1.15 部队改划

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  单位改划

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  While vacationing in Spain, you decide to rent a car. When you fill up the gas tank, you notice that the gas is measured in liters, not gallons, like you're used to. The cost of gas in Spain is 1.44 Euros per liter. If you get 65 Euros' worth of gas, how many gallons did you buy? There are 3.8 liters in a gallon.
  ::当您在西班牙度假时,您决定租车。当您填满油箱时,您会注意到气体是用公升而不是加仑测量的,就像您习惯的那样。西班牙的天然气成本是每公升1.44欧元。如果你得到65欧元的天然气,您购买了多少加仑?加仑有3.8升。

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  Converting Units
  ::转换单位

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  One part of word problems is the unit of measure. It can be confusing when we don’t know what the problem is asking for. For example, how many feet are in a mile? How many cups are in a gallon? Here are a few conversions between different units of measure.
  ::单词问题的一部分是量度单位。 当我们不知道问题要求什么时, 它可能会令人困惑。 例如, 一英里内有多少英尺? 一加仑内有多少杯? 这是不同量度单位之间的几处转换。

  Units	Equivalent Unit
  2 cups (c)	1 pint
  2 pints (pt)	1 quart
  4 quarts (qt)	1 gallon (gal)
  12 inches (in)	1 foot
  3 feet (ft)	1 yard
  1760 yards (yd)	1 mile (mi)
  16 ounces (oz)	1 pound (lb)
  2000 lbs	1 ton
  100 centimeters (cm)	1 meter (m)
  1000 meters	1 kilometer (km)
  2.2 cm	1 inch

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  Let's convert the following units of measure.
  ::让我们转换以下计量单位。

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  1. How many cups are in a gallon?
     ::加仑里有多少杯子?

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  There are 2 cups in a pint, 2 pints in a quart and 4 quarts in a gallon.
  ::一品脱有两杯,一品脱有两品脱,一加仑有4夸特。

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  $\begin{array}{r}\frac{2c}{1pt}\cdot \frac{2pt}{1qt}\cdot \frac{4pt}{1gal}\end{array}$ Cancel out the like terms and multiply across.
  ::2cpt[pt]1qt[pt]4pt1gal 取消类似条件并乘法 。

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  $\begin{array}{r}\frac{2c}{\cancel{1pt}}\cdot \frac{2\cancel{pt}}{1\cancel{qt}}\cdot \frac{4\cancel{pt}}{1gal}=\frac{16c}{1gal}\end{array}$ There are 16 cups in one gallon.
  ::2cpt1pt1qt4pt1gal=16c1gal 1加仑有16个杯子。

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  Make sure to always cancel any units that are in the numerator and denominator of these fractions. Fractions like these are called unit rates because the base is one unit. We write out the unit conversion problems in this way so that we ensure that all of the correct units are cancelled out.
  ::确保总是取消这些分数的分子和分母中的任何单位。 这样的分数被称为单位率, 因为基数是一个单位。 我们这样写出单位转换问题, 这样我们就可以确保取消所有正确的单位 。

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  2. How many feet are in 16 yards?
     ::16码内有几英尺?

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  This problem is not a conversion problem, but asking to extend your knowledge of how many feet are in a yard. We know that there are 3 feet in a yard; therefore there will be $\begin{array}{r}3\cdot 16=48feet\end{array}$ in 16 yards.
  ::这个问题不是转换问题,而是要求扩大你对院子里有多少脚的了解。 我们知道院子里有3英尺,因此16英尺=48英尺,16码。

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  Another way to solve this problem is in a ratio, below:
  ::解决这一问题的另一种方式是按以下比率:

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  $$\begin{array}{rl}\frac{3ft}{1yd}& =\frac{xft}{16yd}\text{To solve a ratio, we cross-multiply.}\\ 3ft\cdot 16yd& =1yd\cdot xft\\ \frac{48ft\cdot \cancel{yd}}{1\cancel{yd}}& =xft\text{Here,}x=48feet\text{and we show that the appropriate units cancel.}\end{array}$$

  
  ::3ft1yd=xft16yd 要解答一个比率, 我们交叉mulply3ft_16yd=1ydxft48ftyd1yd=xft 这里, x=48英尺, 我们显示相应的单位取消 。

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  3. You are making soup for 6 people. The recipe you are using calls for 6 cups of broth, but it is only for 4 people. How many cups of broth will you need?
     ::您正在为6个人做汤。 您使用的食谱是6杯汤, 但只为4个人。 您需要多少杯汤?

