 88 is 11?
      ::88分之11是多少?

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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