Course: 4.13 现实世界情况中习惯计量单位转换

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现实世界情况中习惯计量单位转换
Evana is making a recipe for fruit punch that uses 3 cups of pineapple juice. If she makes 5 batches of the recipe, how many quarts of pineapple juice will she need?
::埃文娜正在制作一个水果果汁配方,需要3杯菠萝汁。如果她做了5批配方,她需要多少菠萝果汁?

In this concept, you will learn to convert customary units of measurement in real-world situations.
::在这个概念中,你会学会在现实世界中转换习惯的计量单位。

Customary System
::习惯制度

The customary system , also known as the Imperial System, is made up of units such as inches , feet, cups, gallons and pounds . Let’s look at conversions within the customary system of measurement.
::传统体系也称为帝国体系,由英寸、脚、杯、加仑和磅等单位组成。让我们看看习惯测量体系内的转换。

Customary Units of Measurement
::习惯计量单位

Let’s look at an example.
::让我们举个例子。

The distance from John’s house to Mike’s house on a map is 4.5 inches. The scale of the map is $\begin{align*}1.5 \text{ inches}= 2 \text{ miles}\end{align*}$ . What is the actual distance from John’s house to Mike’s house in feet?
::从约翰的家到地图上的迈克的家的距离是4.5英寸,地图的大小是1.5英寸=2英里。从约翰的家到迈克的家的实际距离是多少?

First, set up a proportion.
::首先,设定一个比例。

$\begin{aligned} \frac{1.5 inches}{2 miles} = \frac{4.5 inches}{x miles} \end{aligned}$
$\begin{align*}\frac{1.5 \text{ inches}}{2 \text{ miles}}=\frac{4.5 \text{ inches}}{x \text{ miles}}\end{align*}$
::1.5英寸2英里=4.5英寸x英里

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{1.5}{2} & = & \frac{4.5}{x} \\ 1.5 x & = & 2 \times 4.5 \\ 1.5 x & = & 9 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1.5}{2} &=& \frac{4.5}{x} \\ 1.5x &=& 2 \times 4.5 \\ 1.5x &=& 9 \end{array} \end{align*}$
::1.52=4.5x1.5x=2x4.51.5x=9

Then, divide both sides by 1.5 to solve for $\begin{align*}x\end{align*}$ .
::然后将两边除以1.5 解决x

$\begin{aligned} \begin{array}{rcl} 1.5 x & = & 9 \\ \frac{1.5 x}{1.5} & = & \frac{9}{1.5} \\ x & = & 6 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.5x &=& 9 \\ \frac{1.5x}{1.5}&=&\frac{9}{1.5} \\ x &=& 6 \end{array} \end{align*}$
::1.5x=91.5x1.5=91.5x=91.5x=6

Then, if the actual distance is 6 miles, what is this distance in feet.
::那么,如果实际距离是6英里,那么这足的距离是多少?

$\begin{aligned} \frac{1 mile}{5280 feet} = \frac{6 miles}{x feet} \end{aligned}$
$\begin{align*}\frac{1 \text{ mile}}{5280 \text{ feet}}= \frac{6 \text{ miles}}{x \text{ feet}}\end{align*}$
::1,5280英尺=6英里x英尺

Then, cross multiply to solve for $\begin{align*}x\end{align*}$ .
::然后,交叉倍数解答 x 。

$\begin{aligned} \begin{array}{rcl} \frac{1}{5280} & = & \frac{6}{x} \\ 1 x & = & 6 \times 5280 \\ x & = & 31680 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{5280} &=& \frac{6}{x} \\ 1x &=& 6 \times 5280 \\ x &=& 31680 \end{array}\end{align*}$
::15280=6x1x=6x5280x=31680

The answer is 31680.
::答案是31680

The distance between the two houses is 31,680 feet.
::两座房屋之间的距离为31 680英尺。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Evana and her thirsty conversion.
::早些时候,你得到一个问题关于埃娃和她的口渴转变。

