4.10 比例绘图和百分比-interactive

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  比例绘图和百分比

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   Scale Drawings
  ::缩放绘图

  

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  Scale drawings are used by architects and many other types of designers to show what a structure will look like before it is constructed. These drawings are called blueprints and accuracy in a blueprint is extremely important. The people who build the structure use the dimensions of the blueprint and the scale to determine what the dimensions of the structure will be.
  ::建筑师和许多其他类型的设计师都使用比例图来显示结构在构建之前会是什么样子。 这些图纸在蓝图中被称为蓝图和准确性。 构建结构的人利用蓝图和规模的维度来确定结构的维度。

  

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  You  used the letter $\begin{array}{r}k\end{array}$  to express the scale factor which represents the amount that the image is enlarged or shrunk. Use the interactive below to refresh your memory on scale factor.
  ::您使用字母 k 来表达显示图像放大或缩放的缩放量的缩放系数。 使用下面的交互效果来根据缩放系数来刷新您的记忆 。

  

  INTERACTIVE

  Scaling Brainy's Photo

  

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  • Drag the red point to change the dimensions of the original photo and drag the purple point to change the scale factor @$k.@$
    ::拖曳红色点以改变原始照片的尺寸,拖曳紫点以改变比例系数@ $k. @ $

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  ercent-problems" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4575d56acfd760047e25e6&collectionHandle=algebra&collectionCreatorID=3&conceptCollectionHandle=algebra-:ercent-problems&mode=lite" test-id="5f4575d56acfd760047e25e6">

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  Scale Factor and Percents
  ::比例因数和百分比

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  Similar  to how  percents  were  used to represent increases and decreases in , you can use them to represent the copy as a percent of the original. T he equation  $\begin{array}{r}k=\frac{\text{copy}}{\text{original}}\end{array}$  can be rearranged to $\begin{array}{r}\text{copy}=k\cdot \text{original}.\end{array}$
  ::使用百分比来表示增减的方式相似, 您可以使用百分比来表示副本占原件的%。 方程式 k=coptionIstim 可以重新排列为副本=kácription 。

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  This equation  is similar to the equation used for percent , part and whole : $\begin{array}{r}\text{part = percent}\cdot \text{whole}.\end{array}$  The original image is the whole, the  copy is the part of the original image,  and the scale factor is the percent written as a decimal or fraction.
  ::此方程式与百分数、 部分和整数的方程式相似: part = 百分数。 原始图像为整数, 副本为原始图像的一部分, 缩放系数为以小数或分数写成的百分数 。

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  Example
  ::示例示例示例示例

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  A scale factor of $\begin{array}{r}\frac{1}{5}\end{array}$  corresponds to what percent?
  ::15的比额表因数相当于什么百分比?

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       To find $\begin{array}{r}\frac{1}{5}\end{array}$  as a percent, you can use a proportion.
  ::要发现15%的比例,您可以使用比例。

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  $\begin{array}{r}\frac{1}{5}=\frac{x}{100}\end{array}$
  ::15=100 15=100

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  $\begin{array}{rl}100\cdot 1& =x\cdot 5\\ 100& =5x\\ 20& =x\end{array}$
  ::100% 1 =x5=5x20=x

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  Answer: 20%
  ::答复:20%

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. Does 20% represent the amount the whole was decreased or the amount left after the decrease?
     ::20%是整笔减少的数额还是减少后留下的数额?
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  2. Are there any other ways that you could convert $\begin{array}{r}\frac{1}{5}\end{array}$  to a percent?
     ::还有什么其他方法可以把15%转换成百分之十五吗?

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  Use the interactive below to practice converting scale factor to a percent.
  ::使用下面的交互效果来练习将比例系数转换成百分之一。

  

  INTERACTIVE

  Scaling Brainy's Photo and Finding the Percent

  

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  • Move the blue point to change the dimensions of the copied photo.
    ::移动蓝色点以改变复制照片的尺寸 。
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  • Enter the value that represents the percentage conversion of the given ratio.
    ::输入表示给定比率百分比转换的值。

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  Using the Scale Factor as a Percent
  ::使用比例系数作为百分比

  

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  Now that you understand the connection between scale factor and percents, you can use a percent to scale an image.
  ::既然您了解比例系数和百分比之间的联系, 您可以使用百分比来缩放图像 。

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  Example
  ::示例示例示例示例

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  A scale model of a car was built at 12.5% scale. If the width of the model car is 9.75 inches , what is the width of the real car?
  ::汽车规模模型是按12.5%的比例建造的。如果汽车型号宽度为9.75英寸,那么真车的宽度是多少?

