5.12单位比例尺查找实际尺寸

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  单位比例尺查找实际尺寸

  

  [Figure 1]

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  Tanya's room was a mess. She had all sorts of books and toys strewn about, and her grandpa decided it was time to do something about it. He asked Tanya to draw a diagram for him, and he would make bookcase shelves. Tanya's drawing shows that the bookcase is 5.5  inches  high. The scale says, 2 inches = 1  foot .
  ::塔尼娅的房间一团糟。 她有各种书和玩具, 她的祖父决定现在该做点什么了。 他让塔尼娅为他绘制一张图表, 他会做书架。 塔尼娅的画显示书架高5.5英寸。 比例尺上写着, 2英寸等于1英尺。

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  Given this scale, what is the actual height of the bookcase?
  ::鉴于这个规模,书架的实际高度是多少?

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  In this concept, you will learn how to use a  unit scale  to find actual dimensions.
  ::在这个概念中,你将学会如何使用单位规模来找到实际的维度。

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  Using a Unit Scale to Find Actual Dimensions
  ::使用单位比例来查找实际尺寸

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  A  ratio  compares two quantities. Ratios can be written as fractions, with a colon or with the word “to.”
  ::A 比率比较两个数量。 比率可以以分数表示, 用冒号或“ to”字表示 。

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  $\begin{array}{r}\frac{2}{3}\end{array}$ , 2:3, and "2 to 3" are ratios.
  ::2,3,2,3,2,3 和"2,3"是比例。

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  A  proportion  is created when two ratios are found to be  equivalent  or equal.
  ::当发现两个比率对等或相等时,就形成一个比例。

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  $\begin{array}{r}\frac{1}{2}\end{array}$ = $\begin{array}{r}\frac{3}{6}\end{array}$  is a proportion.
  ::1 2 = 3 6 是一个比例。

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  A  unit rate  is a comparison of two measurements, one of which has a value of 1.
  ::A单位费率是两项测量的比较,其中一项测量值为1。

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  55 miles per  hour ,  $\begin{array}{r}\frac{55}{1}\frac{miles}{hour}\end{array}$  is a unit rate. 
  ::每小时55英里 551米 i e s h o u r 是单位费率。

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  A  unit scale  is a ratio that compares the dimensions of an actual object to the dimensions of a scale drawing or model that represents the actual object. Neither value in a unit scale has to equal 1. 
  ::单位比例表是指将实际物体的尺寸与代表实际物体的尺度图示或模型的尺寸进行比较的比率。单位比例表中的数值不一定等于1。

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  The unit scale on a map may read 1" = 100 feet.
  ::地图上的单位比例尺可读 1" = 100英尺。

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    The ratio would be written    $\begin{array}{r}\frac{1}{100}\frac{inch}{feet}\end{array}$  .
  ::比率为1 100 i n c h f e e t。

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  To represent a line 500 feet long, the unit scale would be used to draw a line 5 inches long.
  ::为代表500英尺长的线,单位比例表将用于绘制5英寸长的线。

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  A line 8 inches long would represent an actual line of 800 feet.
  ::8英寸长的一条线等于800英尺的实际线。

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  Unit scales and proportions can be used to calculate actual distances from maps, drawings, or models.
  ::单位比例和比例可用来计算与地图、图纸或模型的实际距离。

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  Actual distances can be represented on maps, drawings, or models by using unit scales.
  ::地图、图纸或模型可使用单位比例表代表实际距离。

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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 Tanya and her messy room.
  ::早些时候,你被问及 坦尼娅和她乱成一团的房间

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  She made a scale drawing so her grandpa could build shelves. Tanya's drawing shows that the bookcase is  $\begin{array}{r}5.5\end{array}$  inches high. The scale says, 2 inches = 1 foot. Give the actual height of the shelf.
  ::塔尼娅的绘画显示书架高5.5英寸。 书架的高度是2英寸=1英尺。 给架子的实际高度。

