5.6单位费率比较

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  单位费率比较

  

  [Figure 1]

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  Connie is decorating cookies for the school bake sale. She has worked for 3 hours and completed 150 cookies. Her friend, Daniel, is also participating in the sale. He decorated 98 cookies in 2 hours. Which cookie decorator was faster, Connie or Daniel? 
  ::康妮正在为学校的烤面包销售装饰饼干,她工作了3个小时,完成了150个饼干。她的朋友丹尼尔也在参与销售。他在2小时内为98个饼干装饰了98个饼干。哪个饼干装饰器更快,康妮还是丹尼尔?

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  In this concept, you will learn to compare unit rates.
  ::在此概念中,您将学会比较单位费率。

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  Comparing Unit Rates
  ::比较单位费率

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  A  unit rate  is a comparison of two measurements, one of which has a value of 1. Given the number of units, the unit rate can be used to calculate a total  rate . Unit rates can be used for comparison purposes. 
  ::单位费率是两项测量的比较,其中一项测量值为1。考虑到单位数目,单位费率可用于计算总费率。单位费率可用于比较。

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  Here is an example.
  ::举一个例子。

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  Felicia needs to buy sugar. She could buy a 16-ounce box of sugar for $1.12, or she could buy a 24-ounce box of sugar for $1.44. Which is the better buy? How much cheaper, in cents  per  ounce, is that buy?
  ::Felicia需要买糖。她可以买16盎司的糖,每盎司1.12美元,或者她可以买24盎司的糖,每盎司1.44美元。哪个更好呢?以每盎司1美分计,买多少便宜?

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  First, find the unit price for the 16-oz box by writing a fraction. 
  ::首先,通过写一个分数来找到 16 oz 盒的单价。

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    $\begin{array}{r}\frac{16}{1.12}\frac{ounces}{dollars}\end{array}$
  ::16 1.12 u n c c e s s d d d l l r r s

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  Next, recognize the answer must be per ounce and  reduce  the fraction to its lowest terms by  reducing  ounces to 1.
  ::其次,承认答案必须是每盎司,并通过将盎司减为1,将分数减到最低值。

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  $\begin{array}{r}\frac{16÷16}{1.12÷16}=\frac{1}{.07}\end{array}$   $\begin{array}{r}\frac{ounce}{dollars}\end{array}$
  ::16 16 1.12 16 = 1 .07 o n c e d d o l r r s

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  Then, find the unit price per ounce for the 24-ounce box. Remember to keep the units consistent. In this case, ounces in the  numerator  and dollars in the  denominator .
  ::然后找到24盎司盒的单位价格每盎司。 记住要保持单位一致。 在此情况下, 请在分子中找到盎司, 在分母中找到美元 。

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    $\begin{array}{r}\frac{24}{1.44}\frac{ounces}{dollars}\end{array}$
  ::241.44 u n c e s d d d l l r r s

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  Next, reduce this fraction to its lowest terms.
  ::其次,将这一分数降低到最低值。

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    $\begin{array}{r}\frac{24÷24}{1.44÷24}=\frac{1}{.06}\frac{ounce}{dollars}\end{array}$
  ::24 24 1.44 24 = 1 .06 o nu c e d o l i r s

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  Then, compare the two unit rates.
  ::然后,比较两个单位费率。

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  1 ounce for $0.07   $\begin{array}{r}>\end{array}$  1 ounce for $0.06
  ::1盎司,0.7美元 > 1盎司,0.06美元

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  The 16-oz box is more expensive than the 24-oz box.
  ::16oz的盒子比24oz的盒子更贵

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  Next, subtract one unit price from the other to find the  difference  in price.
  ::其次,从另一个中减去一个单位价格,以找出差价。

  .07 - .06 = .01

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  The answer is that the best buy is the 24-oz box because it is $0.01 per ounce cheaper than the 16-oz box.
  ::答案是,最好的买家是24oz的盒子,因为它比16oz的盒子便宜每盎司0.1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 Connie and Daniel, who are decorating cookies.
  ::之前,你得到一个问题 关于康妮和丹尼尔, 谁正在装饰饼干。

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  Connie completed 150 cookies in three hours, and it took Daniel 2 hours to decorate 98 cookies.  Who is the faster cookie decorator?
  ::康妮在三小时内完成了150个饼干, 丹尼尔花了两小时装饰了98个饼干。谁是更快的饼干设计师?

