Course: 5.5 使用比例来查找百分比

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使用比例来查找百分比
A senator wants to start a program to encourage more people to vote in his state. In County A, of the 39150 potential voters, 32,100 people voted. In neighboring County B, of the 81400 potential voters, 57,800 people voted. Which county needs the program more?
::一位参议员想要启动一个鼓励更多人在他的州投票的方案。在A县,39150个潜在选民中有32,100人投票。在邻近的B县,8,1400个潜在选民中有57,800人投票。哪个县更需要这个方案?

In this concept, you will use proportions to figure out percent.
::在这个概念中,你将使用比例来计算百分比。

Proportions
::比例比例

A percent is a part of a whole that represents a quantity out of 100. Fractions and decimals are also parts of a whole. Sometimes, you will be given information, but not a percent. You will need to know how to figure out the percent. Percentages, fractions, decimals and proportions can all help to you solve problems and figure out percent.
::A%是整体的一部分,代表了100中的数量。小数和小数也是整体的一部分。有时,你会得到信息,但不会得到1%。你需要知道如何解答百分比。百分数、分数、小数和比例都有助于解决问题和找出百分比。

You began using proportions to figure out a percent when writing fractions as percent. Remember that proportions involve comparing quantities. A proportion is a comparison between two equal ratios . Because both of these are comparing, you can use proportions to help us figure out a percent.
::您开始使用比例来计算写分数时的百分数百分比。记住该比例涉及比较数量。一个比例是两个等值比率之间的比较。由于这两个比例都在比较, 您可以使用比例来帮助我们找出一个百分比。

First, write the proportion using $\begin{align*}a\end{align*}$ over $\begin{align*}b\end{align*}$ .
::首先,用 b 以上来写比例。

$\begin{aligned} \frac{a}{b} \end{aligned}$
$\begin{align*}\frac{a}{b}\end{align*}$
::ab 年 ab

This is equal to the percent which is out of 100.
::这等于百分率的百分率

$\begin{aligned} \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{p}{100}\end{align*}$
::p100 p100 (p100)

Here is the proportion:
::比例如下:

$\begin{aligned} \frac{a}{b} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{a}{b} =\frac{p}{100}\end{align*}$
::ab=p100 (b=p100)

Now let’s apply this proportion to a problem.
::现在让我们对问题应用这个比例。

What percent is 12 out of 45?
::45分之12是多少?

First, write a ratio comparing your given values to the missing percent.
::首先,写一个比例,比较给定的数值和缺失的百分率。

$\begin{aligned} \frac{12}{45} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{12}{45} =\frac{p}{100} \end{align*}$
::1245=p100

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{12}{45} & = & \frac{p}{100} \\ 45 \times p & = & 12 \times 100 \\ 45 \times p & = & 1200 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{12}{45} &=& \frac{p}{100} \\ 45 \times p &=& 12 \times 100 \\ 45 \times p &=& 1200 \end{array}\end{align*}$
::1245=p10045×p=12×10045×p=1200

Then, divide by 45 to isolate $\begin{align*}p\end{align*}$ .
::然后除以45 隔开p

$\begin{aligned} \begin{array}{rcl} 45 \times p & = & 1200 \\ \frac{45 p}{45} & = & \frac{1200}{45} \\ p & = & 26.7 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 45 \times p &=& 1200 \\ \frac{45p}{45}&=& \frac{1200}{45} \\ p&=& 26.7 \end{array}\end{align*}$
::45×p=120045p45=120045p=26.7

The answer is 26.7.
::答案是26.7。

Therefore 12 out of 45 is 26.7%.
::因此,45人中有12人占26.7%。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about the voters.
::早些时候,你对选民有问题

County A has 39150 people and 32100 voted. County B has 81400 people and 57800 voted. Which county had the highest proportion of people voting?
::A县有39150人,32100人投票,B县有81400人,57800人投票,哪个县的投票率最高?

First, write each ratio comparing your given values to the missing percent.
::首先,写下您给定的数值与缺失的百分率之间的每一比率。

County A
::县A

$\begin{aligned} \frac{32100}{39150} = \frac{p}{100} \end{aligned}$
$\begin{align*}\quad \ \frac{32100}{39150} = \frac{p}{100} \end{align*}$
::321000039150=p100

County B
::县B

$\begin{aligned} \frac{57800}{81400} = \frac{p}{100} \end{aligned}$
$\begin{align*}\quad \ \frac{57800}{81400} = \frac{p}{100}\end{align*}$
::5780081400=p100

Next, cross multiply.
::下一个,交叉乘数。

County A
::县A

$\begin{aligned} \begin{array}{rcl} \frac{32100}{39150} & = & \frac{p}{100} \\ 39150 \times p & = & 32100 \times 100 \\ 39150 \times p & = & 3210000 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \quad \ \frac{32100}{39150} &=& \frac{p}{100} \\ 39150 \times p &=& 32100 \times 100 \\ 39150 \times p &=& 3210000 \end{array}\end{align*}$ County B
::3220039150=p10039150×p=32100×10039150×p=321000

