6.3分数转为百分比

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  分数转为百分比

  

  [Figure 1]

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  Mica measures the screw he is using to build a shelf for his sports trophies. He discovers that it is  $\begin{array}{r}\frac{5}{8}\end{array}$  of an inch. Mica wonders what  percentage  of an inch the screw measures. How can he convert this fraction to a percent?
  ::米卡测量他用来建造体育奖杯架的螺丝。他发现这是一寸五十八寸。米卡想知道螺丝的比重是多少。他怎么能将这一分数转换成百分之一呢?

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  In this concept, you will learn to write fractions as percents.
  ::在此概念中, 您将学习以百分比来写分数 。

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

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  A fraction can be written as a percent if it has a  denominator  of 100. Sometimes, you will be given a fraction with a denominator of 100 and sometimes you will have to rewrite the fraction to have a denominator of 100 before you can write it as a percent.
  ::如果分数为100分母, 分数可以写成百分比。 有时, 你将得到分数为100分母的分数。 有时, 在您将分数写成百分比之前, 您必须重写分数为100分母的分数。

  $$\begin{array}{r}\frac{9}{100}\end{array}$$

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  This fraction is already written with a denominator of 100, so you can just change it to a percent.
  ::这个分数已经以 100 的分母写成, 所以您可以将其修改为 1% 。

  $$\begin{array}{r}\frac{9}{100}=9\mathrm{\%}\end{array}$$

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  A  proportion  is two equal ratios. If a fraction does not have a denominator of 100, you can write a fraction equal to it that does have a denominator of 100 and then solve the proportion.
  ::一个比例是两个相等的比例。如果一个分数没有分母为100,您可以写入一个分母为100的分母,然后解答该比例。

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

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  Write  $\begin{array}{r}\frac{3}{5}\end{array}$  as a percent.
  ::百分之三十五写为百分之三十五

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  First, notice that the denominator is not 100. Therefore, you need to create a new fraction equivalent to this one with a denominator of 100.
  ::首先,请注意分母不是100, 因此, 您需要创建一个新的分母, 相当于这个分母, 分母为100。

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  Next, set up a proportion.
  ::接下来,设定一个比例。

  $$\begin{array}{r}\frac{3}{5}=\frac{x}{100}\end{array}$$

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  Then, you can cross multiply to find the value of  $\begin{array}{r}x\end{array}$ .
  ::然后,您可以交叉乘以找到 x 的值 。

  $$\begin{array}{r}\begin{array}{rcl}5x& =& 300\\ x& =& 60\\ \frac{3}{5}& =& \frac{60}{100}\end{array}\end{array}$$

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  Now you have a fraction with a denominator of 100, and you can write it as a percent.
  ::现在你有一个分数,分母为100, 你可以把它写成百分之一。

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  The answer is that the fraction  $\begin{array}{r}\frac{3}{5}\end{array}$  is equal to  $\begin{array}{r}60\mathrm{\%}\end{array}$ .
  ::答案是,第3组第5部分等于60%。

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  To work with an  improper fraction , you have to think about what improper means. An  improper fraction  is greater than 1, so the percent would be greater than 100%. Sometimes you can have percents that are greater than 100%. Most often they are not, but it is important to understand how to work with a percent that is greater than 100%.
  ::要处理不适当的分数,你就必须思考何谓不适当。不适当的分数大于1,因此百分比将大于100%。有时,你可以拥有超过100%的百分数。通常情况下,它们不是,但重要的是要了解如何使用超过100%的百分数。

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  You already know some common fraction equivalents for percents. Think of 25 cents, 50 cents, and 75 cents.
  ::你已经知道一些常见的分数等同百分比。想想25美分,50美分,75美分。

  

  [Figure 2]

   

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  . $\begin{array}{r}\frac{1}{4}=25\mathrm{\%}\end{array}$ 25 cents means 25 cents out of a dollar, or 25% of a dollar. Since a quarter is 25 cents, 
  ::1 4 = 25% 25 美分意味着 美元中25美分,或1美元中25美分。由于四分之一是 25美分,

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  . $\begin{array}{r}\frac{1}{2}=50\mathrm{\%}\end{array}$ 50 cents means 50 cents out of a dollar, or 50% of a dollar. Since a half dollar is 50 cents, 
  ::1 2 = 50% 50 美分意味着 美元50 美分, 或 美元50 美分。 因为 5 美分是 50 美分,

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  $\begin{array}{r}\frac{3}{4}=75\mathrm{\%}\end{array}$ 75 cents means 75 cents out of a dollar, or 75% of a dollar. Since three quarters of a dollar is 75 cents, .
  ::3 4 = 75% 75 美分是指 美元 的 75美分 , 即 美元 的 75美分 , 即 美元 的 75% 。 因为 美元 的 四分之三 是 75美分 。

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  Let’s look at an example with a fraction that doesn‘t convert easily to a percent.
  ::让我们用一个“不容易转换为%”的分数来举个例子。

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  Write  $\begin{array}{r}\frac{2}{3}\end{array}$   as a percent.
  ::写百分之二十三

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  First, set up the proportion. 
  ::首先,设定比例。

  $$\begin{array}{r}\frac{2}{3}=\frac{x}{100}\end{array}$$

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  Next, cross multiply to solve for the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘以解答 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}3x& =& 200\\ x& =& 66.6\end{array}\end{array}$$

