8.4等值率的识别和书写

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  等值率的识别和书写

  

  [Figure 1]

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  Mrs. Williams’ 6 ^th  grade class is going on a hiking trip. She wants to make granola for her students. The recipe says to use 3 cups of oats for 6 servings. There are 30 students in her class. How many cups of oats does she need to make enough for 30 students?
  ::威廉姆斯夫人的六年级班正在徒步旅行,她想为学生做麦片。食谱上说要用三杯燕麦做6次服务。班里有30名学生。她需要多少杯燕麦做30名学生?

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  In this concept, you will learn to identify and write equivalent  .
  ::在此概念中,您将学会识别和写作等值 。

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  Identifying and Writing Equivalent Rates
  ::确定和写写等效率

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  Ratios  compare two quantities. A  rate  is a type of ratio that compares two quantities that have different units of measurement. The word “per” is often used to describe rates.
  ::比率比较两个数量。一个比率是一种比率类型,比较两个具有不同计量单位的数量。“每个”一词常常用来描述比率。

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  Rates can be written as fractions. The first quantity is the  numerator  and the second quantity is the  denominator . Different rates that have the same value are  equivalent rates . You can find an  equivalent rate  the same way you find  — divide  or multiply the numerator and the denominator by the same number.
  ::速率可以以分数写成。第一个量是分子,第二个量是分母。不同值的不同率是等值率。您能找到的等值率与您找到的等值率相同——divide或乘以分子和分母乘以相同数字。

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  Look at the ratio statements below.
  ::下面是比率报表。

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  The car travels 15 miles  per  gallon.
  ::汽车每加仑15英里。

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  John took 21 minutes to run 3 miles.
  ::约翰花了21分钟跑3英里

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  Karen buys 20 pencils for $4.  
  ::凯伦用4块买20支铅笔

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  These ratios are rates that compare two different units of measurements: miles to gallon, minutes to miles, and pencils to dollars.
  ::这些比率是比较两种不同计量单位的费率:英里到加仑,分钟到里程,铅笔到美元。

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  The ratio for 15 miles per gallon as a fraction is
  ::每加仑15英里的比例是

  $$\begin{array}{r}\frac{15\text{ miles}}{1\text{ gallon}}.\end{array}$$

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  The ratio of 21 minutes to 3 miles for John’s speed as a fraction is
  ::约翰的分数速度 21分到3英里的比率是

  $$\begin{array}{r}\frac{21\text{ minutes}}{3\text{ miles}}.\end{array}$$

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  Find the equivalent rate for the number of minutes for each mile.
  ::找到每英里分钟数的等值速率 。

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  First, use the fraction and divide the numerator and denominator by 3 to find the equivalent rate for 1 mile.
  ::首先,使用分数,将分子和分母除以3,以找到1英里的等值速率。

  $$\begin{array}{r}\frac{21\text{ minutes}÷3}{3\text{ miles}÷3}=\frac{7\text{ minutes}}{1\text{ mile}}\end{array}$$

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  An equivalent rate of  $\begin{array}{r}\frac{21\text{ minutes}}{3\text{ miles}}\end{array}$  is  $\begin{array}{r}\frac{7\text{ minutes}}{1\text{ mile}}\end{array}$ .
  ::相当于21分3英里等于7分1英里

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  John’s speed was 7 minutes per mile.
  ::约翰的速度是每英里7分钟。

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  Using the Karen’s information, find the equivalent rate for the cost of 40 pencils.
  ::使用Karen的资料,找到40支铅笔的等值价格。

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  First, write the rate of 20 pencils for $4 as a fraction.
  ::首先,写下20支铅笔的价钱 4美元作为分数

  $$\begin{array}{r}\frac{20\text{ pencils}}{4\text{ dollars}}\end{array}$$

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  Next, multiply the numerator and denominator by 2 to find the equivalent rate for 40 pencils.
  ::接下来,将分子和分母乘以2,以找到40支铅笔的等值率。

  $$\begin{array}{r}\frac{20\text{ pencils}\times 2}{4\text{ dollars}\times 2}=\frac{40\text{ pencils}}{8\text{ dollars}}\end{array}$$

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  An equivalent rate of  $\begin{array}{r}\frac{20\text{ pencils}}{4\text{ dollars}}\end{array}$  is  $\begin{array}{r}\frac{40\text{ pencils}}{8\text{ dollars}}\end{array}$ .
  ::相当于20支铅笔 4美元等于40支铅笔 8美元

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  40 pencils will cost Karen $8.
  ::40支铅笔将花费凯伦8美元

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Mrs. Williams and her granola.
  ::早些时候,你被问及 威廉姆斯太太和她的粮仓。

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  Mrs. Williams has a recipe that uses 3 cups of oats for 6 servings and needs to make enough granola for 30 students. She can use the rate 3 cups per 6 servings to find an equivalent rate for 30 servings.
  ::威廉姆斯夫人的食谱是6种服务3杯燕麦,需要为30个学生制作足够的粮仓。 她可以使用每6种服务3杯的价钱来为30种服务找到等价的价钱。

