2.7给定尺度测量的距离或尺寸

Section outline

• Select section General

  Collapse Expand

  General

  Collapse all Expand all

  • Select activity 新闻通告

    

    新闻通告 Forum
• Select section 给定尺度测量的距离或尺寸

  Collapse Expand

  给定尺度测量的距离或尺寸

  

  播放段落

  Dan is designing a map of a city. He has created a scale to represent the distance between objects on his map. The scale is 1" : 50'. Every inch of space on the map represents 50 feet of actual land. 
  ::丹正在设计一个城市的地图。 他创造了一个比例尺, 以代表其地图上天体之间的距离。 比例尺是 1 : 50 。 地图上每寸空间代表实际土地的50 英尺 。

  播放段落

  There are two skyscrapers that are 9  inches  apart on Dan's map. How far apart are the actual two buildings?
  ::丹的地图上有两座摩天大楼 相距9英寸 实际两座大楼相距有多远?

  播放段落

  In this concept, you will learn about using a scale to determine actual measurements. 
  ::在这个概念中,你将了解如何使用一个尺度来确定实际测量。

  播放段落

  Scale Measurements
  ::尺度计量

  播放段落

  Maps represent real places. Every part of the place has been reduced to fit on a single piece of paper. A map is an accurate representation because it uses a scale.
  ::地图代表真实的地方。 每一个地方都被缩小为适合一张纸。 地图是一个准确的表达方式,因为它使用一个比例尺。

  播放段落

  The  scale  is a ratio that relates the small size representation of a place to the actual size of a place.
  ::比额表是一个比率,将一个地方的面积小与一个地方的实际规模联系起来。

  播放段落

  Maps aren’t the only things that use scales. Architects use a scale when designing a house. A blueprint shows a small size of what the house will look like compared to the actual house. Any time an accurate model is built, it uses a scale. 
  ::地图并不是使用比例尺的唯一东西。 建筑师在设计房屋时使用比例尺。 蓝图显示,与实际房屋相比,房屋的外观很小。 准确模型一旦建立,它就使用比例尺。

  播放段落

  Units of measurement are used to create a ratio that is the scale. The  ratio  compares two things. It compares the small size of the object or place to the actual size of the object or place.
  ::测量单位用于创建比例比。该比例比比较了两个东西。它比较对象或地点的大小与对象或地点的实际大小。

  播放段落

  A scale of 1 inch to 1  foot  means that 1 inch on paper represents 1 foot in real space. This is how the ratio is written:
  ::1英寸到1英尺的尺度表示纸上1英寸代表实际空间1英尺。 比例是这样写的:

  1” : 1' 

  播放段落

  If the distance between two points on a map is 2 inches, the scale tells us that the actual distance in is 2 feet.
  ::如果地图上两点之间的距离是2英寸,则比例表告诉我们实际距离是2英尺。

  播放段落

  Scales can be created in any size. One inch can represent 1,000 miles if the map shows a very large area, such as a continent. One  centimeter  might represent 1  meter  if the map shows a small space, such as a room.
  ::比例尺可以以任何大小创建。 如果地图显示一个非常大的区域, 如大陆, 一英寸可以代表千英里。 如果地图显示一个小的空间, 如一个房间, 一厘米可能代表一公尺 。

  播放段落

  Scales are used in math to find the actual size of an object when only given the scale ratio.
  ::数学中使用缩放来查找对象的实际大小, 仅根据缩放比例 。

  播放段落

  For example, this scale below shows the ratio of  $\begin{array}{r}\frac{3}{4}":20\end{array}$ mi.
  ::例如,下表所示比率为3 4 " :20米。

  

  [Figure 2]

  播放段落

  In other words, on the map, every   $\begin{array}{r}{\frac{3}{4}}^{″}\end{array}$  is equal to 20 miles.
  ::换句话说,在地图上,每三四千公里等于20英里。

  播放段落

  The distance between two cities can be determined then by using this scale.  Consider a map that shows two cities that are   $\begin{array}{r}{\frac{3}{4}}^{″}\end{array}$  apart. This would mean the actual distance between the cities is 20 miles per the scale.
  ::两个城市之间的距离可以通过使用这个比例来决定。 考虑一个显示两个城市相距为 3 4 + 的地图。 这意味着两个城市之间的实际距离是每个比例为 20 英里 。

