Course: 4.15 在现实世界形势下转换计量单位

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在现实世界形势下转换计量单位
Jessica works in a science lab. She needs to convert the liquid measure that she is working with from liters to milliliters. She has been given 3.5 liters to convert. If each container that Jessica has holds 100 milliliters, how many containers will she need?
::Jessica在科学实验室工作。她需要将她使用的液体量度从升到毫升。她已经得到了3.5升的转换。如果Jessica拥有100毫升的每个容器, 她需要多少容器?

In this concept, you will learn to convert metric units of measurement in real-world situations.
::在这个概念中,你们将学会在现实世界中转换计量单位。

Converting Metric Units of Measurements
::转换计量单位

The metric system of measurement is the primary measurement system in many countries; it contains units such as , kilometers and liters. Let’s review the metric units of measurement.
::衡量的计量体系是许多国家的主要计量体系;它包含单位,如千米和升。让我们审查衡量的计量单位。

Metric Units of Measurement
::计量计量单位

Now, let’s look at a real-world problem involving converting metric units.
::现在,让我们来看看一个现实世界的问题,涉及到转换计量单位。

A scale model of a building has a height of 1.5 meters. The scale of the model is $\begin{aligned} 1 c m = 0.5 m \end{aligned}$ . What is the actual height of the building?
::建筑物的规模模型的高度为1.5米。模型的高度为1厘米=0.5米。建筑物的实际高度是多少?

First, set up a proportion to change 1.5 m to cm.
::首先,设定一个比例来改变1.5米到厘米。

$\begin{aligned} \frac{100 c m}{1 m} = \frac{x c m}{1.5 m} \end{aligned}$

::100厘米1 m=x cm1.5 m

Next, cross multiply to solve for the number of for the height of the scale model.
::下一步,交叉乘以解答比例模型高度的数。

$\begin{aligned} \begin{array}{rcl} \frac{100}{1} & = & \frac{x}{1.5} \\ 1 x & = & 100 \times 1.5 \\ x & = & 150 \end{array} \end{aligned}$

::1001=x1.51x=100×1.5x=150

Next, set up a proportion to find the height of the actual model.
::下一步,设定一个比例,以找到实际模型的高度。

$\begin{aligned} \frac{1 c m}{0.5 m} = \frac{150 c m}{x m} \end{aligned}$

::1厘米0.5米=150厘米m

Then, cross multiply to solve for $\begin{aligned} x \end{aligned}$ .
::然后,交叉倍数来解答 x。

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.5} & = & \frac{150}{x} \\ 1 x & = & 0.5 \times 150 \\ x & = & 75 \end{array} \end{aligned}$

::10.5=150x1x=0.5x150x=75

The answer is 75.
::答案是75

The actual height of the building is 75 meters.
::大楼的实际高度是75米

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jessica’s scientific measurements.
::早些时候,有人给了你Jessica科学测量的问题。

Jessica is given 3.5 L of liquid and needs to fill containers with 100 mL each. Jessica needs to know how many containers she will need.
::Jessica得到3.5升的液体,需要用每桶100毫升的液体填充集装箱。 Jessica需要知道她需要多少集装箱。

First, set up a proportion to change 3.5 L to mL.
::首先,设定3.5升至毫升的变动比例。

$\begin{aligned} \frac{1000 m L}{1 L} = \frac{x m L}{3.5 L} \end{aligned}$

::1000 mL1 L=x mL3.5 L

Next, cross multiply to solve for the number of milliliters Jessica has.
::接下来,交叉倍数来解答Jessica的毫升数

$\begin{aligned} \begin{array}{rcl} \frac{1000}{1} & = & \frac{x}{3.5} \\ 1 x & = & 1000 \times 3.5 \\ x & = & 3500 \end{array} \end{aligned}$

::001=x3.51x=1000x3.5x=3500

Next, divide by 100 to find the number of containers.
::其次,除以100以找到集装箱数量。

$\begin{aligned} \frac{3500 m L}{100 m L} = 35 \end{aligned}$

::3500毫升100毫升=35

The answer is 35.
::答案是35岁

Jessica will need 35 containers.
::杰西卡需要35个集装箱

Example 2
::例2

Marcy is making beef stew. Her recipe calls for 900 grams of beef. She looks in the refrigerator and sees that she has 1.5 kilograms of beef wrapped in a package. Marcy isn’t sure how much of the beef she should use. Does Marcy have enough beef for her recipe?
::玛西正在煮牛肉。她的配方需要900克牛肉。她看着冰箱,看到她有1.5公斤的牛肉包裹在包装袋里。 Marcy不确定她应该用多少牛肉。 Marcy有足够的牛肉来配方吗?