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  First, write the fractions with consistent units.
  ::首先,用一致的单位写分数 。

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  Connie    $\begin{array}{r}\frac{150}{3}\frac{cookies}{hours}\end{array}$  
  ::康妮 150 3co o k i e s h o u r s

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  Daniel    $\begin{array}{r}\frac{98}{2}\frac{cookies}{hours}\end{array}$
  ::丹尼尔 98 2 c o k i e s h o u r s

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

  $\begin{array}{r}\frac{150}{3}=50\end{array}$

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  Connie decorated 50 cookies per hour.
  ::康妮每小时装饰50个饼干

    $\begin{array}{r}\frac{98}{2}=49\end{array}$

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  Daniel decorated 49 cookies per hour.
  ::丹尼尔每小时装饰49个饼干

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  Then, compare.
  ::那么,比较。

  50 $\begin{array}{r}>\end{array}$ 49

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  The answer is that Connie decorated faster.
  ::答案是康妮装饰得更快

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  Example 2
  ::例2

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  Compare: 3:1 and 6 to 2.
  ::比较:3:1和6-2。

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  First, write 3:1 as a fraction.
  ::首先,写3: 1作为一个分数。

  $\begin{array}{r}\frac{3}{1}\end{array}$

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

    $\begin{array}{r}\frac{3}{1}=3\end{array}$

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  Then, write 6 to 2 as a fraction and reduce to lowest terms.
  ::然后,写6到2作为一个分数 并降低到最低值。

  $\begin{array}{r}\frac{6}{2}=3\end{array}$  

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  Next, compare the values.
  ::接下来,比较数值。

  3 = 3

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  The answer is that the   are equal.
  ::答案是,平等是平等的。

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  Example 3
  ::例3

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  Which rate is higher? 4 to 5  or   $\begin{array}{r}\frac{16}{20}\end{array}$
  ::哪个比率更高? 4至5或16 20

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  First, write the fractions,and reduce.
  ::首先,写分数,并减少。

    $\begin{array}{r}\frac{4}{5}\end{array}$

    $\begin{array}{r}\frac{16}{20}=\frac{16÷4}{20÷4}=\frac{4}{5}\end{array}$

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  Next, compare.
  ::下一个,比较。

  $\begin{array}{r}\frac{4}{5}=\frac{4}{5}\end{array}$
  

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  The answer is that the rates are equal.
  ::答案是,利率是相等的。

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  Example 4
  ::例4

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  Matt can melt 18 m&ms in his mouth without chewing in 3 minutes. It takes Kelly 5 minutes to melt 15. Who melts the m&ms faster, Matt or Kelly?
  ::马特可以在3分钟内不咀嚼地融化嘴里18米和米。凯利需要5分钟才能熔化15分钟。 谁能更快地熔化嘴里18米和米,马特还是凯利?

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  First, write the fractions.
  ::首先,写分数。

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  Matt  $\begin{array}{r}\frac{18}{3}\frac{m\mathrm{\&}ms}{minutes}\end{array}$
  ::Matt 18 3 m & m s m i ni nu t e s

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  Kelly  $\begin{array}{r}\frac{15}{5}\frac{m\mathrm{\&}ms}{minutes}\end{array}$
  ::Kelly 15 5米和m sm i ni nu t e s

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  Next, calculate each of the unit rates recognizing that the word "faster" applies to minutes and reducing that time to 1.
  ::其次,计算每个单位的费率,确认“更快”一词适用于分钟,并将时间减为1。

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  Matt    $\begin{array}{r}\frac{18}{3}=\frac{6}{1}\end{array}$
  ::马特 18 3 = 6 1

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  Matt can melt 6 m&ms in 1 minute.
  ::马特能在1分钟内熔化6 m&ms。

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  Kelly $\begin{array}{r}\frac{15}{5}=\frac{3}{1}\end{array}$
  ::Kelly 15 5 = 3 1

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  Kelly can melt 3 m&ms in 1 minute.
  ::Kelly可以在1分钟内熔化3m&ms。

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  Then, compare the unit rates.
  ::然后,比较单位费率。

  6  $\begin{array}{r}>\end{array}$ 3 

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  The answer is that Matt melts m&ms faster.
  ::答案是,马特熔化 m&ms更快。

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  Example 5
  ::例5

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  Frank read 8 books in three weeks. It took Bonnie 4 weeks to read 10 books. Who is the faster reader?
  ::弗兰克在三周内读了八本书 Bonnie花了四个星期才读了十本书