  播放段落

  Sometimes, the scale needs to be used to solve for a measurement that is not given directly in the scale. If the scale is 1”: 500 miles, how far is a city that measures  $\begin{array}{r}5{\frac{1}{2}}^{″}\end{array}$  on a map?
  ::有时,需要用比例尺来解决一个不是在比例尺上直接给出的测量标准。 如果比例尺是1, 则500英里, 地图上测量512°C的城市有多远?

  播放段落

  We know that every inch is 500 miles. We have  $\begin{array}{r}5{\frac{1}{2}}^{″}\end{array}$ . Let’s start with the 5.
  ::我们知道每英寸500英里。我们有512英里。让我们从5英里开始。

  播放段落

  $\begin{array}{r}5\times 500=2500+\frac{1}{2}\times 500=2750\end{array}$  mi.
  ::5×500 = 2500 + 1 2× 500 = 2750米。

  播放段落

  Another way to do this is to write two ratios and cross multiply to solve for the missing information. 
  ::另一种方法就是写出两个比率和交叉倍数,以解答缺失的信息。

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Dan and his map. He has a scale drawn on his map of 1" : 50 feet. Two buildings are represented on the map that are 9 inches apart. He needs to figure out how far apart those buildings are in actual scale. 
  ::早些时候,你们曾被告知丹和他的地图有问题。他在地图上绘制了1号尺的尺码:50英尺。地图上有两座相隔9英寸的建筑物。他需要弄清楚这些建筑物的实际距离有多远。

  播放段落

  First, Dan sets up the ratio proportion.
  ::首先,丹确定了比例比例。

  $$\begin{array}{r}\frac{1in}{50ft}=\frac{9in}{x}\end{array}$$

  播放段落

  Next, Dan cross multiplies the equation.
  ::接下来,丹交叉乘以方程

  $$\begin{array}{rl}9in\cdot 50& =1in\cdot x\\ 450& =1x\end{array}$$

  播放段落

  Then, solve for the missing information. 
  ::那么,解决丢失的信息。

  $$\begin{array}{r}450=x\end{array}$$

  播放段落

  The answer is 450 feet. 
  ::答案是450英尺

  播放段落

  Dan has figured out the two skyscrapers are 450 feet apart.
  ::丹发现两座摩天大楼 相距450英尺

  播放段落

  Example 2
  ::例2

  播放段落

  If the scale is 2” : 1 ft, what is the actual measurement if a drawing shows the object as 6” long?
  ::如果比例尺是2”:1英尺,如果绘图显示对象为6”长,则实际计量是什么?

  播放段落

  First, write a ratio that compares the scale.
  ::首先,写一个比比比比比例。

  $$\begin{array}{r}\frac{1ft}{2^{″}}=\frac{xft}{6^{″}}\end{array}$$

  播放段落

  The actual object size is unknown, so a variable is used to represent the unknown quantity. 
  ::实际对象大小未知, 因此变量用于表示未知数量 。

  播放段落

  Next, cross multiply the equation. In this problem, 1 ft. gets multiplied by 6 and x ft. gets multiplied by 2.
  ::接下来,交叉乘以方程。在此问题中, 1 英尺乘以 6, x 英尺乘以 2。

  $$\begin{array}{rl}1\cdot 6& =6\\ 2\cdot x& =2x\\ 2x& =6\end{array}$$

  播放段落

  Then, solve for the variable by isolating it.
  ::然后,通过隔离解决变量。

  $$\begin{array}{rl}x& =6÷2\\ x& =3\end{array}$$

  播放段落

  The answer is that the object is actually 3 feet long.
  ::答案是,该物体实际上有3英尺长。

  播放段落

  Example 3
  ::例3

  播放段落

  If the scale is 1” : 3 miles, how many miles does 5 inches represent?
  ::如果比例尺是1”:3英里,5英寸代表多少英里?

