Section: 习惯计量单位的转换 | 3.21习惯计量单位的转换

Section outline

Leslie is trying to decide which yogurt to buy at the grocery store. There are two yogurts she is considering. The first kind of yogurt is in a 2 pound container and costs $6. The second kind of yogurt is in a 6 ounce container and is being sold in packs of 5 for $6. She sees that both options cost $6 so she figures she should choose whichever option will give her more yogurt. How can Leslie figure out which option will give her more yogurt?
::Leslie正试图决定在杂货店买什么酸奶。她正在考虑的是两个酸奶。第一种酸奶放在一个2磅的容器里, 费用为6美元。第二种酸奶放在一个6盎司的容器里, 以5美圆的包装出售6美元。她看到两个选项都花费6美元, 所以她应该选择哪个选项能给她更多酸奶。 Leslie怎么能想出哪个选项能给她更多酸奶呢?

In this concept, you will learn how to convert and compare customary units of measure.
::在这个概念中,你会学会如何转换和比较习惯计量单位。

Converting Customary Units of Measure
::转换习惯计量单位

The customary system of measurement is the system of measurement primarily used in the United States. The tables below show some of the most common U.S. customary units and how they are related.
::习惯计量制度是主要在美国使用的计量制度,下表显示了美国最常见的一些习惯单位及其相互关系。

U.S. Customary Units of Length
inch (in)
foot (ft) = 12 inches
yard (yd) = 3 feet
mile (mi) = 5,280 feet

U.S. Customary Units of Mass
ounce (oz)
pound (lb) = 16 ounces

U.S Customary Units of Capacity
fluid ounce (oz)
cup (c) = 8 ounces
pint (pt) = 2 cups = 16 ounces
quart (qt) = 4 cups = 2 pints = 32 ounces
gallon (gal) = 4 quarts

U.S Customary Units of Capacity Used in Cooking
teaspoon (tsp)
tablespoon (tbsp) = 3 teaspoons
cup (c) = 16 tablespoons

To move between different U.S. customary units of length, mass, and capacity, you will multiply or divide by a conversion factor.
::要在不同的美国习惯单位之间移动长度、质量和容量,您将乘以或除以转换系数。

Any time you are going from a smaller unit of measure to a larger unit of measure you will need to divide by the conversion factor.
::从一个较小的计量单位到一个较大的计量单位的任何时候,你都需要除以转换系数。

Any time you are going from a larger unit of measure to a smaller unit of measure you will need to multiply by the conversion factor.
::任何从较大的计量单位到较小的计量单位的时间,你都需要乘以转换系数。

Here is an example.
::举一个例子。

Convert 374 inches to feet.
::将374英寸转换成英尺

First, notice that inches are smaller than feet. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 12 inches in a foot, so your conversion factor is 12.
::首先,请注意英寸小于脚。你正在从一个较小的计量单位移动到一个更大的计量单位。这意味着你需要分割。一英尺有12英寸,所以你的转换系数是12。

Now, divide. Take the given number of inches and divide by 12.
::将给定的英寸数除以12

\begin{aligned} 374 \div 12 = \frac{374}{12} = \frac{187}{6} = 31 \frac{1}{6} \end{aligned}

The answer is $\begin{aligned} 374 inches = 31 \frac{1}{6} feet \end{aligned}$ .
::答案是374英寸 = 3116英尺

Once you know how to convert between different units of measurements, you can compare measurements. The best way to compare two measurements is to first make sure they are in the same unit. Then, you can more easily see which measurement is larger and which is smaller.
::一旦知道如何在不同测量单位之间转换, 您可以比较测量。比较两种测量的最佳方法是首先确保它们位于同一个单位中。然后, 您可以更容易地看到哪个测量单位更大,哪个测量单位较小。

Let's look at an example.
::让我们举个例子。

Compare $\begin{aligned} 4 \frac{1}{2} \end{aligned}$ pounds and 74 ounces.
::比较42磅74盎司

First, notice that you have two different units of mass. In order to compare these measurements, convert one of them so that both units are the same. Let's convert $\begin{aligned} 4 \frac{1}{2} \end{aligned}$ pounds to ounces.
::首先,请注意,您有两个不同的质量单位。为了比较这些测量, 请将其中之一转换成两个单位相同。让我们将412磅转换成盎司。

