Course: 4.16 在解决问题时使用计量单位和习惯计量单位

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解决问题时使用计量和习惯计量单位
Omar’s dog, Harry, is a Golden Retriever and weighs 30 pounds. How can Omar figure out Harry’s weight in kilograms?
::奥马尔的狗哈里(Omar’s dog, Harry)是只金色的猎犬,重30磅。奥马尔如何能以公斤计算出哈利的重量?

In this concept, you will learn to use metric and customary units of measurement in problem solving.
::在这个概念中,你们将学会在解决问题时使用计量单位和习惯计量单位。

Measurement Conversions
::计量转换

Sometimes it is necessary to convert between customary and metric units of measurements. These measurement conversions will be estimates, because you cannot make an exact measurement when converting between systems of measurement.
::有时有必要在习惯计量单位和计量单位之间转换。这些计量单位的转换将是估计数,因为在测量系统之间转换时无法精确计量。

Measurement Conversions
::计量转换

Let’s look at an example.
::让我们举个例子。

Randy ran a 20 kilometer race. How many miles did Randy run ?
::兰迪跑了20公里兰迪跑多少英里?

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

$\begin{aligned} \frac{1 m i}{1.6 k m} = \frac{x m i}{20 k m} \end{aligned}$
$\begin{align*}\frac{1 \ mi}{1.6 \ km} = \frac{x \ mi}{20 \ km} \end{align*}$
::1米1.6公里=米20公里

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{1}{1.6} & = & \frac{x}{20} \\ 1.6 x & = & 1 \times 20 \\ 1.6 x & = & 20 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} \frac{1}{1.6}&=& \frac{x}{20} \\ 1.6x&=&1 \times 20 \\ 1.6x&=&20 \end{array}\end{align*}$
::11.6=x201.6x=1x201.6x=20

Then, divide both sides by 1.6 to solve for $\begin{align*}x\end{align*}$ .
::然后将两边除以1.6 解决 x 。

$\begin{aligned} \begin{array}{rcl} 1.6 x & = & 20 \\ \frac{1.6 x}{1.6} & = & \frac{20}{1.6} \\ x & = & 12.5 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} 1.6x&=&20 \\ \frac{1.6x}{1.6}&=& \frac{20}{1.6} \\ x&=&12.5 \end{array} \end{align*}$ The answer is 12.5.
::1.6x=201.6x1.6=201.6x=12.5 答案是12.5。

Randy ran 12.5 miles.
::兰迪跑了12.5英里

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Omar and his dog Harry.
::早些时候,你被问及Omar和他的狗Harry的问题。

Omar wants to know how many kilograms Harry weighs knowing that his weight in pounds is 30.
::Omar想知道Harry身重多少公斤知道他体重30磅

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

$\begin{aligned} \begin{array}{rcl} \frac{1 l b}{0.454 k g} & = & \frac{30 l b}{x k g} \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1 \ lb}{0.454 \ kg}&=& \frac{30 \ lb}{x \ kg} \end{array}\end{align*}$
::1 lb0.454公斤=30 lbx公斤

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

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.454} & = & \frac{30}{x} \\ 1 x & = & 30 \times 0.454 \\ x & = & 13.62 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{0.454}&=& \frac{30}{x} \\ 1x&=&30 \times 0.454 \\ x&=&13.62 \end{array}\end{align*}$
::10.454=30x1x=30x0.454x=13.62

The answer is 13.62.
::答案是13.62。

Harry weighs approximately 13.6 kg.
::哈里重约13.6公斤

Example 2
::例2

How many meters are in 67 feet?
::67英尺有几米?

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

$\begin{aligned} \frac{1 f t}{0.30 m} = \frac{65 f t}{x m} \end{aligned}$
$\begin{align*}\frac{1 \ ft}{0.30 \ m}= \frac{65 \ ft}{x \ m} \end{align*}$
::1平0.30米=65平方厘米

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

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.3} & = & \frac{65}{x} \\ 1 x & = & 0.3 \times 65 \\ x & = & 19.5 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{0.3}&=& \frac{65}{x} \\ 1x&=& 0.3 \times 65 \\ x&=&19.5 \end{array} \end{align*}$ The answer is 19.5.
::10.3=65x1x=0.3x65x=19.5 答案是19.5。

Therefore 65 feet is approximately 19.5 meters.
::因此,65英尺约为19.5米。

Example 3
::例3

John ran 5 kilometers. How many miles did he run?
::约翰跑5公里,他跑多少英里?