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  First, write the fractions being sure to keep the units consistent.
  ::首先,写分数以确保单位保持一致。

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  Frank    $\begin{array}{r}\frac{8}{3}\frac{books}{weeks}\end{array}$
  ::弗兰克 8 3 b o k s w e e e k s

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  Bonnie   $\begin{array}{r}\frac{10}{4}\frac{books}{weeks}\end{array}$  
  ::Bonnie 10 4 b o o k s w e e e e k s

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  Next, reduce to unit rates by reducing the times to 1.Faster can refer to time, not books.
  ::其次,将单位费率降低到单位费率,将时间减到1. 节奏可以指时间,而不是书本。

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  Frank   $\begin{array}{r}\frac{8}{3}=2.67\end{array}$
  ::弗兰克 8 3 = 2.67

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  Frank read 2.67, or 2 $\begin{array}{r}\frac{2}{3}\end{array}$ books per week.
  ::弗兰克每周读2.67本书 或2 2 3本书

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  Bonnie $\begin{array}{r}\frac{10}{4}=2.5\end{array}$
  ::Bonnie 10 4 = 2.5

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  Bonnie read 2.5, or 2 $\begin{array}{r}\frac{1}{2}\end{array}$ books per week.
  ::Bonnie每周读2.5本书 或212本书

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  Then, compare.
  ::那么,比较。

  2.67  $\begin{array}{r}>\end{array}$  2.5

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  The answer is that Frank is the faster reader.
  ::答案是弗兰克读得更快

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  Review
  ::回顾

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  Determine whether each is equivalent or not.
  ::确定每项是否相等。

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  1. 60 units in 3 minutes and 80 units in 4 minutes
     ::60个单位每3分钟60个单位每3分钟,80个单位每4分钟
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  2. $16 for 8 pounds and $22 for 10 pounds
     ::8磅16块,10磅22块22块
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  3. 50 kilometers in 2 hours and 75 kilometers in 3 hours
     ::2小时50公里 3小时75公里

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  Solve each problem.
  ::解决每一个问题。

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  4. Max paid $45 for 15 gallons of gasoline. What was the cost per gallon of gasoline?
     ::Max花了45美元买15加仑汽油 每加仑汽油多少钱?
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  5. Mr. Brown paid $8.28 for 12 cans of green beans. Express this cost as a unit price.
     ::Brown先生为12罐绿豆支付了8.28美元,以单价计算。
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  6. A train travels 480 kilometers in 3 hours. Express this speed as a unit rate.
     ::火车在3小时内行驶480公里 以单位速率表示这个速度
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  7. Mrs. Jenkins paid $50 for 40 square feet of carpeting. What was the cost per square foot for the carpeting?
     ::Jenkins夫人花了50美元买40平方英尺的地毯,每平方英尺的地毯成本是多少?
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  8. A copy machine can produce 310 copies in 5 minute. How many copies can the machine produce per minute?
     ::复印机5分钟内可制作310份,每分钟可印制多少份?

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  Nadia needs to buy some cheddar cheese. An unce package of cheddar cheese costs $2.40. A 12-ounce package of cheddar cheese costs $3.36.
  ::Nadia需要买一些切达干酪 一套8盎司的切达干酪要花2.4美元 一套12盎司的切达干酪要花3.36美元

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  9. Find the unit price for the unce package.
     ::找出8盎司包的单价
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  10. Find the unit price for the 12-ounce package.
      ::找出12盎司货包的单价
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  11. Which is the better buy? How many cents per ounce cheaper is the better buy?
      ::每盎司多少美分更便宜?

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  Joe drove 141 miles in 3 hours. His cousin Amy drove 102 miles in 2 hours. Assume both cousins were driving at constant speeds.
  ::乔在3小时内开车141英里 他的表妹艾米在2小时内开车102英里

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  12. How fast was Joe driving, in miles per hour?
      ::Joe开多快? 时速几英里?
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  13. How fast was Amy driving, in miles per hour?
      ::Amy开多快? 时速几英里?
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  14. Who was driving at a faster rate of speed?
      ::谁开的车速度更快?
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  15. How much faster was the faster person traveling?
      ::跑得更快的人跑多快?

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  Review (Answers)
  ::回顾(答复)

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  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 。

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  Resources
  ::资源