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  You can solve this using either or the scale equation. Since scale is given as a percent, use the percent equation.
  ::您可以使用比例方程式或比例方程式来解决这个问题。由于比例以百分比表示,请使用百分比方程式。

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  $\begin{array}{r}\text{part = percent}\cdot \text{whole}\end{array}$
  ::=整个百分比

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  • Part: 9.75
    ::部分:9.75
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  • Percent: 12.5% = 0.125
    ::百分比:12.5%=0.125
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  • Whole: $\begin{array}{r}x\end{array}$  
    ::整个: x

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  The part will be the width of the model car since it is based on the width of the real car. The whole will be the size of the real car since this represents 100%.
  ::部分是模拟汽车的宽度, 因为它以真车的宽度为基础。 整部是真车的大小, 因为它代表100% 。

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  $\begin{array}{rl}9.75& =0.125\cdot x\\ 9.75÷0.125& =x\\ 78& =x\end{array}$
  ::9.75=0.1.125x9.75=0.125=x78=xx

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  Answer: The width of the real car is 78 inches.
  ::回答:真车宽度为78英寸。

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  Finding Scale Factor as a Percent
  ::查找比例系数为百分比

  

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  Example
  ::示例示例示例示例

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  A model of the F4U Corsair, pictured above, is constructed for an Air Expo in Idaho. If the model has a wingspan of 2.5 feet and the actual wingspan of the plane is approximately 40 feet, what is the scale of the model written as a percent?
  ::F4U Corsair(F4U Corsair)模型如上图,是为爱达荷州的一个航空博览会建造的。 如果模型的翼宽为2.5英尺,而飞机的实际翼宽约为40英尺,那么模型以百分比表示的规模是多少?

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  While you can use either equation, in this case, use the scale equation to determine the scale factor:
  ::当您可以使用任何一种方程式时,在此情况下,使用比例方程式来确定比例系数:

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  $\begin{array}{r}k=\frac{\text{model}}{\text{original}}\end{array}$
  ::k = 模型原型

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  • $\begin{array}{r}k=x\end{array}$  
    ::k=x( k=x)
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  • Model = 2.5
    ::型号=2.5
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  • Original = 40
    ::原件=40

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  $\begin{array}{r}k=\frac{2.5}{40}\end{array}$
  ::k=2.540

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  Now,  write the scale factor as a fraction. To do this, you will need to make the 2.5 in the numerator an integer which you can do by multiplying the numerator and denominator by 10.
  ::现在,请将缩放系数作为一个分数写入。要做到这一点,您需要使分子中的 2.5 成一个整数,您可以通过乘以乘以10 和分母来完成这个整数。

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  $\begin{array}{r}k=\frac{2.5\cdot 10}{40\cdot 10}=\frac{25}{400}=\frac{1}{16}\end{array}$
  ::k=2.5-1040-10=25400=116

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  Now you have to write the scale factor  $\begin{array}{r}\frac{1}{16}\end{array}$   as a percent.
  ::现在,你必须把比额表系数116 写成一个百分比。

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  $\begin{array}{rl}\frac{1}{16}& =\frac{x}{100}\\ 100\cdot 1& =x\cdot 16\\ 100& =16x\\ 6.25& =x\end{array}$
  ::116=x1001001=x16100=16x6.25=x

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  Answer: The wingspan of the model plane is 6.25% of the original plane.
  ::答复:模型平面的翼宽为原平面的6.25%。

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  Discussion Questions
  ::讨论问题 讨论问题

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  1. Why will it result in an integer when we multiply 2.5 by 10?
     ::当我们乘以2.5乘以10时,为什么会得出整数呢?
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  2. Why did we have to multiply the numerator and denominator by 10?
     ::为什么我们要把分子和分母乘以10?
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  3. What other approaches could be have used to convert the numerator and denominator to whole numbers? Which do you feel is the best approach?
     ::用什么其他方法将分子和分母转换成整数?你觉得哪种方法最好?
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  4. What is the percent decrease of the original plane to get the model plane?
     ::原飞机减少多少百分比 以获得模型飞机?

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  Use the interactive below to explore this further.
  ::利用以下互动方式进一步探讨这一问题。

  

  INTERACTIVE

  Scaling as a Percent

  

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  • Enter the percent the original photo is scaled by to get the copy.
    ::输入原始照片的百分率, 以获取副本为缩放比例 。

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  Summary

  播放段落 The scale factor  represents the amount that the image is enlarged or shrunk. ::缩放系数表示图像放大或缩放的大小。 播放段落 Use the equation $\begin{array}{r}k=\frac{\text{copy}}{\text{original}}\end{array}$  to solve problems involving scale factors. ::使用方程式 k = copyIstim 来解决涉及比例因素的问题。 播放段落 The formula $\begin{array}{r}\text{percent}=\frac{\text{part}}{\text{whole}}\end{array}$  can be used to solve problems involving percentages. ::公式百分数=全数,可用于解决涉及百分数的问题。