6.15下降的百分比

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  下降的百分比

  

  [Figure 1]

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  At the end of the summer season, the local farmer’s market marked down its swan gourds to $1.00 apiece. Throughout the summer, the swan gourds had sold for $3.50 each. What was the percent of decrease in cost?
  ::夏季末,当地农户市场将其天鹅瓜标记为每人1美元。 整个夏天,天鹅瓜每售3.50美元。 成本下降的几率是多少?

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  In this concept, you will learn how to calculate the percent of decrease.
  ::在这个概念中,你会学会如何计算 下降的百分率。

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  Finding Percent of Decrease
  ::查找下降百分比

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  Prices can increase. Costs can increase. Numbers can increase. You can find the   when dealing with an increase. All of these things can also decrease. When there has been a decrease from an original  amount  to a new lower amount, you can find the  percent of decrease .
  ::价格可以增加。 成本可以增加。 数字可以增加。 您可以在处理增长时找到增长。 所有这些事情也可以减少。 当最初的金额下降到新的较低的金额时, 您可以找到下降的% 。

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  The  percent of decrease  from one amount to another is the ratio of the amount of decrease to the original amount.
  ::从一个数额到另一个数额的下降百分比是减少数额与原数额的比率。

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  To find the percent of decrease, follow these steps:
  ::为了找到下降的百分率, 遵循这些步骤:

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  First, find the amount of decrease by subtracting the lower amount from the higher amount.
  ::首先,从较高数额中减去较低数额,以找到减少数额。

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  Next, write a fraction in which the  numerator  is the amount of decrease and the  denominator  is the original amount.
  ::下一步,写一个分数,其中分子为减少量,分母为原始量。

  $$\begin{array}{r}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}\end{array}$$

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  Then, write the fraction as a percent.
  ::然后,将分数写成百分比。

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  Now let’s look at how to apply these steps.
  ::现在让我们来看看如何实施这些步骤。

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  Find the percent of decrease from 50 to 40.
  ::发现从50到40的下降百分比

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  First, subtract 40 from 50.
  ::首先,50减40。

  $$\begin{array}{r}50-40=10\end{array}$$

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  Next, write the fraction:
  ::下一步,写分数 :

  $$\begin{array}{r}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{10}{50}\end{array}$$

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  Then, write the fraction as a percent.
  ::然后,将分数写成百分比。

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  One Way
  ::单行

  $$\begin{array}{r}\begin{array}{rcl}\frac{10}{50}& =& \frac{x}{100}\\ 50x& =& 1,000\\ \frac{\cancel{50}x}{\cancel{50}}& =& \frac{1,000}{50}\\ x& =& 20\end{array}\end{array}$$

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  Another Way
  ::另一种方式

  $$\begin{array}{rl}& \frac{10}{50}=\frac{10÷10}{50÷10}=\frac{1}{5}\\ & \stackrel{0.20}{5\overline{)1.00}}\leftarrow \text{Divide to}2\text{decimal places.}\\ & 0.20=20\mathrm{\%}\end{array}$$

  The answer is the percent of decrease from 50 to 40 is 20%.

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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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  Find the percent of decrease from 200 to 170.
  ::发现从200到170的下降率的百分比。

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  First, subtract 170 from 200.
  ::首先,从200中减去170。

  $$\begin{array}{r}200-170=30\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{30}{200}\end{array}$
  ::下一步,写入分数:减少的百分比 = 减少数额 = 原数额 = 30 200

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  Then, write the fraction as a percent.
  ::然后,将分数写成百分比。

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  One Way
  ::单行

  $$\begin{array}{r}\begin{array}{rcl}\frac{30}{200}& =& \frac{x}{100}\\ 200x& =& 3,000\\ \frac{\cancel{200}x}{\cancel{200}}& =& \frac{3,000}{200}\\ x& =& 15\end{array}\end{array}$$

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  Another Way
  ::另一种方式

  $$\begin{array}{rl}& \frac{30}{200}=\frac{30÷10}{200÷10}=\frac{3}{20}\\ & \stackrel{0.15}{20\overline{)3.00}}\leftarrow \text{Divide to}2\text{decimal places.}\\ & 0.15=15\mathrm{\%}\end{array}$$

  The answer is the percent of decrease from 200 to 170 is 15%.

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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 the end of summer sale at the farmer’s market.
  ::更早之前, 农民市场夏季销售结束时,

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  The swan gourds were marked down from $3.50 to $1.00. What was the percent of decrease?
  ::天鹅瓜从3.50美元下降到1美元。 下降的几率是多少?