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  First, write the unit scale as a ratio.
  ::首先,将单位比例表写成比例。

  $$\begin{array}{r}\frac{inches}{feet}=\frac{2}{1}\end{array}$$

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  Next, keeping the units consistent, write a ratio that compares the scale distance to the actual distance. 
  ::接下来,保持单位的一致性, 写一个比例比 来比较比幅距离与实际距离。

  $$\begin{array}{r}\frac{5.5}{h}\end{array}$$

   Then, set the ratios equal to one another to form a proportion. 

  $$\begin{array}{r}\frac{2}{1}=\frac{5.5}{h}\end{array}$$

   Next, cross multiply

  $$\begin{array}{rl}2h& =5.5\\ h& =2.75feet\end{array}$$

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  The answer is that the actual height of the book shelf is 2.75 feet.
  ::答案是书架的实际高度是2.75英尺

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  Example 2
  ::例2

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  Hector made this scale model of the Statue of Liberty. The scale height of his model, from the base to the torch, is 4.65  . Find the actual height of the Statue of Liberty if the scale is 1 cm = 10 m.
  ::Hector制作了自由女神像的这个比例模型。他的模型,从基底到火炬的高度是4.65。如果比例为1厘米=10米,请查找自由女神像的实际高度。

  

  [Figure 2]

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  First, write the unit scale as a ratio.
  ::首先,将单位比例表写成比例。

  $$\begin{array}{r}\frac{centimeters}{meters}=\frac{1}{10}\end{array}$$

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  Next, keeping the units consistent, write a ratio that compares the scale height to the actual height.
  
  ::其次,保持单位的一致性,写出比例尺高度与实际高度之间的比值。

  $$\begin{array}{r}\frac{4.65}{h}=\frac{centimeters}{meters}\end{array}$$

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  Then, set the ratios equal to one another to form a proportion. 
  ::然后,设定一个比例。

  $$\begin{array}{r}\frac{1}{10}=\frac{4.65}{h}\end{array}$$

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  Next, cross multiply.
  ::下一个,交叉乘数。

  $$\begin{array}{r}h=46.5meters\end{array}$$

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  The answer is that the actual height of the Statue of Liberty from the base to the torch is 46.5  .
  ::答案是自由女神像从基地到火炬的实际高度是46.5。

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  Example 3
  ::例3

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  A beetle that Amelia observed was too small to draw at its actual size. So, she made this scale drawing.
  ::艾米莉亚观察到的甲虫太小 无法按其实际大小画画。所以,她画了这个比例尺图。

  

  [Figure 3]

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  In her drawing, the  length  of the beetle was 4.8 cm. What was the length of the actual beetle?
  ::在她的绘画中,甲虫的长度为4.8厘米。 实际甲虫的长度是多少?

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  First, write the unit scale as a ratio.
  ::首先,将单位比例表写成比例。

  $$\begin{array}{r}\frac{centimeters}{millimeters}=\frac{0.4}{1}\end{array}$$

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  Next, keeping the units consistent, write a ratio that compares the scale size to the actual size. 
  ::其次,保持单位的一致性,写出比例比,将规模与实际规模进行比较。

  $$\begin{array}{r}\frac{4.8}{x}=\frac{centimeters}{millimeters}\end{array}$$

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  Then, set the ratios equal to one another to form a proportion.
  
  ::然后,设定一个比例。

  $$\begin{array}{r}\frac{0.4}{1}=\frac{4.8}{x}\end{array}$$

  Next, cross multiply.

  $$\begin{array}{r}x=12millimeters\end{array}$$

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  The answer is that the beetle is 12 millimeters long.
  ::答案是甲虫长12毫米

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  Example 4
  ::例4

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  A map has a scale of 1" = 10 miles. How far away is a city that measures 12 inches on the map?
  ::地图的大小为 1 = 10 英里。 距离这个城市有多远, 以地图上 12 英寸计?