$\begin{aligned} \begin{array}{rcl} \frac{57800}{81400} & = & \frac{p}{100} \\ 81400 \times p & = & 57800 \times 100 \\ 81400 \times p & = & 5780000 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \quad \ \frac{57800}{81400} &=& \frac{p}{100} \\ 81400 \times p &=& 57800 \times 100 \\ 81400 \times p &=& 5780000 \end{array}\end{align*}$
::57808-1400=p10081400×p=57800×10081400×p=57800×5780000

Then, divide to isolate $\begin{align*}p\end{align*}$ .
::然后,分开隔离p。

County A
::县A

$\begin{aligned} \begin{array}{rcl} 39150 \times p & = & 3210000 \\ \frac{39150 p}{39150} & = & \frac{3210000}{39150} \\ p & = & 81.99 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 39150 \times p &=& 3210000 \\ \quad \frac{39150 p}{39150} &=& \frac{3210000}{39150} \\ \qquad \qquad p &=& 81.99 \end{array} \end{align*}$
::39150xp=32100039150p39150=32100039150p=81.99

County B
::县B

$\begin{aligned} \begin{array}{rcl} 81400 \times p & = & 5780000 \\ \frac{81400 p}{81400} & = & \frac{5780000}{81400} \\ p & = & 71.0 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 81400 \times p &=& 5780000 \\ \quad \frac{81400 p}{81400} &=& \frac{5780000}{81400} \\ \qquad \qquad p &=& 71.0 \end{array}\end{align*}$
::81400×p=5780000814000p81400=578000081400=578000081400p=71.0

The answer is that 82% of the people in County A voted and 71% of the people in County B voted. Therefore, County A had the highest voter turnout and County B needs the senator’s program more.
::答案是82%的A县人投票,71%的B县人投票。因此,A县的选民投票率最高,B县更需要参议员的计划。

Example 2
::例2

John ran 8 out of 9 miles. What percent of the total miles did he run ?
::约翰在9英里外跑8英里他跑的英里占总里程的多少?

First, write a ratio comparing your given values to the missing percent.
::首先,写一个比例,比较给定的数值和缺失的百分率。

$\begin{aligned} \frac{8}{9} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{8}{9} =\frac{p}{100} \end{align*}$
::89=p100

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{8}{9} & = & \frac{p}{100} \\ 9 \times p & = & 8 \times 100 \\ 9 \times p & = & 800 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{8}{9} &=& \frac{p}{100} \\ 9 \times p &=& 8 \times 100 \\ 9 \times p &=& 800 \end{array}\end{align*}$
::89=p1009xp=8x1009xp=800

Then, divide by 9 to isolate $\begin{align*}p\end{align*}$ .
::然后除以9 隔开p

$\begin{aligned} \begin{array}{rcl} 9 \times p & = & 800 \\ \frac{9 p}{9} & = & \frac{800}{9} \\ p & = & 88.9 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} 9 \times p &=& 800 \\ \frac{9p}{9}&=& \frac{800}{9} \\ p&=& 88.9 \end{array}\end{align*}$
::9×p=8009p9=8009p=88.9

The answer is 88.9.
::答案是88.9

Therefore, John ran 88.9% of the total miles.
::因此,约翰跑出了总英里的88.9%。

Example 3
::例3

What percent is 18 out of 50?
::50分的18分是多少?

First, write a ratio comparing your given values to the missing percent.
::首先,写一个比例,比较给定的数值和缺失的百分率。

$\begin{aligned} \frac{18}{50} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{18}{50} =\frac{p}{100} \end{align*}$
::1850=p100

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{18}{50} & = & \frac{p}{100} \\ 50 \times p & = & 18 \times 100 \\ 50 \times p & = & 1800 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{18}{50} &=& \frac{p}{100} \\ 50 \times p &=& 18 \times 100 \\ 50 \times p &=& 1800 \end{array}\end{align*}$
::1850=p10050xp=18x10050xp=1800

Then, divide by 50 to isolate $\begin{align*}p\end{align*}$ .
::然后除以50 隔开p

$\begin{aligned} \begin{array}{rcl} 50 \times p & = & 1800 \\ \frac{50 p}{50} & = & \frac{1800}{50} \\ p & = & 36 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 50 \times p &=& 1800 \\ \frac{50p}{50}&=& \frac{1800}{50} \\ p&=& 36 \end{array}\end{align*}$
:=180050p50=180050p36

The answer is 36. Therefore 18 out of 50 is 36%.
::答案是36,因此,50人中有18人占36%。

Example 4
::例4

What percent is 22 out of 40?
::40分中的22分是多少?