Evana needs to make 5 batches with each batch needing 3 cups of juice. She needs to find the total amount of juice in quarts.
::Evana每批需要5批果汁,每批需要3杯果汁。她需要找到夸脱果汁的总量。

First, find the total number of cups she needs. If there are 3 cups in one batch, and she is making 5 batches, then she will need:
::首先,找到她需要的杯子总数。如果每批中有3个杯子,而且她正在做5个杯子,那么她就需要:

$\begin{aligned} 3 \times 5 = 15 cups \end{aligned}$
$\begin{align*}3 \times 5 = 15 \text{ cups}\end{align*}$
::3x5=15 杯

Next, set up a proportion.
::接下来,设定一个比例。

$\begin{aligned} \frac{4 cups}{1 quart} = \frac{15 cups}{x quarts} \end{aligned}$
$\begin{align*}\frac{4 \text{ cups}}{1 \text{ quart}} = \frac{15 \text{ cups}}{x \text{ quarts}}\end{align*}$
::4 杯1 夸特= 15 杯sx 夸特

Then, cross multiply.
::然后,交叉倍增。

$\begin{aligned} \begin{array}{rcl} \frac{4}{1} & = & \frac{15}{x} \\ 4 x & = & 1 \times 15 \\ 4 x & = & 15 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{4}{1} &=& \frac{15}{x} \\ 4x &=& 1 \times 15 \\ 4x &=& 15 \end{array} \end{align*}$
::41=15x4x=1x154x=15

Then, divide both sides by 4 to solve for $\begin{align*}x\end{align*}$ .
::然后把两边除以4 解决x

$\begin{aligned} \begin{array}{rcl} 4 x & = & 15 \\ \frac{4 x}{4} & = & \frac{15}{4} \\ x & = & 3.75 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 4x &=& 15 \\ \frac{4x}{4} &=& \frac{15}{4} \\ x &=& 3.75 \end{array} \end{align*}$
The answer is 3.75.
::4x=154x4=154x4=154x=3.75 答案是3.75。

Evana needs to make 3.75 quarts of punch.
::埃娃需要做3.75夸脱的拳头

Example 2
::例2

A scale model of a building has a height of 3.5 feet. The scale of the model is $\begin{align*}1 \frac{1}{2} \text{ inch}= 10 \text{ feet}\end{align*}$ . What is the actual height of the building?
::建筑规模模型的高度为3.5英尺。模型的高度为112英寸=10英尺。建筑的实际高度是多少?

First, set up a proportion to find the height in inches.
::首先,设定一个比例以找到高度英寸。

$\begin{aligned} \frac{12 inches}{1 foot} = \frac{x inches}{3.5 feet} \end{aligned}$
$\begin{align*}\frac{12 \text{ inches}} {1 \text{ foot}} = \frac{x \text{ inches}}{3.5 \text{ feet}}\end{align*}$
::12英寸1英尺=x英寸3.5英尺

Next, cross multiply to solve for $\begin{align*}x\end{align*}$ .
::下一个, 交叉乘以x 解析。

$\begin{aligned} \begin{array}{rcl} \frac{12}{1} & = & \frac{x}{3.5} \\ 1 x & = & 12 \times 3.5 \\ x & = & 42 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{12}{1} &=& \frac{x}{3.5} \\ 1x &=& 12 \times 3.5 \\ x &=& 42 \end{array}\end{align*}$
::121=x3.51x=12x3.5x=42

The answer is 42.
::答案是42岁

The scale model is 42 inches high.
::规模模型高42英寸。

Then, set up a proportion to solve for the actual height of the building.
::然后设定一个比例解决大楼实际高度的问题

$\begin{aligned} \frac{1.5 inches}{10 feet} = \frac{42 inches}{x feet} \end{aligned}$
$\begin{align*}\frac{1.5 \text{ inches}}{10 \text{ feet}} = \frac{42 \text{ inches}}{x \text{ feet}}\end{align*}$
::1.5英寸10英尺=42英寸x英尺

