4.7 变化百分比-interactive

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  变化百分比

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  Win Percentage
  ::中 赢百分比

  

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  A volleyball team currently has 7 wins and 3 losses. Their win percentage is 70% because they have 7 wins in 10 games.  You can obtain this using the equation $\begin{array}{r}\text{part = percent}\cdot \text{whole}.\end{array}$
  ::排球队目前有7个赢3个输赢。他们的赢率是70 % , 因为他们在10场比赛中有7个赢。 您可以使用公式部分 =% = 整体来获得这个分数 。

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  • Part: 7
    ::部分:7
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  • Percent: x
    ::百分比: x
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  • Whole: 10
    ::全体:10名

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  $\begin{array}{rl}\text{part}& =\text{percent}\cdot \text{whole}\\ 7& =x\cdot 10\\ 0.7& =x\end{array}$
  ::部分=百分率=7=x100.7=x

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  When  you convert 0.7 from  a decimal,  you get the win percentage of 70%. Use the interactive below to explore how playing more games will affect the team’s win percentage.  You will use this idea that percents change to solve a range of problems.
  ::将 0. 7 从小数点转换为 0. 7 时, 就会得到 70 % 的 赢率。 使用下面的交互来探索玩更多的游戏会如何影响球队的赢率。 您会使用这个百分比变化的理念来解决一系列问题。

  

  INTERACTIVE

  Winning Percentage

  

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  • Use the buttons to increase the wins and losses.
    ::使用按钮来增加赢负和损失。
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  • See how the changes affect the win percentage.
    ::看看这些变化如何影响获胜率。
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  • Notice that after more games are played the change in percentage tends to become smaller.
    ::请注意,在玩了更多的游戏之后,百分比的变化往往越来越小。

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  ercent-problems" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4576d92b1ea59f8080b1ce&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:ercent-problems&mode=lite" test-id="5f4576d92b1ea59f8080b1ce">

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  Using a Model 
  ::使用模型

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  Example
  ::示例示例示例示例

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  An elementary school had 20% more girls than  boys last year. This year there are 35 fewer girls than last year . If there are only 10% more girls than  boys this year, how many girls were there last year?
  ::去年小学女生比男生多20%,今年比去年少35名,如果今年女生比男生多10%,去年有多少女生?

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  To solve a problem like this,  you can use a double tape diagram representing the population this year and the population last year.
  ::为了解决这样的问题, 你可以使用一个双磁带图, 来代表今年的人口和去年的人口。

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  T he percentages were given  relative to the number of boys, which did not change, so  let   the  number of boys be  100%.
  ::这些百分比与男孩人数相对,男生人数没有变化,因此男孩人数为100%。

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  Last year, there were 20% more girls so the girls will be represented by the number 120%. This year, there were 10% more girls so the girls will be represented by the number 110%.
  ::去年,女孩增加了20%,女孩将占120%;今年,女孩增加了10%,女孩将占110%。

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  The difference between the number of girls and boys this year is 35. 
  ::今年女孩和男孩人数的差别是35人。

  

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  From the tape diagram representing this year's student population, you can see that each 10% cell represents 35 students. Use this information to fill in the rest of the cells.
  ::从显示今年学生人数的磁带图中可以看出,每10%的细胞代表35名学生。使用这些信息填充其余的细胞。

  

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  Last year, there were 20% more girls than boys. This year, there are 35 fewer girls and  only 10% more girls than boys. Since the number of boys didn't change, the 10% drop is girls relative to boys corresponds to a drop of 35 female students.
  ::去年,女孩比男孩多20%,今年,女孩比男孩少35个,女孩比男孩少10%,由于男孩的数量没有改变,女孩比男孩少10%,女孩比男孩少10%,女孩比男孩少35人。

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  You know that the number of girls was  120% the number of boys last year. Since 10% = 35 students and 10% × 12 = 120%, the number of girls last year can be calculated as  35 × 12 = 420 .
  
  Answer: T here were 420  girls last year.
  ::你知道,去年女孩人数是男孩人数的120%,因为10%=35名学生,10%=12=120%,去年女孩人数可以计算为35×12=420。答复:去年有420名女孩。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. How many girls were there this year?
     ::今年有多少女孩在那里?
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  2. How many boys were there last year?
     ::去年有多少男孩在那里?
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  3. How many boys were there this year?
     ::今年有多少男孩在那里?
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  4. How many total students were there total last year?
     ::去年学生总数是多少?
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  5. How many total students were there total this year?
     ::今年学生总数是多少?