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  Notice that you end up with a decimal and it is a  repeating decimal . If you keep dividing, you will keep ending up with 6s. Therefore, you can leave this percent with one decimal place represented.
  ::注意您最后的十进制为小数点, 这是重复的十进制。 如果您继续分隔, 您会继续以六进制结束。 因此, 您可以将这个百分比保留在小数点后的一个位数 。

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  The answer is 66.6%.
  ::答案是66.6%。

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  Sometimes, you will see fractions like this, but you will get used to them and often you can learn the percent equivalents of these fractions by heart.
  ::有时候,你会看到像这样的分数, 但你会习惯这些分数, 并且常常你可以从心底学习这些分数的百分数。

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  As a final example, let’s take a look at a real-life word problem.
  ::最后一个例子,让我们看看一个真实的文字问题。

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  James ate three out of ten pieces of pizza. What percent of the pizza did he eat? What percent didn’t he eat?
  ::James在十块比萨中吃了三块。 他吃了多少比萨? 他没有吃多少?

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  First, let’s write a fraction to show the part of the pizza that James did eat. 
  ::首先,让我们写下一点, 来展示詹姆斯吃的那部分披萨。

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

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  Next, you convert that to a fraction out of 100 by setting up a proportion. 
  ::下一步,通过设定比例,将该比例转换为100分之一。

  $$\begin{array}{r}\frac{3}{10}=\frac{x}{100}\end{array}$$

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  Then you can write it as a percent.
  ::然后,你可以把它写成百分之一。

  $$\begin{array}{r}\begin{array}{rcl}10x& =& 300\\ x& =& 30\end{array}\end{array}$$

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  The answer is James ate 30% of the pizza, and James did not each 70% of the pizza.
  ::答案是詹姆斯吃了30%的比萨饼 詹姆斯没有每人吃70%的比萨饼

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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 Mica and his shelf screw.
  ::早些时候,你得到一个问题 关于米卡和他的架子螺丝。

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  It measured  $\begin{array}{r}\frac{5}{8}\end{array}$  of an inch. What percent of an inch does this length represent?
  ::它测量了58%英寸。这个长度代表的英寸是多少?

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  First, set up the proportion. 
  ::首先,设定比例。

  $$\begin{array}{r}\frac{5}{8}=\frac{x}{100}\end{array}$$

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  Next, cross multiply to solve for the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘以解答 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}8x& =& 500\\ x& =& 62.5\end{array}\end{array}$$

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  So, 62.5% of an inch is  $\begin{array}{r}\frac{5}{8}\end{array}$ .
  ::所以,62.5%的英寸是5 8。

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  Example 2
  ::例2

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  Write  $\begin{array}{r}\frac{9}{4}\end{array}$  as a percent.
  ::百分之九十四写成百分之九十四

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  First, you write a proportion with a denominator of 100.
  ::首先,你写一个比例 与分母100。

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

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  Next, you cross multiply to find the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,您交叉乘以找到 x 的值 。

  $$\begin{array}{r}\begin{array}{rcl}4x& =& 900\\ x& =& 225\\ \frac{225}{100}& =& 225\mathrm{\%}\end{array}\end{array}$$

  The answer is  $\begin{array}{r}\frac{9}{4}\end{array}$  is equal to 225%. 

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  Example 3
  ::例3

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  Write  $\begin{array}{r}\frac{1}{4}\end{array}$  as a percent.
  ::写14成百分比。

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  First, set up the proportion. 
  ::首先,设定比例。

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

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  Next, cross multiply to solve for the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘以解答 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}4x& =& 100\\ x& =& 25\end{array}\end{array}$$

  The answer is 25%.

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  Example 4
  ::例4

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  Write  $\begin{array}{r}\frac{2}{5}\end{array}$  as a percent.
  ::百分之二十五写成百分之二十五

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  First, set up the proportion.
  ::首先,设定比例。

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

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  Next, cross multiply to solve for the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘以解答 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}5x& =& 200\\ x& =& 40\end{array}\end{array}$$

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  The answer is 40%.
  ::答案是40%。

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  Example 5
  ::例5

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  Write  $\begin{array}{r}\frac{4}{40}\end{array}$  as a percent.
  ::写作440 百分比。

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  First, set up the proportion. 
  ::首先,设定比例。

  $$\begin{array}{r}\frac{4}{40}=\frac{x}{100}\end{array}$$

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  Next, cross multiply to solve for the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘以解答 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}40x& =& 400\\ x& =& 10\end{array}\end{array}$$

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  The answer is 10%.
  ::答案是10%。

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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. $\begin{array}{r}\frac{1}{4}\end{array}$
  2. $\begin{array}{r}\frac{1}{2}\end{array}$  
  3. $\begin{array}{r}\frac{3}{4}\end{array}$
  4. $\begin{array}{r}\frac{11}{100}\end{array}$  
  5. $\begin{array}{r}\frac{1}{5}\end{array}$
  6. $\begin{array}{r}\frac{4}{8}\end{array}$  
  7. $\begin{array}{r}\frac{17}{100}\end{array}$
  8. $\begin{array}{r}\frac{125}{100}\end{array}$
  9. $\begin{array}{r}\frac{250}{100}\end{array}$  
  10. $\begin{array}{r}\frac{233}{100}\end{array}$  
  11. $\begin{array}{r}\frac{27}{50}\end{array}$   
  12. $\begin{array}{r}\frac{18}{36}\end{array}$  
  13. $\begin{array}{r}\frac{21}{50}\end{array}$
  14. $\begin{array}{r}\frac{20}{50}\end{array}$
  15. $\begin{array}{r}\frac{30}{60}\end{array}$   

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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