Now, when converting pounds to ounces you are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 16 ounces in a pound, so your conversion factor is 16.
::现在, 当将磅转换成盎司时, 您正在从一个较大的计量单位移动到一个较小的计量单位。这意味着您需要乘以。每磅有16盎司, 所以您的换算系数是 16。

Next, multiply. Take the given number of pounds and multiply by 16.
::下一个乘以。以给定的磅数乘以 16 乘以。

\begin{aligned} \begin{array}{rcl} 4 \frac{1}{2} \times 16 = \frac{9}{2} \times \frac{16}{1} = \frac{144}{2} & = & 72 \\ 4 \frac{1}{2} pounds & = & 72 ounces \end{array} \end{aligned}

Now you are looking to compare 72 ounces and 74 ounces. 72 ounces is less than 74 ounces, so $\begin{aligned} 4 \frac{1}{2} \end{aligned}$ pounds is less than 74 ounces.
::现在你想比较72盎司和74盎司 72盎司小于74盎司所以412磅小于74盎司

The answer is $\begin{aligned} 4 \frac{1}{2} pounds < 74 ounces \end{aligned}$ .
::答案是412磅 < 74盎司.

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Leslie, who is trying to buy yogurt.
::早些时候,你得到一个问题关于莱斯利, 谁试图买酸奶。

She has two options. Her first option is a 2 pound container. Her second option is five 6-ounce containers. Both options will cost her $6. She wants to choose the option that will give her more yogurt.
::她有两个选择,第一个选择是2磅集装箱,第二个选择是5盎司6盎司集装箱,两个选择都将花费6美元。她想选择给更多酸奶的选项。

First Leslie should realize that five 6-ounce containers is 30 ounces of yogurt. Leslie needs to compare 2 pounds and 30 ounces. Since Leslie has two different units of mass, in order to compare these measurements she should convert one of them so that both units are the same. She can convert pounds to ounces.
::首先,莱斯利应该意识到五个6盎司的容器是30盎司的酸奶。莱斯利需要比较2磅和30盎司。由于莱斯利有两个不同的质量单位,为了比较这些测量,她应该转换其中的一个单位,以使两个单位都相同。她可以将磅转换成盎司。

Now, when converting pounds to ounces she is moving from a larger unit of measure to a smaller unit of measure. This means she will need to multiply. There are 16 ounces in a pound, so her conversion factor is 16.
::当将磅转换成盎司时,她正从一个较大的计量单位向一个较小的计量单位移动。这意味着她需要乘以。每磅有16盎司,所以她的换算系数是16。

Next, she should multiply. Take the given number of pounds and multiply by 16.
::接下来,她应该乘以乘以。拿给定的磅数乘以16乘以16。

\begin{aligned} \begin{array}{rcl} 2 \times 16 & = & 32 \\ 2 pounds & = & 32 ounces \end{array} \end{aligned}

Now Leslie is looking to compare 32 ounces and 30 ounces. 32 ounces is more than 30 ounces, so 2 pounds is greater than 30 ounces.
::现在Leslie正在比较32盎司和30盎司。 32盎司超过30盎司, 所以2磅超过30盎司。

The answer is Leslie should buy the 2 pound container of yogurt.
::答案是莱斯利应该买2磅的酸奶容器

Example 2
::例2

Henrietta is having her 7 best friends over for a luncheon. She wants to prepare salads in which she uses exactly 7 tablespoons of Romano cheese. If she is preparing 8 salads, how many cups of Romano cheese does Henrietta require?
::Henrietta有7个最好的朋友来参加午餐会。她想准备沙拉,其中她完全使用7个罗马乳酪。如果她准备8个沙拉,Henrietta需要多少杯罗马乳酪?

First, figure out how many tablespoons of Romano cheese Henrietta will need. She is making 8 salads and each salad requires 7 tablespoons of cheese.
::首先,先弄清楚需要多少吉他奶酪的餐桌。她正在做8份沙拉,每份沙拉需要7份奶酪。

\begin{aligned} 8 \times 7 = 56 \end{aligned}

Henrietta will need 56 tablespoons of Romano cheese.
::Henrietta需要56盒罗马奶酪

Now, convert 56 tablespoons to cups. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 16 tablespoons in a cup, so your conversion factor is 16.
::现在, 将 56 个汤匙转换为杯子。您正在从一个较小的计量单位向一个更大的计量单位移动。这意味着您需要分割。杯子里有 16 个汤匙, 所以您的换算系数是 16 个。

