4.3 解决涉及增减百分比的问题-interactive

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  解决涉及增减百分比的问题

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  Action Comics!
  ::动画动画动画!

  

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  In 2014, Action Comics #1, a comic book with the first appearance of Superman, was sold for about $3,200,000. This comic book was originally sold in 1938 for $0.10. How can we measure how the value of Action Comics #1 changed since 1938?
  ::2014 年, 《 行动动画1 》 ( Action Commics # 1) , 一本漫画书,首次出现超人,以约3 200 000美元的价格出售。这本漫画书最初于 1938 年以 0.10美元的价格出售。 我们如何衡量自 1938 年以来《行动动画1 》 ( Action Camics # 1) 的价值变化?

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  Many items increase or decrease in value over time. One way to express this is by using a percent. The new price is expressed as a percentage of the old price. For example, if the new price is 50% of the old price, this means that the new price is half the old price. If the new price is 200% of the old price, this means that the new price is double the old price.
  ::许多项目随时间而增减。 表达这一点的方法之一是使用一个百分比。 新价格以旧价格的百分率表示。 例如,如果新价格是旧价格的50%,这意味着新价格是旧价格的一半。 如果新价格是旧价格的200 % , 则新价格是旧价格的两倍。

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  One example of an object with a value that could either increase or decrease over time is a house. Many factors determine the value of a house: market, location, nearby schools, appearance, condition, etc. If any of those variables change, the value of the house  could  go up or down. Use the interactive below to explore this idea.
  ::房屋是具有可随时间增加或减少价值的物品的一个例子。许多因素决定房屋的价值:市场、地点、附近学校、外观、条件等等。如果这些变数有任何变化,房屋的价值可以上下浮动。使用下面的互动来探索这个想法。

  ercent-of-increase" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f45789caf5602e09ca3791a&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:ercent-of-increase&mode=lite" test-id="5f45789caf5602e09ca3791a">

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  Car Depreciation
  ::汽车折旧

  

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  There are two ways to express a decrease using a percent. Explore them in the context of the value of a car.
  ::使用一定百分比来表示下降有两种方式。 从汽车价值的角度来探讨这些方法。

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  Example
  ::示例示例示例示例

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  Over time, the value of a car decreases. If the value of a car purchased for $25,000 decreases by 20% throughout a year, what will its value be in at the end of the year?
  ::汽车价值随时间推移而下降。 如果以25 000美元购买的汽车价值全年下降20%,那么年终其价值会是多少?

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  Option 1 :  Think of this as taking 20% off the value which means that you can find 20% of $25,000 and subtract it from the $25,000. You can do this using  the percent formula .
  ::选项1: 将此视为从值中减去20%, 这意味着您可以找到 20% 的 25 000 美元, 然后从 25 000 美元中减去。 您可以使用百分比公式来做到这一点 。

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  $\begin{array}{r}\text{percent}\cdot \text{whole = part}\end{array}$
  ::全百分率=部分

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  • Percent: 0.20
    ::百分比: 0.20
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  • Part: x
    ::部分:xx
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  • Whole: 25,000
    ::整个:25 000人

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  $\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ 0.2\cdot 25,000& =x\\ 5,000& =x\end{array}$
  ::=================================================================================================================================================================================================================x===========================================================================================================================================================================================================================================================================================================

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  Answer: The $5,000 represents the amount the value decreased. The value of the car after a year will be $20,000.
  ::答复:5 000美元是价值下降的数额,一年后汽车价值为20 000美元。

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  Option 2 : Instead of thinking about how much the value is being decreased, think about how much of the value will be left. If the value of the car decreases by 20%, this means that there will be 80% of the value left. Use  $\begin{array}{r}\text{percent}\cdot \text{whole = part}\end{array}$  to determine what 80% of 25,000 is.
  ::选项2: 不考虑价值减少多少, 而不考虑剩下多少价值。 如果汽车价值减少20%, 这意味着剩余价值将减少80%。 使用% = llole = part 来决定 $ 80% = 25 000 是多少。

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  • Percent: 0.80
    ::百分比:0.80
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  • Part: x
    ::部分:xx
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  • Whole: 25,000
    ::整个:25 000人

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  $\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ 0.8\cdot 25,000& =x\\ 20,000& =x\end{array}$
  ::=x20,000=xx

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  Answer: $20,000
  ::答复:20 000美元

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  Discussion Question
  ::讨论问题

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  Which method do you feel was easier? Why?
  ::你觉得哪一种方法比较容易?

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  Use the interactive below to explore percent decreases further.
  ::使用下面的互动来进一步探索百分比的下降。

  ercent-of-decrease" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4578a33e6deba41794aff5&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:ercent-of-decrease&mode=lite" test-id="5f4578a33e6deba41794aff5">

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  Fixer Upper 
  ::上层断层器

  

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  House flipping is a practice where someone buys a house, renovates it, and sells it at a greater value than the value at which it was purchased. We can use a percent to express the change in price. As with decreases, there are two ways to express an increase using a percent.
  ::房屋翻转是一种做法,有人购买、翻新房屋,并以比购买房屋价值更高的价值出售房屋。我们可以用1%来表示价格的变化。与下降一样,有两种方法使用1%来表示增长。

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  Example
  ::示例示例示例示例

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  A  house was bought for $200,000 and the value was increased by 50%.
  ::一栋房子以20万美元的价格买下,价值增加了50%。