First, set up a proportion to change 1.5 kg to g.
::首先,设定一个比例,将1.5公斤改为g。

$\begin{aligned} \frac{1000 g}{1 k g} = \frac{x g}{1.5 k g} \end{aligned}$

::1000千克1公斤=x g1.5公斤

Next, cross multiply to solve for the number of grams of beef Marcy has in her refrigerator.
::接下来,交叉倍数来解答她冰箱里的马西牛肉的克数

$\begin{aligned} \begin{array}{rcl} \frac{1000}{1} & = & \frac{x}{1.5} \\ 1 x & = & 1000 \times 1.5 \\ x & = & 1500 \end{array} \end{aligned}$

The answer is 1500 g.
::10001=x1.51x=1000x1.5x=1500 答案是 1500克。

Marcy has 1500 grams of meat, but only needs 900 grams for her recipe. She will have 600 grams of meat left over.
::玛西有1500克肉但食谱只需要900克她还有600克肉

Example 3
::例3

If the scale used for a model is $\begin{aligned} 1 c m = 0.5 m \end{aligned}$ and the scale measurement is 3.2 meters, what is the actual measurement?
::如果模型所用的比例尺是1厘米=0.5米,而尺度测量是3.2米,那么实际测量是什么?

First, set up a proportion to change 3.2 m to cm.
::首先,设定一个比例来改变3.2米到厘米。

$\begin{aligned} \frac{100 c m}{1 m} = \frac{x c m}{3.2 m} \end{aligned}$

::100厘米1 m=x cm3.2 m

Next, cross multiply to solve for the number of centimeters for the height of the scale model.
::下一步,交叉乘以解答比例模型高度的厘米数。

$\begin{aligned} \begin{array}{rcl} \frac{100}{1} & = & \frac{x}{3.2} \\ 1 x & = & 100 \times 3.2 \\ x & = & 320 \end{array} \end{aligned}$

::1001=x3.21x=100x3.2x=320

Next, set up a proportion to find the height of the actual model.
::下一步,设定一个比例,以找到实际模型的高度。

$\begin{aligned} \frac{1 c m}{0.5 m} = \frac{320 c m}{x m} \end{aligned}$

::1厘米0.5米=320厘米m

Then, cross multiply to solve for $\begin{aligned} x \end{aligned}$ .
::然后,交叉倍数来解答 x。

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.5} & = & \frac{320}{x} \\ 1 x & = & 0.5 \times 320 \\ x & = & 160 \end{array} \end{aligned}$

::10.5=320x1x=0.5x320x=160

The answer is 160.
::答案是160个。

The actual height of the building is 160 meters.
::大楼的实际高度为160米。

Example 4
::例4

If the scale used for a model is $\begin{aligned} 1 c m = 0.5 m \end{aligned}$ and the scale measurement is 0.75 meters, what is the actual measurement?
::如果模型所用的比例尺是1厘米=0.5米,而比例尺测量是0.75米,那么实际测量是什么?

First, set up a proportion to change 0.75 m to cm.
::首先,设定一个比例来改变0.75米到厘米。

$\begin{aligned} \frac{100 c m}{1 m} = \frac{x c m}{0.75 m} \end{aligned}$

::100厘米1 m=x cm0.75 m

Next, cross multiply to solve for the number of centimeters for the height of the scale model.
::下一步,交叉乘以解答比例模型高度的厘米数。

$\begin{aligned} \begin{array}{rcl} \frac{100}{1} & = & \frac{x}{0.75} \\ 1 x & = & 100 \times 0.75 \\ x & = & 75 \end{array} \end{aligned}$

::1001=x0.751x=100x0.75x=75

Next, set up a proportion to find the height of the actual model.
::下一步,设定一个比例,以找到实际模型的高度。

$\begin{aligned} \frac{1 c m}{0.5 m} = \frac{75 c m}{x m} \end{aligned}$

::1厘米0.5米=75厘米m

Then, cross multiply to solve for $\begin{aligned} x \end{aligned}$ .
::然后,交叉倍数来解答 x。

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.5} & = & \frac{75}{x} \\ 1 x & = & 0.5 \times 75 \\ x & = & 37.5 \end{array} \end{aligned}$

::10.5=75x1x=0.5x75x=37.5

The answer is 37.5.
::答案是37.5

The actual height of the building is 37.5 meters.
::大楼的实际高度为37.5米。

Example 5
::例5

If the scale used for a model is $\begin{aligned} 1 c m = 0.5 m \end{aligned}$ and the scale measurement is 0.25 m, what is the actual measurement?
::如果模型所用的比例尺是1厘米=0.5米,而比例尺测量是0.25米,那么实际测量是什么?