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

$\begin{aligned} \frac{1 m i}{1.6 k m} = \frac{x m i}{5 k m} \end{aligned}$
$\begin{align*}\frac{1 \ mi}{1.6 \ km} = \frac{x \ mi}{5 \ km}\end{align*}$ Next, cross multiply.
::1 mi1.6公里=x mi5公里下一个,交叉乘以。

$\begin{aligned} \begin{array}{rcl} \frac{1}{1.6} & = & \frac{x}{5} \\ 1.6 x & = & 1 \times 5 \\ 1.6 x & = & 5 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{1.6}&=& \frac{x}{5} \\ 1.6x&=& 1 \times 5 \\ 1.6x&=&5 \end{array}\end{align*}$
::11.6=x51.6x=1x51.6x=5

Then, divide both sides by 1.6 to solve for $\begin{align*}x\end{align*}$ .
::然后将两边除以1.6 解决 x 。

$\begin{aligned} \begin{array}{rcl} 1.6 x & = & 5 \\ \frac{1.6 x}{1.6} & = & \frac{5}{1.6} \\ x & = & 3.125 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 1.6x &=& \ \ 5 \\ \frac{1.6x}{1.6} &=& \frac{5}{1.6} \\ x &=& 3.125 \end{array}\end{align*}$
::1.6x=51.6x1.6=51.6x=3.125

The answer is 3.125.
::答案是3.125。

Therefore, 5 kilometers is approximately 3.1 miles.
::因此,5公里大约是3.1英里。

Example 4
::例4

Kary measured out 12 inches on a ruler. About how many centimeters would that be?
::Kary测量了尺尺上12英寸的距离。关于多少厘米的距离?

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

$\begin{aligned} \frac{1 i n}{2.54 c m} = \frac{12 i n}{x c m} \end{aligned}$
$\begin{align*}\frac{1 \ in}{2.54 \ cm} = \frac{12 \ in}{x \ cm} \end{align*}$ Next, cross multiply.
::1 in2.54 cm = 12 inx cmNext, 交叉乘以。

$\begin{aligned} \begin{array}{rcl} \frac{1}{2.54} & = & \frac{12}{x} \\ 1 x & = & 12 \times 2.54 \\ x & = & 30.48 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{2.54} &=& \frac{12}{x} \\ 1x &=& 12 \times 2.54 \\ x &=& 30.48 \end{array}\end{align*}$
::12.54=12x1x=12x2.54x=30.48

The answer is 30.48.
::答案是30.48。

Therefore, 12 inches is approximately 30.5 centimeters.
::因此,12英寸约30.5厘米。

Example 5
::例5

Sandy ran 15 meters. About how many feet is that?
::桑迪跑15米,大概几英尺?

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

$\begin{aligned} \frac{1 f t}{0.30 m} = \frac{x f t}{15 m} \end{aligned}$
$\begin{align*}\frac{ 1 \ ft}{0.30 \ m} = \frac{x \ ft}{15 \ m} \end{align*}$
::1英尺0.30米=x英尺15米

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{1}{0.3} & = & \frac{x}{15} \\ 0.3 x & = & 1 \times 15 \\ 0.3 x & = & 15 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{1}{0.3}&=& \frac{x}{15} \\ 0.3x&=&1 \times 15 \\ 0.3x&=&15 \end{array}\end{align*}$
::10.3=x150.3x=1x150.3x=15

Then, divide both sides by 0.3 to solve for $\begin{align*}x\end{align*}$ .
::然后将两边除以0.3 解决x

$\begin{aligned} \begin{array}{rcl} 0.3 x & = & 15 \\ \frac{0.3 x}{0.3} & = & \frac{15}{0.3} \\ x & = & 50 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 0.3x &=& 15 \\ \frac{0.3x}{0.3} &=& \frac{15}{0.3} \\ x &=& 50 \end{array}\end{align*}$
::0.3x=150.3x0.3=150.3x=50

The answer is 50.
::答案是50

Therefore, 15 meters is approximately 50 feet.
::因此,15米大约为50英尺。

Review
::回顾

Answer each question by using benchmarks.
::使用基准回答每个问题。

About how many centimeters is in one inch?
::关于一英寸内有多少厘米?

About how many centimeters is in three inches?
::三英寸内有多少厘米?

About how many inches is in 5 centimeters?
::5厘米内有多少英寸?

About how many centimeters is in 1 foot?
::一英尺内有多少厘米?

About how many centimeters is in 3 feet?
::三英尺内有多少厘米?

About how many centimeters is in 1 yard?
::关于一码内有多少厘米?

About how many meters are there in one yard?
::一个院子里有多少米?

About how many meters are there in three yards?
::三码内有几米?

About how many yards are there in twenty -four meters?
::24米内有多少码?

About how many feet are there in eighteen meters?
::18米内有多少英尺?

About how many kilometers are there in 1.8 miles?
::在1.8英里内有多少公里?

About how many miles are there in 10 kilometers?
::10公里内有多少英里?

About how many miles are there in 30 kilometers?
::30公里内有多少英里?

About how many miles are there in 15 kilometers?
::15公里内有多少英里?

About how many kilometers are there in 10 miles?
::10英里内有多少公里?

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

解决问题时使用计量和习惯计量单位

Measurement Conversions ::计量转换

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

Measurement Conversions
::计量转换

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