First, write a ratio comparing your given values to the missing percent.
::首先,写一个比例,比较给定的数值和缺失的百分率。

$\begin{aligned} \frac{22}{40} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{22}{40} =\frac{p}{100} \end{align*}$
::2240=p100

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{22}{40} & = & \frac{p}{100} \\ 40 \times p & = & 22 \times 100 \\ 40 \times p & = & 2200 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{22}{40} &=& \frac{p}{100} \\ 40 \times p &=& 22 \times 100 \\ 40 \times p &=& 2200 \end{array}\end{align*}$
::2240=p10040xp=22x10040xp=2200

Then, divide by 40 to isolate $\begin{align*}p\end{align*}$ .
::然后除以40 隔开p

$\begin{aligned} \begin{array}{rcl} 40 \times p & = & 2200 \\ \frac{40 p}{40} & = & \frac{2200}{40} \\ p & = & 55 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 40 \times p &=& 2200 \\ \frac{40p}{40}&=& \frac{2200}{40} \\ p&=& 55 \end{array}\end{align*}$
::40×p=220040p40=220040p=55

The answer is 55.
::答案是55岁

Therefore 22 out of 40 is 55%.
::因此,40人中有22人占55%。

Example 5
::例5

What percent is 78 out of 80?
::80分中78分是多少?

First, write a ratio comparing your given values to the missing percent.
::首先,写一个比例,比较给定的数值和缺失的百分率。

$\begin{aligned} \frac{78}{80} = \frac{p}{100} \end{aligned}$
$\begin{align*}\frac{78}{80} =\frac{p}{100} \end{align*}$
::7880=p100

Next, cross multiply.
::下一个,交叉乘数。

$\begin{aligned} \begin{array}{rcl} \frac{78}{80} & = & \frac{p}{100} \\ 80 \times p & = & 78 \times 100 \\ 80 \times p & = & 7800 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} \frac{78}{80} &=& \frac{p}{100} \\ 80 \times p &=& 78 \times 100 \\ 80 \times p &=& 7800 \end{array}\end{align*}$
::7880=p10080xp=78x10080xp=7800

Then, divide by 80 to isolate $\begin{align*}p\end{align*}$ .
::然后除以80 隔开p

$\begin{aligned} \begin{array}{rcl} 80 \times p & = & 7800 \\ \frac{80 p}{80} & = & \frac{7800}{80} \\ p & = & 97.5 \end{array} \end{aligned}$
$\begin{align*} \begin{array}{rcl} 80 \times p &=& 7800 \\ \frac{80p}{80}&=& \frac{7800}{80} \\ p&=& 97.5 \end{array}\end{align*}$
::80xp=780080p80=780080p=97.5

The answer is 97.5.
::答案是97.5

Therefore 78 out of 80 is 97.5%.
::因此,80人中有78人占97.5%。

Review
::回顾

Find $\begin{align*}p\end{align*}$ in the given problems using cross product. Round to the nearest tenths place.
::使用交叉产品在给定问题中查找 p。圆到最近的十分位。

1. $\begin{align*}\frac{7}{15} = \frac{p}{100}\end{align*}$
::1. 715=p100

2. $\begin{align*}\frac{52}{3810} = \frac{p}{100}\end{align*}$
::2. 523810=p100

3. $\begin{align*}\frac{16}{17} = \frac{p}{100}\end{align*}$
::3. 1617=p100

4. $\begin{align*}\frac{3}{4} = \frac{p}{100}\end{align*}$
::4. 34=p100

5. $\begin{align*}\frac{3}{5} = \frac{p}{100}\end{align*}$
::5. 35=p100

6. $\begin{align*}\frac{1}{5} = \frac{p}{100}\end{align*}$
::6. 15=p100

7. A dentist filled cavities in 8 of his 30 patients on Tuesday. What percent had cavities filled?
::7. 星期二,30名病人中有8名是牙医,其中8名是牙医。

8. A florist delivered 18 out of 25 bouquets. What percent was delivered?
::8. 花店交付了25个花束中的18个,交付的百分比是多少?

9. The baker sold 3 out of 4 dozen rolls. What percent was sold?
::9. 面包师出售了40个卷中的3个卷,售出的百分比是多少?

10. What percent is 85 out of 5000?
::五千块的百分之八十五是百分之十?

11. What percent is 15 out of 30?
::30人中有15人占11个百分点?

12. What percent is 88 out of 1200?
::1200人中,88人占12.0%?

13. What percent is 99 out of 200?
::200人中有百分之九十九是百分之三十三?

14. What percent is 100 out of 330?
::330人中,百分之百是百分之十四?

15. What percent is 224 out of 5400?
::5400分中224分占15%?

Review (Answers)
::回顾(答复)

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。

Resources
::资源

Section outline

General

使用比例来查找百分比

Proportions ::比例比例

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Proportions
::比例比例

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源