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  Using a Model Continued
  ::使用 " 继续使用 " 模型

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  Jerry and Christian have been raising money for a charity. Last week Jerry had raised the same amount as Christian, but Jerry did not raise any money this week. Christian raised an additional $150 this week and now Jerry's total is 25% less than Christian's total.
  ::杰瑞和克里斯蒂安一直在为慈善募捐。 上周,杰里筹集了与克里斯蒂安相同的金额,但杰里本周没有筹集到任何资金。 克里斯蒂安本周又筹集了150美元,现在杰瑞的总额比基督徒的总额少25%。

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  Use the interactive to answer the questions following it.
  ::使用交互方式回答随后的问题。

  

  INTERACTIVE

  Raising Money

  

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  • Use the slider to break up the diagram into different percentages.
    ::使用滑块将图表细分为不同的百分比。
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  • Use the information above to determine how much money Christian & Jerry raised for charity.
    ::利用上述信息确定基督教和Jerry为慈善募集了多少钱。
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  • Do not include a dollar sign in your answers.
    ::在您的答复中不包含美元符号 。

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  ercent-of-increase" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4576dcfcdc134c6962885a&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:ercent-of-increase&mode=lite" test-id="5f4576dcfcdc134c6962885a">

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  Using an Equation
  ::使用等量

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  In addition to using a double tape diagram,  you can also use an equation to solve a problem involving changing percents.  Explore  this using the same example from the previous activity and see if  you can  get the same answer.
  ::除了使用双磁带图外,您还可以使用方程式来解决一个涉及百分比变化的问题。使用与上一个活动相同的示例来探索这个问题,看看您能否得到相同的答案。

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  Example
  ::示例示例示例示例

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  An elementary school had 20% more girls than boys last year. This year there are 35 fewer girls than last year . If there are only 10% more girls than boys this year, how many girls were there last year?
  ::去年小学女生比男生多20%,今年比去年少35名,如果今年女生比男生多10%,去年有多少女生?

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  Since there  were 20% more girls last year and 10% more girls this year, the percent dropped by 10 percentage points. Those ten percentage points represent the 35 fewer girls.
  ::因为去年女孩增加了20%,今年又增加了10%,所以这一百分比下降了10个百分点,这10个百分点是减少35个女孩。

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  The number of girls this year can be thought of as: 
  ::今年的女童人数可视为:

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  • the number of boys  + 35 , or
    ::男孩数+35,或
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  • the number of boys + 10% the number of boys
    ::男孩人数+男孩人数的10%+男孩人数的10%

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  Therefore,  10% of the number of boys is 35. 
  ::因此,男孩人数的10%是35人。

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  Then,  use the equation  $\begin{array}{r}\text{part = percent}\cdot \text{whole}:\end{array}$
  ::然后,使用方程式部分 =% 和整个:

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  • Part: 35
    ::部分:35
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  • Percent: 10% = 0.10
    ::百分比:10%=0.10
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  • Whole: x (the number of boys)
    ::整个: x (男孩人数)

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  $\begin{array}{rl}\text{part}& =\text{percent}\cdot \text{whole}\\ 35& =0.10\cdot x\\ x& =350\end{array}$
  ::部分=百分数35=0.10xx=350

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  By solving  this  equation,  you can see that there are 350 boys .  Since there were 20% more girls than boys,  you can find 20% of 350 and add it to the number of boys.
  ::通过解决这个方程式,你可以看到有350个男孩。 由于女孩比男孩多20%,你可以找到350个女孩中的20%,并加入男孩的数量。

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  You  already know that 10% is 35, so 20% must equal 35 · 2 = 70. This gives us 350 + 70 = 420 girls.
  ::你知道10%是35岁 所以20%必须等于35岁 2 = 70 这让我们有了350 + 70 = 420个女孩

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. If 10% is 35 what would 150% represent?
     ::如果10%是35,150%代表什么?
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  2. If one year there were 10% fewer girls and the next year there were 5% more girls, what would be the difference in the percents from last year to this year?
     ::如果一年女孩少10%,下一年女孩多5%,那么从去年到今年,百分比的差别是什么?

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  Win Percentage Continued
  ::续 续

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  Two volleyball teams, the Sharks and the Tornadoes currently have the same number of wins with 5 games left in the season. The Sharks won 3 of their final 5 games, and the Tornadoes didn’t win any of their final 5 games. The Sharks currently have 10% more wins than the Tornadoes.
  ::两支排球队、鲨鱼队和龙卷风队目前赢得的比赛数量与本季剩下的5场比赛相同。 鲨鱼队赢得了最后5场比赛中的3场,而龙卷风队没有赢得最后5场比赛中的1场。 鲨鱼队目前比龙卷风队赢得了10 % 。

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  Use the tape measure interactive or  the equation method to answer the questions below.
  ::使用磁带测量交互或方程式方法回答下列问题。

  

  INTERACTIVE

  Win/Loss Records

  

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  • Use the slider to change the percentage.
    ::使用滑块更改百分比。
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  • Enter the value for the total number of wins for the Sharks. Then enter the total number of wins for the Tornadoes.
    ::输入 " 鲨鱼 " 的胜者总数。然后输入 " 龙卷风 " 的胜者总数。
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  • See how the Tornadoes did compared to the Sharks.
    ::看看龙卷风和鲨鱼的比对

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  Summary

  播放段落 Rearrange the formula $\begin{array}{r}\text{percent}=\frac{\text{part}}{\text{whole}}\end{array}$ to solve problems involving percentages. ::重新排列公式百分比=全方位,以解决涉及百分比的问题。 播放段落 You can convert a percentage into a decimal by dividing by 100. For example, 87% can be represented by the decimal value 0.87. ::您可以将百分数除以100将百分数转换为十进制数,例如,小数值0.87可以表示87%。