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  First, subtract to find the  difference .
  ::首先,减去以找到差数。

  $$\begin{array}{r}3.50-1.00=2.50\end{array}$$

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  Next,  divide  that difference by the original amount.
  ::接下来,将差额除以原来的数额。

  $$\begin{array}{r}2.50÷3.50=0.714\end{array}$$

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  Finally, convert this decimal to a percent.
  ::最后,将这个小数点转换为百分之一。

  $$\begin{array}{r}0.714=71.4\mathrm{\%}\end{array}$$

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  The answer is the percent of decrease from $3.50 to $1.00 is 71.4%.
  ::答案是,从3.50美元降至1美元的百分比为71.4%。

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  Example 2
  ::例2

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  Jessie’s work schedule went from 20 hours to 18 hours. What was the percent of the decrease?
  ::杰西的工作时间表从20小时到18小时不等。 减幅的几率是多少?

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  First, subtract to find the difference.
  ::首先,减去以找到差数。

  $$\begin{array}{r}20-18=2\end{array}$$

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  Next, divide that difference by the original amount.
  ::接下来,将差额除以原来的数额。

  $$\begin{array}{r}2÷20=0.1\end{array}$$

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  Finally, convert this decimal to a percent.
  ::最后,将这个小数点转换为百分之一。

  $$\begin{array}{r}0.1=10\mathrm{\%}\end{array}$$

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  The answer is the percent of decrease from 20 hours to 18 hours was 10%.
  ::答案是,从20小时减少到18小时的比例是10%。

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  Example 3
  ::例3

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  Find the percent of decrease from 10 to 5.
  ::发现从10到5下降的百分比。

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  First, subtract 5 from 10.
  ::首先,从10减5。

  $$\begin{array}{r}10-5=5\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{5}{10}\end{array}$
  ::下一步,写入分数:减少的百分比=减少的原数额=5 10

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  Then, write the fraction as a percent:
  ::然后,将分数写成百分比:

  $$\begin{array}{r}\begin{array}{rcl}\frac{5}{10}& =& \frac{x}{100}\\ 10x& =& 500\\ \frac{10x}{10}& =& \frac{500}{10}\\ x& =& 50\end{array}\end{array}$$

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  The answer is the percent decrease from 10 to 5 is 50%.
  ::答案是,10%到5%的下降率是50%。

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  Example 4
  ::例4

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  Find the percent of decrease from 25 to 15.
  ::发现从25下降到15的百分比下降。

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  First, subtract to find the difference.
  ::首先,减去以找到差数。

  $$\begin{array}{r}25-15=10\end{array}$$

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  Next, divide that difference by the original amount.
  ::接下来,将差额除以原来的数额。

  $$\begin{array}{r}10÷25=0.4\end{array}$$

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  Finally, convert this decimal to a percent.
  ::最后,将这个小数点转换为百分之一。

  $$\begin{array}{r}0.4=40\mathrm{\%}\end{array}$$

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  The answer is the percent of decrease from 25 to 15 is 40%.
  ::答案是,25%到15%的下降率是40%。

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  Example 5
  ::例5

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  Find the percent of decrease from 125 to 70.
  ::发现从125下降到70的下降百分比。

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  First, subtract 70 from 125.
  ::首先,从125中减去70。

  $$\begin{array}{r}125-70=55\end{array}$$

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  Next, write the fraction:  $\begin{array}{r}\text{Percent of Decrease }=\frac{\text{Amount of Decrease}}{\text{Original Amount}}=\frac{55}{125}\end{array}$
  ::下一步,写入分数:减少的百分比=减少的原数额=55 125

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  Then, write the fraction as a percent: 
  ::然后,将分数写成百分比:

  $$\begin{array}{r}\begin{array}{rcl}\frac{55}{125}& =& \frac{x}{100}\\ 125x& =& 5,500\\ \frac{10x}{125}& =& \frac{5,500}{125}\\ x& =& 44\end{array}\end{array}$$

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  The answer is the percent decrease from 125 to 70 is 44%.
  ::答案是,从125下降到70的比例下降了44%。

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  Review
  ::回顾

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  Find the percent of decrease given the original amount. Round to the nearest tenths place when needed.
  ::查找根据原始数量减少的百分比。 如果需要, 回合到最近的十分位数 。

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  1. From 25 to 10
     ::25至10
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  2. From 30 to 11
     ::30至11
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  3. From 18 to 8
     ::18-8
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  4. From 30 to 28
     ::30至28
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  5. From 12 to 8
     ::12-8
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  6. From 90 to 85
     ::90至85
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  7. From 200 to 150
     ::200至150
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  8. From 97 to 90
     ::97至90
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  9. From 56 to 45
     ::56至45
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  10. From 15 to 2
      ::15至2
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  11. From 220 to 110
      ::220至110
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  12. From 75 to 66
      ::75至66
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  13. From 180 to 121 
      ::180至121
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  14. From 1500 to 1275 
      ::1500至1275年
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  15. From 18,000 to 900
      ::18 000至900

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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