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  Set up a ratio, like in the previous example.
  ::设置比例, 如上一个示例一样 。

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  $$\begin{array}{rl}\frac{6people}{xcups}& =\frac{4people}{6cups}\\ 6\cdot 6c& =4\cdot xc\\ 36& =4x\\ x& =9cups\end{array}$$

  
  ::6peoplexcup=4people6cup6c=4xc36=4xx=9cups=4people6cup6c=4xc36=4xx=9cups

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  You will need 9 cups of broth.
  ::你需要9杯汤

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were asked to find the number of gallons of gas  you bought.
  ::早些时候,你被要求去寻找 你买的汽油加仑的数量。

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  First, let's figure out how many liters of gas you put in the car.
  ::首先,让我们弄清楚你把多少升汽油放进车里

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  $$\begin{array}{r}65=1.44l\\ l& =65÷1.44\\ l& =45.14\end{array}$$

  
  ::65=1.44ll=651.44l=45.14

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  Now, we need to divide again to get the number of gallons.
  ::现在,我们需要再分裂一次 才能得到加仑的数量

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  $$\begin{array}{r}g=l÷3.8\end{array}$$

  
  ::g=l3.8

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  Substituting for l , we get:
  ::替代l,我们得到:

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  $$\begin{array}{rl}g& =45.14÷3.8\\ g& =11.88\end{array}$$

  
  ::g=45.14=3.8g=11.88

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  You bought 11.88 gallons of gas.
  ::你买了11.88加仑的汽油

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  Example 2
  ::例2

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  How many centimeters are in a foot?
  ::脚里有几厘米?

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  Set up the conversion.
  ::设置转换。

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  $$\begin{array}{rl}\frac{2.2cm}{1in}& \cdot \frac{12in}{1ft}\text{Cancel out the inches and multiply.}\\ \frac{2.2cm}{1\cancel{in}}& \cdot \frac{12\cancel{in}}{1ft}=\frac{26.4cm}{1ft}\end{array}$$

  
  ::2.2cm1in1in1in1ftCancel 释放英寸和乘数.2.2cm1in1in1in1ft=26.4cm1ft

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  Example 3
  ::例3

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  How many ounces are in 3.5 pounds?
  ::3.5磅内有多少盎司?

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  If there are 16 ounces in a pound, then there will be $\begin{array}{r}16\cdot 3.5=56ounces\end{array}$ in 3.5 pounds.
  ::如果每磅有16盎司,那么每磅将有163.5=56盎司,每磅3.5磅。

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  Review
  ::回顾

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  For questions 1-6, set up a unit conversion to find:
  ::对于问题1-6,设置一个单位转换以查找:

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  1. Feet in a mile?
     ::一英里的脚?
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  2. Cups in a quart?
     ::杯子里的杯子吗?
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  3. Centimeters in a kilometer?
     ::一公里内有厘米吗?
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  4. Pints in a gallon?
     ::一加仑的油吗?
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  5. Centimeters in a mile?
     ::一英里内有厘米吗?
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  6. Gallons in a quart?
     ::加仑在夸特?
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  7. How many inches are in 5.25 yards?
     ::525码内有几英寸?
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  8. How many pints are in 7.5 gallons?
     ::多少品脱在7.5加仑?
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  9. How many pounds are in 2.6 tons?
     ::2.6吨是多少磅?
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  10. How many centimeters are in 4.75 meters?
      ::4.75米内有多少厘米?
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  11. Claire is making chocolate chip cookies. If the recipe calls for 3.5 cups of flour, how many cups will Claire need to use if she triples the recipe?
      ::如果食谱需要3.5杯面粉 她要用多少杯?
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  12. The recipe also calls for 8 oz. of chocolate chips. Claire wants to make the cookies with three-quarters bittersweet chips and one-quarter semi-sweet chips. Again, tripling the recipe, how many ounces of each type of chocolate chip will she need?
      ::配方也要求8盎司巧克力薯片。克莱尔想用四分之三的苦甜薯片和四分之一的半甜薯片做饼干。再说一次,配方增加了三倍,她需要每类巧克力薯片的几盎司?

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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 。