Course: 5.5单位费率 | The Way To Learn

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单位费率
Hannah is a runner on her school's track team. In order to perform well in races, she trains nearly every day. The running coach requires that all athletes run at least 35 miles per week. So far this week, Hannah ran 3 miles on Sunday, 6 miles on Monday, and 5 miles on Tuesday. At her current rate , will Hannah meet the requirement?
::汉娜是她学校赛马队的选手。为了在赛跑中表现良好,她几乎每天都在训练。跑步教练要求所有运动员每周至少跑35英里。本周到目前为止,汉娜在星期天跑3英里,星期一跑6英里,星期二跑5英里。以她目前的速度,汉娜能达到要求吗?

In this concept, you will learn how to work with unit rates.
::在这个概念中,你们将学会如何使用单位费率。

Working with Unit Rates
::采用单位费率

A unit rate is a comparison of two measurements, one of which has a value of 1.
::A单位费率是两项测量的比较,其中一项测量值为1。

For example:
::例如:

The cost for 1 pound of apples is $1.50
::1磅苹果的费用为1.50美元

This can be written as $\begin{aligned} \frac{1}{1.50} \frac{p o u n d}{d o l l a r s} \end{aligned}$
::这可以写成 1 1.50 p o u n d d d o l r s

Based on this unit rate, the cost for any number of pounds of apples can be calculated. Given the number of units, the unit rate can be used to calculate a total rate. The unit rate can be calculated by dividing one term of a fraction by the other, and reducing the desired term to 1 .
::根据该单位费率,可以计算任何数量苹果磅的成本。根据单位数量,单位费率可用于计算总费率。单位费率可以通过将一个学期的分数除以另一个学期,并将理想学期减为1来计算。

Here is an example.
::举一个例子。

A cyclist pedaled 36 miles in 2 hours. What is her unit rate? In other words, how many miles did she pedal in 1 hour?
::2小时36英里的骑自行车的车程,她的单车速率是多少?换句话说,她1小时行驶了多少英里?

First, write the rate as a fraction. The term that needs to be reduced to 1 is hours in order to get a distance per 1 hour. In this case, the term to be reduced to 1 is the denominator .
::首先,将速率写成一个分数。需要减为 1 的用词是每 1 小时的距离。在这种情况下, 减为 1 的用词是分母。

$\begin{aligned} \frac{36}{2} \frac{m i l e s}{h o u r s} \end{aligned}$
::36 2米 i l e s h o u r s

Next, divide both the numerator and denominator by 2 to get a denominator of 1.
::下一步,将分子和分母除以 2 以获得 1 的分母。

A unit rate must have 1 in one of its terms. It can be either the numerator or the denominator.
::单位率必须有一个条件。可以是分子,也可以是分母。

$\begin{aligned} \frac{36 \div 2}{2 \div 2} = \frac{18}{1} \frac{m i l e s}{h o u r} \end{aligned}$

::= 18 1米 i i e s h o u r

The answer is 18 miles/hour.
::答案是每小时18英里

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Hannah, who is on the school's track team.
::早些时候,你得到一个问题关于汉娜, 谁在学校的轨道队。

The coach requires all runners to complete 35 miles per week. So far Hannah has run 4 miles on Sunday, 6 miles on Monday, and 5 miles on Tuesday. At her current rate, will Hannah meet the requirement?
::教练要求所有赛跑者每周完成35英里。到目前为止,Hannah在星期天跑4英里,星期一跑6英里,星期二跑5英里。以她目前的速度,Hannah能达到要求吗?

First, recognize that the unit rate (miles per day) needs to be found first in order to determine whether or not Hannah will meet her goal.
::首先,认识到需要首先找到单位费率(每天英里),以确定汉娜是否达到目标。

Next, add the number of miles together that Hannah has already run.
::接下来,加上汉娜已经跑过的英里数。

4 + 6 + 5 = 15

Hannah has run a total of 15 miles in 3 days this week.
::Hannah本周三天内总共跑15英里

Then, write a fraction that compares the number of miles Hannah has already run to the number of days she ran to get her unit rate per day.
::然后写一个小数来比较汉娜的英里数已经跑到她每天领取单位费率的天数

$\begin{aligned} \frac{15}{3} \frac{m i l e s}{d a y s} \end{aligned}$
::15 3米 i l e s y s

Next, reduce to lowest terms.
::其次,降低到最低值。

$\begin{aligned} \frac{15 \div 3}{3 \div 3} = \frac{5}{1} \end{aligned}$

Hannah has run 5 miles per day.
::汉娜每天跑5英里

Then, think. If Hannah runs 5 miles per day, how many miles will she run in a week?
::想想看,如果Hannah每天跑5英里她一周能跑多少英里?