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  First, write the unit scale as a ratio.
  ::首先,将单位比例表写成比例。

  $$\begin{array}{r}\frac{inch}{miles}=\frac{1}{10}\end{array}$$

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  Next, keeping the units consistent, write a ratio that compares the scale distance to the actual distance. 
  ::接下来,保持单位的一致性, 写一个比例比 来比较比幅距离与实际距离。

  $$\begin{array}{r}\frac{12}{d}=\frac{in}{mi}\end{array}$$

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  Then, set the ratios equal to one another to form a proportion. 
  ::然后,设定一个比例。

  $$\begin{array}{r}\frac{1}{10}=\frac{12}{d}\end{array}$$

   Next, cross multiply.

  $$\begin{array}{r}d=120miles\end{array}$$

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  The answer is that the city is 120 miles away.
  ::答案是这座城市在120英里外

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  Example 5
  ::例5

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  The map below shows the distances between three towns. On the map, the distance between Smithville and Frankton is   $\begin{array}{r}2\frac{1}{4}\end{array}$   inches. Find the actual straight-line distance between Smithville and Frankton.
  ::下面的地图显示了三个城镇之间的距离。 在地图上, Smithville 和 Frankton 之间的距离是 24 英寸。 找到 Smithville 和 Frankton 之间的实际直线距离 。

  

  [Figure 4]

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  First, write the unit scale as a ratio.
  ::首先,将单位比例表写成比例。

  $$\begin{array}{r}\frac{inches}{miles}=\frac{0.25}{2}\end{array}$$

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  Next, keeping the units consistent, write a ratio that compares the scale distance to the actual distance. 
  ::接下来,保持单位的一致性, 写一个比例比 来比较比幅距离与实际距离。

  $$\begin{array}{r}\frac{2.25}{d}\end{array}$$

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  Then, set the ratios equal to one another to form a proportion. 
  ::然后,设定一个比例。

  $$\begin{array}{r}\frac{0.25}{2}=\frac{2.25}{d}\end{array}$$

   Next, cross multiply.

  $$\begin{array}{rl}0.25d& =4.50\\ d& =18miles\end{array}$$

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  The answer is that the actual distance from Smithville and Frankton is 18 miles.
  ::答案是 距离史密斯维尔和弗兰克顿 的实际距离是18英里

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  Review
  ::回顾

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  Use the given scale to determine the actual distance.
  ::使用给定的尺度确定实际距离 。

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  Given: Scale 1” = 100 miles
  ::比例尺1”=100英里

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  1. How many miles is 2” on the map?
     ::地图上多少英里是2英里?
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  2. How many miles is  $\begin{array}{r}2\frac{1}{2}inch\end{array}$  on the map?
     ::地图上多少英里是 212 i n ch?
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  3. How many miles is  $\begin{array}{r}\frac{1}{4}inch\end{array}$  on the map?
     ::地图上14 i n ch有几英里?
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  4. How many miles is 10 inches on the map?
     ::地图上有多少英里是10英寸?
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  5. How many miles is 11 inches on the map?
     ::地图上11英寸有几英里?
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  6. How many miles is 12.5 inches on the map?
     ::地图上有12.5英吋是多少英里?
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  7. How many miles is  $\begin{array}{r}\frac{1}{2}\end{array}$  inch on the map?
     ::地图上12英寸有几英里?
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  8. How many miles is  $\begin{array}{r}5\frac{1}{4}\end{array}$  inch on the map?
     ::地图上514英寸有几英里?

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  Given: 1 cm = 20 mi
  ::百分比:1厘米=20米

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  9. How many miles is 2 cm on the map?
     ::地图上2厘米有几英里?
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  10. How many miles is 4 cm on the map?
      ::地图上4厘米有几英里?
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  11. How many miles is 8.5 cm on the map?
      ::地图上8.5厘米有几英里?
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  12. How many miles is 19 cm on the map?
      ::地图上19厘米有几英里?
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  13. How many miles is 13 cm on the map?
      ::地图上13厘米有几英里?
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  14. How many miles is  $\begin{array}{r}\frac{1}{2}\end{array}$  cm on the map?
      ::地图上12厘米有几英里?
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  15. How many miles is  $\begin{array}{r}1\frac{1}{2}\end{array}$  cm on the map?
      ::地图上12厘米有几英里?

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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