First, set up a proportion to change 0.25 m to cm.
::首先,设定一个比例来改变0.25米到厘米。

$\begin{aligned} \frac{100 c m}{1 m} = \frac{x c m}{0.25 m} \end{aligned}$

::100厘米1 m=x cm0.25 m

Next, cross multiply to solve for the number of centimeters for the height of the scale model.
::下一步,交叉乘以解答比例模型高度的厘米数。

$\begin{aligned} \begin{array}{rcl} \frac{100}{1} & = & \frac{x}{0.25} \\ 1 x & = & 100 \times 0.25 \\ x & = & 25 \end{array} \end{aligned}$

::1001=x0.251x=100xxxxxxxxxxxxx0x0.25x=25

Next, set up a proportion to find the height of the actual model.
::下一步,设定一个比例,以找到实际模型的高度。

$\begin{aligned} \frac{1 c m}{0.5 m} = \frac{25 c m}{x m} \end{aligned}$

::1厘米0.5米=25厘米m

Then, cross multiply to solve for $\begin{aligned} x \end{aligned}$ .
::然后,交叉倍数来解答 x。

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.5} & = & \frac{25}{x} \\ 1 x & = & 0.5 \times 25 \\ x & = & 12.5 \end{array} \end{aligned}$

::10.5=25x1x=0.5x25x=12.5

The answer is 12.5.
::答案是12.5

The actual height of the building is 12.5 meters.
::大楼的实际高度为12.5米。

Review
::回顾

Figure out the measurements if the scale is $\begin{aligned} 1 c m = 0.5 m \end{aligned}$ .
::如果比例尺为1厘米=0.5米,请找出测量方法。

1. 3.5 m
::1. 3.5米

2. 10 m
::2. 10米

3. 6.5 m
::3. 6.5米

4. 0.5 m
::4. 0.5米

5. 2.5 m
::5. 2.5米

6. 2.2 m
::6. 2.2米

7. 4.5 m
::7.4.5米

8. 4 m
::8. 4米

9. 3 m
::9. 3米

10. 11 m
::10. 11米

Solve each problem.
::解决每一个问题。

11. A recipe calls for 400 grams of flour. If Leena makes one quarter of the recipe, how many kilograms of flour will she need?
::11. 食谱需要400克面粉,如果Leena做了四分之一的食谱,她需要多少公斤面粉?

12. Two buildings are 9 centimeters apart on a map. The scale of the map is $\begin{aligned} 0.5 centimeter = 2 kilometers \end{aligned}$ .. What is the actual distance between the two buildings in meters?
::12. 在地图上,两座建筑物相距9厘米,比例尺为0.5厘米=2公里,这两座建筑物之间的实际距离是多少?

13. A scale model of a tower is 1.25 meters tall. The scale of the model is $\begin{aligned} 0.5 c m = 5 m e t e r s \end{aligned}$ . What is the actual height of the tower in meters?
::13. 一座塔的标尺模型是1.25米高,模型的标尺是0.5厘米=5米。

14. A scale drawing of a conference center includes a meeting room that measures 1.5 centimeters by 2.5 centimeters. If the scale of the drawing is $\begin{aligned} 1 centimeter = 2 meters \end{aligned}$ , what is the area of the meeting room in square centimeters?
::14. 会议中心的规模图包括一个会议室,用2.5厘米测量1.5厘米乘2.5厘米,如果面积为1厘米=2米,会议室面积是多少?

15. Samir ran a race that was 10 kilometers long. About how many meters did Samir run?
::15. Samir跑了一个10公里长的赛跑,关于Samir跑多少米?

Review (Answers)
::回顾(答复)

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。

Resources
::资源

Section outline

General

在现实世界形势下转换计量单位

Converting Metric Units of Measurements ::转换计量单位

Metric Units of Measurement ::计量计量单位

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Converting Metric Units of Measurements
::转换计量单位

Metric Units of Measurement
::计量计量单位

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源