3.10 比率

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  Ratios 
  ::比率比率比率

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  A ratio is a way to compare two numbers, measurements or quantities. When we write a ratio, we divide one number by another and express the answer as a fraction. There are two distinct ratios in the example below.
  ::比例是比较两个数字、测量量或数量的一种方式。 当我们写一个比例时, 我们将一个数字除以另一个, 然后以一个分数表示答案。 下面的例子中有两个不同的比例 。

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  Using Ratios as an Explanation 
  ::使用比率作为解释

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  Nadia is counting out money with her little brother. She gives her brother all the nickels and pennies. She keeps the quarters and dimes for herself. Nadia has four quarters and six dimes. Her brother has fifteen nickels and five pennies and is happy because he has more coins than his big sister. How would you explain to him that he is actually getting a bad deal?
  ::Nadia和她的弟弟一起数钱,她给她弟弟所有的硬币和硬币,她自己留着零钱和零钱。Nadia有4/4和6个硬币。她弟弟有15个硬币和5个硬币,因为他的硬币比他姐姐还多,所以很高兴。你如何向他解释,他实际上交易不顺利呢?

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  The ratio of the number of Nadia’s coins to her brother’s is $\begin{array}{r}\frac{4+6}{15+5}\end{array}$ , or $\begin{array}{r}\frac{10}{20}=\frac{1}{2}\end{array}$ . (Ratios should always be simplified.) In other words, Nadia has half as many coins as her brother.
  ::Nadia的硬币数与其兄弟的硬币数之比是4+615+5或1020=12。 (Ratios应该总是简化。 )换句话说,Nadia的硬币数是她兄弟的一半。

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  Another ratio we could look at is the value of the coins. The value of Nadia’s coins is $\begin{array}{r}(4\times 25)+(6\times 10)=160cents\end{array}$ . The value of her brother’s coins is $\begin{array}{r}(15\times 5)+(5\times 1)=80cents\end{array}$ . The ratio of the value of Nadia’s coins to her brother’s is $\begin{array}{r}\frac{160}{80}=\frac{2}{1}\end{array}$ . So the value of Nadia’s money is twice the value of her brother’s.
  ::我们可以看到的另一个比率是硬币的价值。 Nadia的硬币的价值是(4x25)+(6x10)=160美分。她兄弟的硬币的价值是(15x5)+(5x1)=80美分。Nadia的硬币价值与其兄弟的硬币价值之比是(16080=21 ) 。因此Nadia的钱价值是她兄弟的两倍。

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  Notice that even though the denominator is one, we still write it out and leave the ratio as a fraction instead of a whole number. A ratio with a denominator of one is called a unit rate .
  ::请注意,即使分母是一个分母,我们仍然把它写出来,把比率保留成一个分数,而不是一个整数。一个分母与一个分母的比率称为单位比率。

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  Comparing Prices 
  ::比较价格

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  The price of a Harry Potter Book on Amazon.com is $10.00. The same book is also available used for $6.50. Find two ways to compare these prices.
  ::在Amazon.com上的《哈利波特书》的价格是10.00美元,同本书的价钱是6.50美元。找到两种方法比较这些价格。

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  We could compare the numbers by expressing the difference between them: $\begin{array}{r}\mathrm{\$}10.00-\mathrm{\$}6.50=\mathrm{\$}\mathrm{3.50.}\end{array}$
  ::我们可以通过表示数字之间的差异来比较数字:$0.00-6.50=3.50美元。

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  We can also use a ratio to compare them: $\begin{array}{r}\frac{10.00}{6.50}=\frac{100}{65}=\frac{20}{13}\end{array}$ (after to remove the decimals, and then simplifying).
  ::我们也可以使用一个比率来比较它们:10.006.50=10065=2013(然后去掉小数点,然后简化)。

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  So we can say that the new book is $3.50 more than the used book , or we can say that the new book costs $\begin{array}{r}\frac{20}{13}\end{array}$ times as much as the used book .
  ::我们可以说新书比旧书多3.

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  Comparing Length and Width 
  ::长度和宽度比较

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  A tournament size shuffleboard table measures 30 inches wide by 14 feet long. Compare the length of the table to its width and express the answer as a ratio.
  ::比赛规模的打乱板桌用30英寸宽乘以14英尺长。将表长度与其宽比,并将答案作为比例表示。

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  We could just write the ratio as $\begin{array}{r}\frac{14feet}{30inches}\end{array}$ . But since we’re comparing two lengths, it makes more sense to convert all the measurements to the same units. 14 feet is $\begin{array}{r}14\times 12=168inches\end{array}$ , so our new ratio is $\begin{array}{r}\frac{168}{30}=\frac{28}{5}\end{array}$ .
  ::我们可以只写14英尺/30英寸。但由于我们比较了两个长度,将所有测量数据转换成相同的单位更合理。 14英尺是14x12=168英寸,所以我们的新比率是16830=285。

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  Example 
  ::示例示例示例示例

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  Example 1
  ::例1

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  A family car is being tested for fuel efficiency. It drives non-stop for 100 miles and uses 3.2 gallons of gasoline. Write the ratio of distance traveled to fuel used as a unit rate .
  ::家用汽车正在接受燃料效率测试,驾驶不停车100英里,并使用3.2加仑汽油。

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  The ratio of distance to fuel is $\begin{array}{r}\frac{100miles}{3.2gallons}\end{array}$ . But a unit rate has to have a denominator of one, so to make this ratio a unit rate we need to divide both numerator and denominator by 3.2. $\begin{array}{r}\frac{\frac{100}{3.2}miles}{\frac{3.2}{3.2}gallons}=\frac{31.25miles}{1gallon}\end{array}$ or 31.25 miles per gallon.
  ::距离与燃料的比重是100英里3.2加仑。但单位率必须有一个分母,因此,要使这个比率成为一个单位率,我们需要将分子和分母除以3.2. 1003.23.23.2加仑=31.251加仑,或每加仑31.25英里。

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  Review 
  ::回顾

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  Write the following comparisons as ratios. Simplify fractions where possible.
  ::将下列比较写成比率。尽可能简化分数。

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  1. $150 to $3.
     ::150美元到3美元。
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  2. 150 boys to 175 girls.
     ::150名男孩对175名女孩。
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  3. 200 minutes to 1 hour.
     ::200分钟到1小时
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  4. 10 days to 2 weeks.
     ::10天到2个星期

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  Write the following ratios as a unit rate.
  ::将下列比率写成单位比率。

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  5. 54 hotdogs to 12 minutes.
     ::54只热狗到12分钟
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  6. 5000 lbs to 250 square inches.
     ::5000磅到250平方英寸
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  7. 20 computers to 80 students.
     ::20台电脑到80个学生
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  8. 180 students to 6 teachers .
     ::180名学生到6名教师。
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  9. 12 meters to 4 floors .
     ::12米到4楼
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  10. 18 minutes to 15 appointments.
      ::18分钟到15分钟的预约时间。

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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 。