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  Option 1 :  You can express an increase by stating the increase as a percent of the original whole.  U se the formula  $\begin{array}{r}\text{percent}\cdot \text{whole = part}\end{array}$  to determine what the new value of the house is.
  ::选项1:您可以通过将增长表示为整个原始值的百分率来表示增长。使用公式百分率=整体=部分来确定房屋的新价值。

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  • Percent: 0.50
    ::百分比:0.50
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  • Part: x
    ::部分:xx
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  • Whole: 200,000
    ::整个:200 000

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  $\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ 0.5\cdot 200,000& =x\\ 100,000& =x\end{array}$
  ::全百分数=0.5 20万=x100 000=x

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  Answer: The $100,000 represents the amount the value increased. The value of the house after the increase will be $200,000 + $100,000 = $300,000.
  ::答复:100 000美元是增加的价值,增加后的房屋价值为200 000美元+100 000美元=300 000美元。

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  Option 2 : Instead of thinking about how much the value is being increased,  think about what the new value is compared to the old value.  Set  the original value of the house to be 100%. An increase of 50% will make the new value 100% + 50% = 150% of the original value.  Then use   $\begin{array}{r}\text{percent}\cdot \text{whole = part}\end{array}$  to determine what 150% of 200,000 is.
  ::选项2: 不考虑增加值的多少, 而不考虑新值与旧值的比较。 设定房屋的原始值为100%。 增加50%将使新值达到100%+50%=原值的150%。 然后使用%==全值=部分来决定20万中的150 % 。

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  • Percent: 1.50
    ::百分比:1.50
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  • Part: x
    ::部分:xx
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  • Whole: 200,000
    ::整个:200 000

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  Even though the new value will be greater than the original value, we still consider the original value to be the whole and the new value to be the part.
  ::尽管新价值将大于原始价值,但我们仍然认为原有价值是整体,新价值是整体。

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  $\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ 1.5\cdot 200,000& =x\\ 300,000& =x\end{array}$
  ::=x300,000=xx

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  Answer: $300,000
  ::答复:300 000美元

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  Discussion Question
  ::讨论问题

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  Prove that both of the methods presented above are equivalent.
  ::证明上述两种方法相同。

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  Use the interactives below to explore percent increases further.
  ::使用下面的交互数据来进一步探索百分比增长。

  ercent-of-increase" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4578abd9f7e38aee785bd3&collectionHandle=arithmetic&collectionCreatorID=3&conceptCollectionHandle=arithmetic-:ercent-of-increase&mode=lite" test-id="5f4578abd9f7e38aee785bd3">

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  The Million Dollar Comic Book Revisited
  ::重审了百万元漫画书

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  In the introduction, you read about Action Comics #1 was sold for about $3,200,000 after originally being sold for $0.10 in 1938. Use a percent to compare the current value to the original value.
  ::在引言中,您读到了关于行动动漫片1的一号在1938年以0.10美元出售后以大约3,200,000美元的价格售出。使用1%来比较当值和原值。

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  You  can solve this using the equation $\begin{array}{r}\text{percent}\cdot \text{whole = part}.\end{array}$
  ::您可以使用公式百分率=整体=部分来解决这个问题 。

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  • Percent: x
    ::百分比: x
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  • Part: 3,200,000
    ::部分:3 200 000美元
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  • Whole: 0.10
    ::整个:0.10

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  $\begin{array}{rl}\text{percent}\cdot \text{whole}& =\text{part}\\ x\cdot 0.10& =3,200,000\\ 32,000,000& =x\end{array}$
  ::=3 200 000 32 000 000 =x

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  Remember  that this equation will produce the percent as a decimal. Even though  the "decimal"  answer is a whole number,  you still need to turn it into a percent by moving the decimal two places to the right. This means that this comic book has increased in value by 3,200,000,000% or 3.2 billion percent!
  ::记住此方程式将生成百分数作为小数。 即使“ 十进制” 答案是一个整数, 您仍然需要将小数点后两个位移到右边, 将其转换为百分数 。 这意味着这本漫画书的价值增加了 3, 200,000,000 % , 即32亿 。

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  Discussion Question
  ::讨论问题

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  Sandra thinks that increasing a value by 100% will keep the value the same. Dan thinks that increasing a value by 100% Will double the value. Who do you agree with? Use evidence to support your argument.
  ::桑德拉认为,将值增加100%会使值保持不变。 丹认为,将值增加100%会使值增加一倍。 你同意谁的意见? 使用证据支持你的论点。

  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 播放段落 A value of 1 can represent 100%. Values lower than 1 correspond to a percent decrease while values greater than 1 correspond to a percent increase. ::1 的值代表100%。 低于 1 的值相当于减少%, 而值大于 1 的值相当于增加% 。 播放段落 For example, a 20% off discount means the price will only be 80% of the original cost. Use the value 0.8 in your calculations. ::例如,20%的贴现折扣意味着价格只相当于原成本的80%。在计算时使用0.8值。 播放段落 A price increase of 15% means the total cost will be 115% of the original. Use the value 1.15 in your calculations. ::涨价15%意味着总成本为原价的115%。在计算时使用价值1.15。 ::1 的值代表100%。 低于 1 的值相当于 下降%, 而大于 1 的值代表 增长%。 例如, 20% 的折扣表示价格仅为 原始成本 的 80% 。 在计算中使用 0. 8 的值。 15% 的 价格增长表示总成本为 原成本 115。 在计算中使用 1.15 的值 。