$\begin{aligned} \frac{5}{1} \frac{m i l e s}{d a y} \times \frac{7}{1} \frac{d a y s}{w e e k} = \frac{35}{1} \frac{m i l e s}{w e e k} \end{aligned}$
::5 1米 i l e s d a y × 7 1 d y y e e e k = 35米 1 i i e e k

The answer is that at her current rate of 5 miles per day, Hannah will run 35 miles per week and will meet the coach's requirements.
::答案是,按照她目前每天5英里的速度, 汉娜每周跑35英里, 并满足教练的要求。

Example 2
::例2

Thomas has the record among all his friends for being the fastest texter. Yesterday, the boys decided to find out just how fast. Irwin gave him a message with 240 characters in it, and set a timer. Thomas completed the text in exactly 3 minutes. What is his texting rate per minute?
::Thomas是所有朋友中最快的发短信人。昨天,男孩们决定找出速度有多快。Irwin给了他一条有240个字符的信息,并设定了一个定时器。Thomas在3分钟内完成文本。他每分钟发短信的速度是多少?

First, write a fraction.
::首先,写一个分数。

$\begin{aligned} \frac{240}{3} \frac{c h a r a c t e r s}{m i n u t e s} \end{aligned}$
::240 3 c h a r a c t e r s s i i i i t e s

Next, recognize that the problem is asking for a rate per minute and reduce the fraction to its lowest terms by reducing the number of minutes to 1.
::其次,认识到问题在于要求每分钟的费率,将分数减到最低,将分数减到1分。

$\begin{aligned} \frac{240 \div 3}{3 \div 3} = \frac{80}{1} \end{aligned}$

The answer is 80 characters per minute.
::答案是每分钟80个字符

Example 3
::例3

Nathaniel's car gets 45 miles for 3 gallons of gasoline. How many miles does he get per gallon?
::Nathaniel的汽车每加仑三加仑汽油能卖45英里,每加仑能卖多少英里?

First, write a fraction. It does not matter which value is on top.
::首先,写一个分数。这与哪个值在顶部无关。

$\begin{aligned} \frac{45}{3} \frac{m i l e s}{g a l l o n s} \end{aligned}$
::45 3米 i l e s g g a l l o n s

Next, recognize which value needs to be reduced to 1. In this case, "per gallon" signals that gallons must be reduced to 1. 3 gallons must be divided by 3 to get 1.
::下一步,承认哪些值需要降低到1。在这种情况下,“每加仑”的信号是,加仑必须降低到1,3加仑,再除以3才能得到1。

$\begin{aligned} \frac{45 \div 3}{3 \div 3} = \frac{15}{1} \end{aligned}$

The answer is 15 miles per gallon.
::答案是每加仑15英里

Example 4
::例4

Cassandra has a part time job after school in her mom's office. She spent 6 hours this week filing a stack of 850 folders. How many folders did she file each hour?
::Cassandra在她妈妈的办公室放学后有兼职工作,她本周花了6小时提交850个文件夹。她每小时提交多少文件夹?

First, write a fraction showing the relationship between hours and folders. Remember, it does not matter which is in the numerator or which is in the denominator.
::首先, 请写一个分数, 显示小时和文件夹之间的关系。记住, 数字中的或分母中的无关紧要。

$\begin{aligned} \frac{6}{850} \frac{h o u r s}{f o l d e r s} \end{aligned}$
::6 850小时 u r s f o d d r r s

Next, reduce to lowest terms based on which value the problem calls for. In this problem, it is per hour.
::下一步, 降低到最低值, 以什么值来看待问题。这个问题是每小时一次。

$\begin{aligned} \frac{6 \div 6}{850 \div 6} = \frac{1}{142} \end{aligned}$

The answer is 142 folders per hour.
::答案是每小时142个文件夹。

Example 5
::例5

Find the unit rate for 1 minute: 18 inches in 2 minutes
::查找1分钟的单位费率: 2分钟18英寸

First, write a fraction.
::首先,写一个分数。

$\begin{aligned} \frac{18}{2} \frac{i n c h e s}{m i n u t e s} \end{aligned}$
::18 i 2 i n c h e s m i i i i t e s

Next, reduce to lowest terms.
::其次,降低到最低值。

$\begin{aligned} \frac{18 \div 2}{2 \div 2} = \frac{9}{1} \end{aligned}$

The answer is 9 inches per minute.
::答案是每分钟9英寸

Review
::回顾

Write a unit rate for each ratio.
::每一比率的单位费率。

2 for $10.00
::2美元$10.00

3 for $15.00
::3美元15.00美元

5 gallons for $12.50
::5加仑,12.50美元

16 pounds for $40.00
::16磅$40.00$40.00$ 16磅$40.00$

18 inches for $2.00
::18英寸 $2.00

5 pounds of blueberries for $20.00
::5磅蓝莓$20.00

40 miles in 80 minutes
::80分钟40英里

20 miles in 4 hours
::4小时20英里

10 feet in 2 minutes
::2分钟内10英尺

12 pounds in 6 weeks
::6周12磅

14 pounds for $7.00
::14磅$7.00

18 miles in 3 hours
::3小时18英里

21 inches of cloth costs $7.00
::21英寸布费7.00美元

45 miles on 3 gallons of gasoline
::45英里加3加仑汽油

200 miles in four hours
::4小时200英里

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

单位费率

Working with Unit Rates ::采用单位费率

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

Working with Unit Rates
::采用单位费率

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