Now, divide.
::现在,分裂。

\begin{aligned} 56 \div 16 = 3 \frac{1}{2} \end{aligned}

The answer is Henrietta will need $\begin{aligned} 3 \frac{1}{2} \end{aligned}$ cups of Romano cheese.
::答案是亨丽埃塔需要 312杯罗马奶酪

Example 3
::例3

Convert 82 pints to quarts.
::将82品脱转换成夸脱

First, notice that pints are smaller than quarts. You are moving from a smaller unit of measure to a larger unit of measure. This means you will need to divide. There are 2 pints in a quart, so your conversion factor is 2.
::首先,请注意品脱小于夸脱。您正在从一个较小的量度单位向一个更大的量度单位移动。这意味着您需要分割。夸特有两品脱, 所以转换系数是 2 。

Now, divide. Take the given number of pints and divide by 2.
::现在,分开。拿给定的品脱数除以 2。

\begin{aligned} 82 \div 2 = 41 \end{aligned}

The answer is $\begin{aligned} 82 pints = 41 quarts \end{aligned}$ .
::答案是82品脱=41夸脱。

Example 4
::例4

Compare 80 ounces and 3 quarts.
::比较80盎司和3夸特。

First, notice that you have two different units of capacity. In order to compare these measurements, convert one of them so that both units are the same. Let's convert 3 quarts to ounces.
::首先,请注意您有两种不同的容量单位。为了比较这些测量, 请将其中之一转换成两个单位相同。让我们将3 夸特转换成盎司。

Now, when converting quarts to ounces you are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 32 ounces in a quart, so your conversion factor is 32.
::将 quarts 转换成盎司时, 您正在从较大的度量单位移动到较小的度量单位。这意味着您需要乘以。在夸特中 , 有 32 盎司 , 所以您的换算系数是 32 。

Next, multiply. Take the given number of quarts and multiply by 32.
::下一个,乘以。取给定数量 quarts 乘以 32 。

\begin{aligned} \begin{array}{rcl} 3 \times 32 & = & 96 \\ 3 quarts & = & 96 ounces \end{array} \end{aligned}

Now you are looking to compare 80 ounces and 96 ounces. 80 ounces is less than 96 ounces, so 80 ounces is less than 3 quarts.
::现在你想比较80盎司和96盎司。80盎司小于96盎司,80盎司小于3夸特。

The answer is $\begin{aligned} 80 ounces < 3 quarts \end{aligned}$ .
::答案是80盎司 < 3夸特。

Example 5
::例5

Convert $\begin{aligned} 8 \frac{1}{2} \end{aligned}$ gallons to quarts.
::转换 812加仑到夸特。

First, notice that gallons are larger than quarts. You are moving from a larger unit of measure to a smaller unit of measure. This means you will need to multiply. There are 4 quarts in a gallon, so your conversion factor is 4.
::首先,请注意加仑大于夸特。您正在从一个较大的计量单位移动到一个较小的计量单位。这意味着您需要乘以。加仑里有4夸特, 所以您的换算系数是 4 。

Now, multiply. Take the given number of gallons and multiply by 4.
::现在,乘以。拿给定的加仑数乘以4。

\begin{aligned} 8 \frac{1}{2} \times 4 = \frac{17}{2} \times \frac{4}{1} = \frac{68}{2} = 34 \end{aligned}

The answer is $\begin{aligned} 8 \frac{1}{2} gallons = 34 quarts \end{aligned}$ .
::答案是 812加仑=34夸特

Review
::回顾

Convert the following measurements into yards. Round to the nearest tenth when necessary.
::将以下测量数据转换成码。必要时,将圆形转换到最接近的十分之一。

195 inches
::195英寸

0.2 miles
::0.2英里

88 feet
::88英尺

90 feet
::90英尺

900 feet
::900英尺

Convert the following measurements into pounds.
::将以下测量数据转换成磅。

2,104 ounces
::2 104盎司

96 ounces
::96盎司

3 tons
::3吨3吨

15 tons
::15吨

Convert the following measurements into pints.
::将以下测量值转换成品脱。

102 quarts
::102 夸特

57 ounces
::57盎司

9.5 gallons
::9.5加仑

4 quarts
::4 夸特

18 quarts
::18 夸特

67 gallons
::67加仑

Section outline

Converting Customary Units of Measure ::转换习惯计量单位

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