7.1 比率形式

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  比率形式

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  Ratios
  ::比率比率比率

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  A ratio is a way to compare two numbers. Ratios can be written in three ways: $\begin{array}{r}\frac{a}{b}\end{array}$ , $\begin{array}{r}a:b\end{array}$ , and $\begin{array}{r}a\end{array}$ to $\begin{array}{r}b\end{array}$ .
  ::比率是比较两个数字的一种方法。 比率可以用三种方式来表示: ab、 a. b、 a. b. a. 和 b. 。

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  We always reduce ratios just like fractions. When two or more ratios reduce to the same ratio they are called equivalent ratios . For example, 50:250 and 2:10 are equivalent ratios because they both reduce to 1:5.
  ::我们总是像分数一样降低比率。 当两个或两个以上比率降低到同一比率时,它们被称为等值比率。 比如,50:250和2:10是等值比率,因为它们都下降到1:5。

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  One common use of ratios is as a way to convert measurements.
  ::比率的一个常见用途是转换测量数据。

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  What if you were told that there were 15 birds on a pond and that the ratio of ducks to geese is 2:3? How could you determine how many ducks and how many geese are on the pond?
  ::如果有人告诉你池塘里有15只鸟,鸭子与鹅的比例是2: 3呢?你怎么确定池塘里有多少鸭子和多少鹅?

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  Examples
  ::实例

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  For Examples 1 and 2, use the following information:
  ::关于例1和例2,请使用以下信息:

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  The total bagel sales at a bagel shop for Monday is in the table below.
  ::星期一百吉饼店的百吉饼销售总额见下表。

  Type of Bagel	Number Sold
  Plain	80
  Cinnamon Raisin	30
  Sesame	25
  Jalapeno Cheddar	20
  Everything	45
  Honey Wheat	50

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  Example 1
  ::例1

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  What is the ratio of honey wheat bagels to total bagels sold?
  ::蜂蜜小麦百吉饼与销售总百吉饼的比例是多少?

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  Order matters. Honey wheat is listed first, so that number comes first in the ratio (or on the top of the fraction). Find the total number of bagels sold, $\begin{array}{r}80+30+25+20+45+50=250\end{array}$ .
  ::顺序 。 蜜麦首先列出, 因此数字在比例( 或分数的顶部) 中位居首位 。 查找销售的百吉饼总数, 80+30+25+20+45+50=250。

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  The ratio is $\begin{array}{r}\frac{50}{250}=\frac{1}{5}\end{array}$ .
  ::比率为50250=15。

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  Example 2
  ::例2

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  What is the ratio of cinnamon raisin bagels to sesame bagels to jalapeno cheddar bagels?
  ::肉桂葡萄干百吉饼与芝麻面包的比例是多少?

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  You can have ratios that compare more than two numbers and they work just the same way. The ratio for this problem is 30:25:20, which reduces to 6:5:4.
  ::您可以拥有两个以上数字的比较比率, 并且它们的工作方式相同。 这个问题的比重是 30: 25: 20, 降为 6: 5: 4 。

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  Example 3
  ::例3

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  There are 14 girls and 18 boys in your math class. What is the ratio of girls to boys?
  ::你们的数学班有14名女生和18名男生,女生与男生的比例是多少?

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  Remember that order matters. The question asked for the ratio of girls to boys . The ratio would be 14:18. This can be simplified to 7:9.
  ::问题涉及女孩与男孩的比例,比例为14:18,可以简化为7:9。

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  Example 4
  ::例4

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  Simplify the following ratios.
  ::简化以下比率。

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  1. $\begin{array}{r}\frac{7ft}{14in}\end{array}$
     ::7吨14英寸

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   Change the ratio so that each part is in the same units. Remember that there are  12 inches in a foot.
  ::更改比例, 使每部分都在同一单位。 请记住每英尺有12英寸的宽度 。

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  $$\begin{array}{r}\frac{7\bcancel{ft}}{14\cancel{in}}\cdot \frac{12\cancel{in}}{1\bcancel{ft}}=\frac{84}{14}=\frac{6}{1}\end{array}$$

  
  ::1英尺=8414=61

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   The inches and feet cancel each other out. Simplified ratios do not have units.
  ::英寸和脚互相取消。 简化比率没有单位 。

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  2. 9m:900cm
     ::9时:900厘米

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   Change the ratio so that each part is in the same units. It is easier to simplify a ratio  when written as a fraction.
  ::修改比例, 使每个部分都在同一单位中。 将比例写成分数更容易简化 。

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  $$\begin{array}{r}\frac{9\bcancel{m}}{900\cancel{cm}}\cdot \frac{100\cancel{cm}}{1\bcancel{m}}=\frac{900}{900}=\frac{1}{1}\end{array}$$

  
  ::9m900厘米/100厘米/厘米1米=900900=11

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  3. $\begin{array}{r}\frac{4gal}{16gal}\end{array}$
     ::4千16千 4千16千

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   Change the ratio so that each part is in the same units.
  ::修改比例,使每个部分都在同一单位。

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  $$\begin{array}{r}\frac{4\bcancel{gal}}{16\bcancel{gal}}=\frac{1}{4}\end{array}$$

  
  ::4个16个14个14个16个14个16个14个14个14个

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  Example 5
  ::例5

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  A talent show has dancers and singers. The ratio of dancers to singers is 3:2. There are 30 performers total, how many of each are there?
  ::舞蹈演员与歌手的比例是3: 2,共有30名表演者,其中各有多少人?