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  First, write the rate of cups to servings as a fraction.
  ::首先,写下杯子的速率作为分数。

  $$\begin{array}{r}\frac{3\text{ cups}}{6\text{ servings}}\end{array}$$

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  Next, multiply the numerator and denominator by 5 to find the equivalent rate for 30 servings.
  ::下一步,将分子和分母乘以5,以找到30个服务对象的等值率。

  $$\begin{array}{r}\frac{3\text{ cups}\times 5}{6\text{ servings}\times 5}=\frac{15\text{ cups}}{30\text{ servings}}\end{array}$$

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  Mrs. Williams will need 15 cups of oats to make 30 servings of granola.
  ::威廉姆斯太太需要15杯燕麦 来做30份麦片

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  Example 2
  ::例2

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  Find the equivalent rate.
  ::找到相等的汇率。

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  Ron ate five hot dogs in one minute. Find the  unit rate . How many hot dogs can Ron eat in 2 minutes?
  ::罗恩在一分钟内吃了五只热狗 找出单位费率

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  First, write the rate of 5 hot dogs per minute as a fraction.
  ::首先,将每分钟5个热狗的速率写成一个分数。

  $$\begin{array}{r}\frac{5\text{ hot dogs}}{1\text{ minute}}\end{array}$$

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  Next, multiply the numerator and the denominator by 2 to find the equivalent rate for 2 minutes.
  ::下一步,将分子和分母乘以 2 以找到2 分钟的等值速率。

  $$\begin{array}{r}\frac{5\text{ hot dogs}\times 2}{1\text{ minute}\times 2}=\frac{10\text{ hot dogs}}{2\text{ minutes}}\end{array}$$

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  Ron can eat 10 hot dogs in 2 minutes.
  ::罗恩可以在两分钟内吃10只热狗

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  Use the rate  $\begin{array}{r}\frac{6\text{ shirts}}{2\text{ boxes}}\end{array}$  to answer the following questions.
  ::使用6件衬衫2箱,回答下列问题。

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  Example 3
  ::例3

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  How many shirts are there in 6 boxes?
  ::6箱里有多少件衬衫?

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  First, multiply the numerator and the denominator by 3 to find the equivalent rate for 3 boxes.
  ::首先,将分子和分母乘以3,以找到3箱的等值率。

  $$\begin{array}{r}\frac{6\text{ shirts}\times 3}{2\text{ boxes}\times 3}=\frac{18\text{ shirts}}{6\text{ boxes}}\end{array}$$

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  There are 18 shirts in 6 boxes.
  ::6个箱子里有18件衬衫

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  Example 4
  ::例4

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  How many shirts are there in one box?
  ::一个盒子里有多少件衬衫?

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  First, divide the numerator and denominator by 2 to find the equivalent rate for 1 box.
  ::首先,将分子和分母除以 2,以找到1箱的等值率。

  $$\begin{array}{r}\frac{6\text{ shirts}÷2}{2\text{ boxes}÷2}=\frac{3\text{ shirts}}{1\text{ box}}\end{array}$$

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  There are 3 shirts in 1 box.
  ::1箱里有3件衬衫

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  Example 5
  ::例5

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  How many boxes would you need for 24 shirts?
  ::24件衬衫需要几箱?

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  First, multiply the numerator and the denominator by 4 to find the equivalent rate for 24 shirts.
  ::首先,将分子和分母乘以4,以找到24件衬衫的等值率。

  $$\begin{array}{r}\frac{6\text{ shirts}\times 4}{2\text{ boxes}\times 4}=\frac{24\text{ shirts}}{8\text{ boxes}}\end{array}$$

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  You would need 8 boxes for 24 shirts.
  ::24件衬衫需要8箱

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  Review
  ::回顾

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  Write the rate as a fraction and find an equivalent rate.
  ::将利率写成一个分数, 并找到等值利率 。

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  1. Fourteen apples in two barrels
     ::两桶14个苹果
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  2. Thirty-two crayons in two boxes
     ::两盒内32个蜡笔
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  3. Eighteen bottles in three carriers
     ::三艘运货机中的十八瓶
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  4. Twenty students on four teams
     ::四队20名学生
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  5. Twenty-five students on five teams
     ::五队25名学生
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  6. Fifty students in two classes
     ::分两个班班,50名学生,每班50名
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  7. Ninety students on three buses
     ::90名学生乘坐三辆公共汽车
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  8. Thirteen students ate twenty-six cupcakes
     ::十三名学生吃了二十六个纸杯蛋糕
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  9. Twelve campers in two tents
     ::两个帐篷中的12个营地
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  10. Twenty-four hikers per trail
      ::每条路线24名徒步者
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  11. Six campers per tent
      ::每个帐篷6个营地
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  12. If there are six campers per tent, how many tents for 18 campers?
      ::如果每个帐篷有6个营房,18个营房有多少帐篷?
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  13. How many tents for 30 campers?
      ::30辆露营车有多少帐篷?
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  14. How many campers can you fit if you have 12 tents?
      ::如果你有12个帐篷,你有多少露营者适合?
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  15. Sixty students on five teams
      ::5个小组的60名学生