Section: 单位费率比较 | 8.5单位费率比较

Section outline

Mark adopted a dog today and is at the pet store looking for dog food. He researched the different brands before coming to the store and now he just needs to decide between two brands. Doggie Delights costs $46 for a 20 pound bag. Nature’s Choice costs $55 for a 25 pound bag. Mark wants to compare the cost of dog food per pound to find the better deal. Which bag should Mark buy?
::Mark今天收养了一只狗,现在在宠物商店寻找狗食。他来到商店之前研究了不同的品牌,现在他只需要在两个品牌之间做决定。 Doggie Delights花了46美元买一个20磅的袋子。大自然的选择花了55美元买一个25磅的袋子。 Mark想比较每磅狗食的成本以找到更好的交易。马克应该买哪个包?

In this concept, you will learn to write and compare unit rates.
::在此概念中,您将学会编制和比较单位费率。

Comparing Unit Rates
::比较单位费率

Equivalent can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate . The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.
::等值可以用来比较具有相同价值的不同数量组。比较一个数量与一个数量之间的比率称为单位比率。单位比率有一个分母,当以分数表示时等于一个。单位比率可以用来找到较大的等值率。

Let’s use a unit rate to solve a problem.
::让我们用单位利率解决问题。

Mrs. Harris’ class went apple picking. Each student picked 8 apples. At this rate, how many apples were picked by 7 students?
::哈里斯夫人的班级去摘苹果,每个学生都摘了8个苹果。照这个速度,7个学生摘了多少苹果?

The problem gives the unit rate of 8 apples per student. Solve by finding the equivalent rate where the number of students is 7.
::问题给出了每个学生8个苹果的单位比率。通过找到学生人数为7人的相应比率来解决问题。

First, write the unit rate as a fraction.
::首先,将单位费率写成一个分数。

$\begin{aligned} \frac{8 apples}{1 student} \end{aligned}$

Next, multiply the numerator and denominator by 7 to find the equivalent rate for 7 students.
::其次,将分子和分母乘以7,以找到7名学生的同等比例。

$\begin{aligned} \frac{8 apples \times 7}{1 student \times 7} = \frac{56 apples}{7 students} \end{aligned}$

There were 56 apples picked by 7 students.
::7名学生挑选了56个苹果。

Now let’s solve to find the unit rate.
::现在让我们解决找到单位费率的问题。

Laquita picked 12 peaches in 6 minutes. How many peaches did Laquita pick per minute?
::Laquita在6分钟内摘了12个桃子,Laquita每分钟摘了多少桃子?

The problem gives the larger rate of 12 peaches per 6 minutes. Simplify the rate so the denominator is equal to 1 to find the unit rate.
::问题给出了每6分钟12桃的更大速度。简化速度, 使分母等于 1 以找到单位速度。

First, write the rate as a fraction.
::首先,将利率写成一个分数。

$\begin{aligned} \frac{12 peaches}{6 minutes} \end{aligned}$

Next, simplify the denominator to equal 1. Divide the numerator and denominator by 6.
::下一步,将分母简化为等于 1. 将分子和分母除以6。

$\begin{aligned} \frac{12 peaches \div 6}{6 minutes \div 6} = \frac{2 peaches}{1 minute} \end{aligned}$

Laquita picked 2 peaches per minute.
::Laquita每分钟摘两个桃子。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Mark at the pet store.
::之前,你在宠物店遇到马克的问题

Mark is trying to make a choice. Doggie Delights costs $46 for a 20 pound bag and Nature’s Choice costs $55 for a 25 pound bag. To find the better deal, Mark must compare the price per pound.
::马克试图做出一个选择。狗食道(Doggie Delights)为20磅袋花费46美元,自然选择(National’s choice)为25磅袋花费55美元。要找到更好的方案,马克必须比较每磅的价格。

First, find the unit price for each brand.
::首先,找到每个品牌的单位价格。

$\begin{aligned} \begin{array}{rcl} Doggie Delights & = & \frac{$ 46}{20 pound} = \frac{46 \div 20}{20 \div 20} = \frac{2.30}{1} \\ Nature’s Choice & = & \frac{$ 55}{25 pound} = \frac{55 \div 25}{25 \div 25} = \frac{2.20}{1} \end{array} \end{aligned}$