  播放段落

  First, write the ratio proportion.
  ::首先,写出比例比例比例。

  $$\begin{array}{r}\frac{1"}{3mi}=\frac{5in}{xmi.}\end{array}$$

  播放段落

  Next, cross multiply the equation.
  ::下一个,交叉乘以方程。

  $$\begin{array}{r}3\cdot 5=x\cdot 1\end{array}$$

  播放段落

   Then, solve for the missing information.
  ::那么,解决丢失的信息。

  $$\begin{array}{r}15=x\end{array}$$

  播放段落

  The answer is 15 miles.
  ::答案是15英里

  播放段落

  Example 4
  ::例4

  播放段落

  If the scale is 2” : 500  , how many meters does 4 inches represent?
  ::如果比例尺是2”:500, 4英寸代表多少米?

  播放段落

  First, write the ratio proportion.
  ::首先,写出比例比例比例。

  $$\begin{array}{r}\frac{2in}{500m}=\frac{4in}{x}\end{array}$$

  播放段落

  Next, cross multiply the equation.
  ::下一个,交叉乘以方程。

  $$\begin{array}{rl}4in\cdot 500m& =2in\cdot x\\ 2000& =2x\end{array}$$

  播放段落

  Then, solve for the missing information (x).
  ::然后解决缺失的信息 (x) 。

  $$\begin{array}{rl}2000÷2& =x\\ 1000& =x\end{array}$$

  播放段落

  The answer is 1000 meters.
  ::答案是1000米

  播放段落

  Example 5
  ::例5

  播放段落

  If the scale is 5 in : 1000 feet, how many feet is 15 inches?
  ::如果比例尺是 5 英寸: 1000英尺, 多少英尺是 15 英寸?

  播放段落

  First, write the ratio proportion.
  ::首先,写出比例比例比例。

  $$\begin{array}{r}\frac{5in}{1000ft}=\frac{15in}{x}\end{array}$$

  播放段落

  Next, cross multiply the equation.
  ::下一个,交叉乘以方程。

  $$\begin{array}{rl}15in\cdot 1000& =5in\cdot x\\ 15000& =5x\end{array}$$

  播放段落

  Then, solve for the missing information.
  ::那么,解决丢失的信息。

  $$\begin{array}{rl}15000÷5& =x\\ 3000& =x\end{array}$$

  播放段落

  The answer is 3,000 feet.
  ::答案是3000英尺

  播放段落

  Review
  ::回顾

  播放段落

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

  播放段落

  Given: 1” = 100 mi
  ::参照:1”=100米

  播放段落
  1. How many miles is 2” on the map?
     ::地图上多少英里是2英里?
  播放段落
  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?
  播放段落
  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?
  播放段落
  4. How many miles is 8 inches on the map?
     ::地图上多少英里是8英寸?
  播放段落
  5. How many miles is 16 inches on the map?
     ::地图上16英寸有几英里?
  播放段落
  6. How many miles is 12 inches on the map?
     ::地图上12英寸有几英里?
  播放段落
  7. How many miles is  $\begin{array}{r}\frac{1}{2}inch\end{array}$  on the map?
     ::地图上12英哩是多少英哩?
  播放段落
  8. How many miles is  $\begin{array}{r}5\frac{1}{4}inches\end{array}$  on the map?
     ::地图上514英哩是多少?

  播放段落

  Given: 1 cm = 20 mi
  ::百分比:1厘米=20米

  播放段落
  9. How many miles is 2 cm on the map?
     ::地图上2厘米有几英里?
  播放段落
  10. How many miles is 4 cm on the map?
      ::地图上4厘米有几英里?
  播放段落
  11. How many miles is 8 cm on the map?
      ::地图上8厘米有几英里?
  播放段落
  12. How many miles is 18 cm on the map?
      ::地图上18厘米有几英里?
  播放段落
  13. How many miles is 11 cm on the map?
      ::地图上11厘米有几英里?
  播放段落
  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?
  播放段落
  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?
  播放段落
  16. How many miles is  $\begin{array}{r}4\frac{1}{4}\end{array}$  cm on the map?
      ::地图上414厘米有几英里?

  播放段落

  Review (Answers) 
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源