Then, cross multiply.
::然后,交叉倍增。

$\begin{aligned} \begin{array}{rcl} \frac{1.5}{10} & = & \frac{42}{x} \\ 1.5 x & = & 10 \times 42 \\ 1.5 x & = & 420 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1.5}{10} &=& \frac{42}{x} \\ 1.5x &=& 10 \times 42 \\ 1.5x &=& 420 \end{array}\end{align*}$
::1.510=42x1.5x=10x421.5x=420

Then, divide both sides by 1.5 in order to solve for $\begin{align*}x\end{align*}$ .
::然后,将两边除以1.5, 以便解决x。

$\begin{aligned} \begin{array}{rcl} 1.5 x & = & 420 \\ \frac{1.5 x}{1.5} & = & \frac{420}{1.5} \\ x & = & 280 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.5x &=& 420 \\ \frac{1.5x}{1.5} &=& \frac{420}{1.5} \\ x &=& 280 \end{array}\end{align*}$
The answer is 280.
::1.5x=4201.5x=4201.5x=4201.5x=280 答案是280。

The building is 280 feet tall.
::这栋楼高280英尺

Example 3
::例3

Karin has a recipe that calls for 3 gallons of cider. How many quarts will she need?
::卡琳有三加仑苹果酒的配方她需要多少夸脱?

First, set up a proportion.
::首先,设定一个比例。

$\begin{aligned} \frac{1 gallon}{4 quarts} = \frac{3 gallons}{x quarts} \end{aligned}$
$\begin{align*}\frac{1\text{ gallon}}{4 \text{ quarts}} = \frac{3 \text{ gallons}}{x \text{ quarts}}\end{align*}$
::1加仑4 夸特=3加仑x 夸特

Next, cross multiply to solve for $\begin{align*}x\end{align*}$ .
::下一个, 交叉乘以x 解析。

$\begin{aligned} \begin{array}{rcl} \frac{1}{4} & = & \frac{3}{x} \\ 1 x & = & 3 \times 4 \\ x & = & 12 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{4} &=& \frac{3}{x} \\ 1x &=& 3 \times 4 \\ x &=& 12 \end{array} \end{align*}$
The answer is 12.
::14=3x1x=3x4x=12 答案是12。

Karin will need 12 quarts of cider.
::卡琳需要12夸脱的苹果酒

Example 4
::例4

Jack threw the ball 12 feet. How many inches did he throw the ball?
::杰克把球扔了12英尺他扔了多少英寸?

First, set up a proportion.
::首先,设定一个比例。

$\begin{aligned} \frac{1 foot}{12 inches} = \frac{12 feet}{x inches} \end{aligned}$
$\begin{align*}\frac{1 \text{ foot}}{12 \text{ inches}} = \frac{12 \text{ feet}}{x\text{ inches}}\end{align*}$
::1英尺12英寸=12英尺x英寸

Next, cross multiply to solve for $\begin{align*}x\end{align*}$ .
::下一个, 交叉乘以x 解析。

$\begin{aligned} \begin{array}{rcl} \frac{1}{12} & = & \frac{12}{x} \\ 1 x & = & 12 \times 12 \\ x & = & 144 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{12} &=&\frac{12}{x} \\ 1x &=& 12 \times 12 \\ x &=& 144 \end{array} \end{align*}$
The answer is 144.
::112=12x1x=12x12x=144 答案是144。

Jack threw the ball 144 inches.
::杰克把球扔了144英寸

Example 5
::例5

Carl drank 3 pints of lemonade. How many ounces did he drink?
::卡尔喝了三品脱柠檬汁他喝了多少盎司?