Next, compare the price per pound. Doggie Delights is $2.30 per pound. Nature’s Choice is $2.20 per pound.
::接下来,比较每磅的价格。狗食是每磅2. 30美元。大自然的选择是每磅2. 20美元。

$\begin{aligned} $ 2.30 > $ 2.20 \end{aligned}$

Nature’s Choice is cheaper than Doggie Delights.
::大自然的选择比狗食更便宜。

Mark decides to buy Nature’s Choice.
::Mark决定买下大自然的选择。

Example 2
::例2

Find the unit rate for the following problem: Harold cuts 7 lawns in 4 hours. How many lawns does Harold cut per hour?
::找到以下问题的单位费率:哈罗德在4小时内削减7个草坪。哈罗德每小时削减多少个草坪?

First, write the rate as a fraction.
::首先,将利率写成一个分数。

$\begin{aligned} \frac{7 lawns}{6 hours} \end{aligned}$

Next, simplify the denominator to equal 1. Divide the numerator and denominator by 4.
::下一步,将分母简化为等于 1. 将分子和分母除以 4。

$\begin{aligned} \frac{7 lawns \div 4}{4 hours \div 4} = \frac{1.75 lawns}{1 hour} \end{aligned}$

Harold cuts 1.75 lawns per hour.
::哈罗德每小时切1.75个草坪

Example 3
::例3

Find the unit rate for the following problem: 24 buttons on 4 shirts.
::查找以下问题的单位费率: 4件衬衫上的24个按钮。

First, write the rate as a fraction.
::首先,将利率写成一个分数。

$\begin{aligned} \frac{24 buttons}{4 shirts} \end{aligned}$

Next, divide the numerator and denominator by 4.
::下一步,将分子和分母除以 4。

$\begin{aligned} \frac{24 buttons \div 4}{4 shirts \div 4} = \frac{6 buttons}{1 shirt} \end{aligned}$

The unit rate is 6 buttons per shirt.
::每件衬衫的单位费率是6个按钮。

Example 4
::例4

Find the unit rate for the following problem: 4 ice cream cones for 2 people.
::找出下列问题的单位费率:2人4个冰淇淋甜筒。

First, write the rate as a fraction.
::首先,将利率写成一个分数。

$\begin{aligned} \frac{4 ice cream cones}{2 people} \end{aligned}$

Next, divide the numerator and denominator by 2.
::下一步,将分子和分母除以 2。

$\begin{aligned} \frac{4 ice cream cones \div 2}{2 people \div 2} = \frac{2 ice cream cones}{1 person} \end{aligned}$

The unit rate is 2 ice cream cones per person.
::单位费率是每人2个冰淇淋锥。

Example 5
::例5

Find the unit rate for the following problem: 45 gallons in 3 miles.
::找出下列问题的单位费率:45加仑,3英里。

First, write the rate as a fraction.
::首先,将利率写成一个分数。

$\begin{aligned} \frac{45 miles}{3 gallons} \end{aligned}$

Next, divide the numerator and denominator by 3.
::下一步,将分子和分母除以3。

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

The unit rate is 15 miles per gallon.
::单位费率是每加仑15英里。

Review
::回顾

Find the unit rate.
::找出单位费率。

Fourteen apples in two barrels
::两桶14个苹果

Thirty-two crayons in two boxes
::两盒内32个蜡笔

Eighteen bottles in three carriers
::三艘运货机中的十八瓶

Twenty students on four teams
::四队20名学生

Twenty-five students on five teams
::五队25名学生

Fifty students in two classes
::分两个班班,50名学生,每班50名

Ninety students on three buses
::90名学生乘坐三辆公共汽车

Thirteen students ate twenty-six cupcakes
::十三名学生吃了二十六个纸杯蛋糕

Twelve campers in two tents
::两个帐篷中的12个营地

Forty- eight hikers on two trails
::四十八个徒步徒步者在两条小径上

16 hikers on 4 trails
::16名徒步徒步者在4条小径上

72 bikes on 6 racks
::6架机架上的72辆自行车

15 backpacks for 5 children
::5名儿童15个背包

28 slices of pizza for 7 teenagers
::为7名青少年提供28片比萨饼

$24.00 for 2 people
::2人24.00美元

Section outline

Comparing Unit Rates ::比较单位费率

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

Comparing Unit Rates
::比较单位费率

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