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  To solve, notice that 3:2 is a reduced ratio, so there is a number, $\begin{array}{r}n\end{array}$ , that we can multiply both by to find the total number in each group. Represent dancers and singers as expressions in terms of $\begin{array}{r}n\end{array}$ . Then set up and solve an equation.
  ::要解决,请注意 3: 2 是减少比率, 因此有一个数字, n, 我们可以乘以两个数字, 以找到每个组的总数字。 以 n 表示舞者与歌手。 然后设置并解析一个方程 。

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  $$\begin{array}{rl}\text{dancers}=3n,\text{singers}=2n⟶3n+2n& =30\\ 5n& =30\\ n& =6\end{array}$$

  
  ::舞者=3n,歌手=2n 3n+2n=305n=30n=6

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  There are $\begin{array}{r}3\cdot 6=18\end{array}$ dancers and $\begin{array}{r}2\cdot 6=12\end{array}$ singers.
  ::有3 6=18名舞蹈演员和2 6=12名歌手。

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  Review
  ::回顾

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  1. The votes for president in a club election were: $\begin{array}{r}\text{Smith}:24\text{ Munoz}:32\text{ Park}:20\end{array}$ Find the following ratios and write in simplest form.
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     • Votes for Munoz to Smith
       ::投票支持穆诺兹到史密斯
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     • Votes for Park to Munoz
       ::公园投票给穆诺兹
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     • Votes for Smith to total votes
       ::Smith获得总票数的票数
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     • Votes for Smith to Munoz to Park
       ::选史密斯到穆诺兹到公园
     
     ::在俱乐部选举中,总统的选票是:史密斯:24 穆诺兹:32 朴:20 找到以下比率并以最简单的形式写作。 穆诺兹投给史密斯的选票,史密斯投给穆诺兹,史密斯投给穆诺兹,史密斯投给史密斯,史密斯投给穆诺兹,公园投给史密斯

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  Use the picture to write the following ratios for questions 2-6.
  ::使用图片来写出问题2-6的下列比率。

  

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  $\begin{array}{r}AEFD\text{is a square}ABCD\text{is a rectangle}\end{array}$
  ::AEFD 是一个平方ABCD是一个矩形

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  2. $\begin{array}{r}AE:EF\end{array}$
     ::中英:英英法
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  3. $\begin{array}{r}EB:AB\end{array}$
     ::EB:AB
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  4. $\begin{array}{r}DF:FC\end{array}$
     ::DF:FC
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  5. $\begin{array}{r}EF:BC\end{array}$
     ::英法:BC
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  6. Perimeter $\begin{array}{r}ABCD\end{array}$ :Perimeter $\begin{array}{r}AEFD\end{array}$ :Perimeter $\begin{array}{r}EBCF\end{array}$
     ::ABCD: AEFD: EBCFF 精密铀化铀化铀化铀化铀化铀化铀

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  Simplify the following ratios. Remember that there are 12 inches in a foot, 3 feet in a yard, and 100 centimeters in a meter.
  ::简化以下比例。 记住, 一英尺有12英寸, 院子里有3英尺, 和一米有100厘米。

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  7. $\begin{array}{r}\frac{25in}{5ft}\end{array}$
     ::25英寸5英尺
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  8. $\begin{array}{r}\frac{9ft}{3yd}\end{array}$
     ::9英尺3 yd
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  9. $\begin{array}{r}\frac{95cm}{1.5m}\end{array}$
     ::95厘米1.5米

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  10. The measures of the angles of a triangle are have the ratio 3:3:4. What are the measures of the angles?
      ::三角形角度的度量为3:3:4。角度的度量是多少?
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  11. The length and width of a rectangle are in a 3:5 ratio. The perimeter of the rectangle is 64. What are the length and width?
      ::矩形的长度和宽度为 3 : 5 之比。 矩形的周边是 64 。 长度和宽度是多少 ?
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  12. The length and width of a rectangle are in a 4:7 ratio. The perimeter of the rectangle is 352. What are the length and width?
      ::矩形的长度和宽度为 4 : 7 之比。 矩形的周边是 352 。 长度和宽度是多少 ?
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  13. A math class has 36 students. The ratio of boys to girls is 4:5. How many girls are in the class?
      ::数学班有36名学生,男生与女生的比例是4:5。
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  14. The senior class has 450 students in it. The ratio of boys to girls is 8:7. How many boys are in the senior class?
      ::高中有450名学生,男生与女生的比例是8:7,高中有多少男生?
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  15. The varsity football team has 50 players. The ratio of seniors to juniors is 3:2. How many seniors are on the team?
      ::大学足球队有50个球员,高年级和初中的比例是3比2, 有多少高年级队员?

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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