First, set up a proportion.
::首先,设定一个比例。

$\begin{aligned} \frac{1 pint}{16 ounces} = \frac{3 pints}{x ounces} \end{aligned}$
$\begin{align*}\frac{1 \text{ pint}}{16 \text{ ounces}} = \frac{3 \text{ pints}}{x \text{ ounces}}\end{align*}$
::1 pent16 盎司= 3 pentsx 盎司

Next, cross multiply to solve for $\begin{align*}x\end{align*}$ .
::下一个, 交叉乘以x 解析。

$\begin{aligned} \begin{array}{rcl} \frac{1}{16} & = & \frac{3}{x} \\ 1 x & = & 16 \times 3 \\ x & = & 48 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{16} &=& \frac{3}{x} \\ 1x &=& 16 \times 3 \\ x &=& 48 \end{array} \end{align*}$
The answer is 48.
::116=3x1x=16x3x=48 答案是48

Carl drank 48 ounces of lemonade.
::卡尔喝了48盎司柠檬水

Review
::回顾

Solve each problem.
::解决每一个问题。

Justin ran 3 miles. How many feet did he run?
::贾斯汀跑了3英里他跑了几英尺?

If the flour weighed four pounds, how many ounces did it weigh?
::如果面粉重四磅,它有几盎司重?

How many pounds is equal to 4 tons?
::多少磅等于4吨?

Mary needs 3 cups of juice for a recipe. How many ounces does she need?
::玛丽需要三杯果汁配方她需要多少盎司?

Jess bought 3 quarts of pineapple juice. How many pints did she purchase?
::Jess买了3夸脱菠萝汁她买了多少品脱?

If Karen bought 16 quarts of ice cream, how many gallons did she buy?
::如果凯伦买了16夸脱的冰淇淋她买了多少加仑?

The length of the garden is four yards. How many feet is that?
::花园的长度是四码,是几英尺?

If the width of the garden is 4 yards, how many inches is that?
::如果花园的宽度是4码,那是多少英寸?

Will eight cups of water fit in a two quart saucepan?
::八杯水能装在两杯半酸酱里吗?

A recipe calls for 2 pints of milk. If Jorge cuts the recipe in half, how many cups of milk will he need?
::如果Jorge把配方切成两半,他需要多少杯牛奶?

Audrey is making brownies for a bake sale. The recipe calls for 8 ounces of flour for every 24 brownies. If she makes 96 brownies, how many pounds of flour will she need?
::奥黛丽正在做蛋糕蛋糕,每24个蛋糕要8盎司面粉。如果她做了96个巧克力蛋糕,她需要多少磅面粉?

Two buildings are 5 inches apart on a map. The scale on the map is $\begin{align*}\frac{1}{4} \text{ inch}=1 \text{ mile}\end{align*}$ . What is the actual distance between the two buildings?
::两座建筑物在地图上相隔5英寸。地图上的规模是14英寸=1英里。两座建筑物之间的实际距离是多少?

The length of a classroom on a floor plan is 2.5 inches. The scale of the map is $\begin{align*}\frac{1}{2} \text{ inches}= 5 \text{ feet}\end{align*}$ What is the actual length of the classroom in inches?
::平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,平面平面平面平面平面平面平面平面平面平面平面平面平面平面,平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面,平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面平面

A scale model of a mountain is 2.75 feet tall. The scale of the model is $\begin{align*}\frac{1}{4}\text{ inch}=50 \ \text{ feet}\end{align*}$ What is the actual height of the mountain in feet?
::山体模型是2.75英尺高, 山体模型是14英寸=50英尺, 山体实际高度是多少?

A scale drawing of a town includes a park that measures 0.5 inch by 1.5 inches. If the scale of the map is $\begin{align*}0.5 \text{ inches} = 1\text{ mile}\end{align*}$ , what is the area of the park in square feet?
::城市比例图包括一个面积为0.5英寸乘1.5英寸的公园。如果地图的面积是0.5英寸=1英里,那么以平方英尺计的公园面积是多少?

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。

Section outline

General

现实世界情况中习惯计量单位转换

Customary System ::习惯制度

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)

Customary System
::习惯制度

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)