课程： 5.8 使用百分率来查找百分率

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选择节使用百分数来查找百分比

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使用百分数来查找百分比
Donna is framing a picture with a blue border. Her picture has an area of 400 square inches. After framing with the border, Donna wants her final framed picture to be 1200 square inches. What percent of the final size is her original picture?
::唐娜在设计一张蓝色边界的图片。她的照片有400平方英寸的面积。在与边界的构造之后,唐娜希望她的最后一张相框是1200平方英寸。她的原始照片占最终大小的多少比例?

In this concept, you will use the percent equation to find a percent.
::在这个概念中,你将使用百分比方程来找到百分之一。

Percent Equation
::百分比等量

You can use the proportion $\begin{align*}\frac{a}{b}= \frac{p}{100}\end{align*}$ to solve for a percent. You can also solve by using an equation. In this concept, you will use a proportion to create a different kind of equation that will help you solve percent problems.
::您可以使用比例 ab=p100 来解答一个百分比。您也可以使用方程式解答一个百分比。在此概念中,您将使用一个比例来创建一种不同的方程式,帮助您解答百分比问题。

To find percent, you know that the number being compared ( $\begin{align*}a\end{align*}$ ) to the base ( $\begin{align*}b\end{align*}$ ) is equal to the percent ( $\begin{align*}p\end{align*}$ ).
::要找到百分比,你知道,与(a)和(b)相比的数字等于(p)的百分比。

Therefore the equation to use is:
::因此,需要使用的方程式是:

$\begin{aligned} a = \frac{p}{100} \times b \end{aligned}$
$\begin{align*}a = \frac{p}{100} \times b\end{align*}$
::a=p100xb =p100xb

Let’s look at a problem.
::让我们来看看一个问题。

What percent of 32 is 18?
::32%是18?

First, you know that you are looking for a percent. You want to set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,你知道你正在寻找百分之一。你想设置百分比方程式来解决p。

$\begin{aligned} 18 = \frac{p}{100} \times 32 \end{aligned}$
$\begin{align*}18 = \frac{p}{100} \times 32\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 32.
::18=p100x32 下一步,通过将两边除以32来解析 p100 的值。

$\begin{aligned} \begin{array}{rcl} 18 & = & \frac{32 p}{100} \\ \frac{18}{32} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.5625 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 18 &=& \frac{32p}{100}\\ \frac{18}{32} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.5625 \end{array}\end{align*}$ Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::18=32p1001832=p100p100=0.5625 然后 p, 解答百分率, 以两边乘以100 的方式解决百分率。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.5625 \\ 100 \times \frac{p}{100} & = & 0.5625 \times 100 \\ p & = & 56.25 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.5625\\ 100 \times \frac{p}{100} &=& 0.5625 \times 100\\ p &=& 56.25 \end{array}\end{align*}$ The answer is 56.25%.
::p100=0.5625100×p100=0.5625×100p=56.25。答案为56.25%。

Therefore, 18 is 56.25% of 32.
::因此,18人占32人的56.25%。

Let’s try another example.
::让我们再试一个例子。

10 is what percent of 12?
::百分之十是12的百分之十吗?

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 10 = \frac{p}{100} \times 12 \end{aligned}$
$\begin{align*}10 = \frac{p}{100} \times 12\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 12.
::10=p100x12 下一步,通过将两边除以12来解析 p100 的值。

$\begin{aligned} \begin{array}{rcl} 10 & = & \frac{12 p}{100} \\ \frac{10}{12} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.833 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 10 &=& \frac{12p}{100}\\ \frac{10}{12} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.833 \end{array}\end{align*}$ Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::10=12p1001012=p100p100=0.833 然后 p, 解答百分比, 以将两边乘以100 。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.833 \\ 100 \times \frac{p}{100} & = & 0.833 \times 100 \\ p & = & 83.3 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.833\\ 100 \times \frac{p}{100} &=& 0.833 \times 100\\ p &=& 83.3 \end{array}\end{align*}$ The answer is 83.3%.
::p100=0.833100xp100=0.833x100p=0.833x100p=83.3 答案为83.3%。

Therefore, 10 is 83.3% of 12.
::因此,10人占12人的83.3%。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Donna and her frame.
::早些时候,你得到一个问题关于唐娜和她的框框。

Donna’s picture is 400 square inches and the final framed picture is 1200 square inches. She wants to know what percent of the final framed picture is her photo.
::唐娜的图片是400平方英寸,最后的图片是1200平方英寸。她想知道最后的图片中有多少是她的照片。

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 400 = \frac{p}{100} \times 1200 \end{aligned}$
$\begin{align*}400 = \frac{p}{100} \times 1200\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 1200.
::400=p100x1200 下一个,通过将两边除以 1200 来解析 p100 的值。

$\begin{aligned} \begin{array}{rcl} 400 & = & \frac{1200 p}{100} \\ \frac{400}{1200} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.333 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 400 &=& \frac{1200p}{100}\\ \frac{400}{1200} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.333 \end{array}\end{align*}$
::400=1200p100001200=p100p100=0.333

Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::然后,解决p, 百分率通过乘以双方100。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.333 \\ 100 \times \frac{p}{100} & = & 0.333 \times 100 \\ p & = & 33.3 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.333\\ 100 \times \frac{p}{100} &=& 0.333 \times 100\\ p &=& 33.3 \end{array}\end{align*}$ The answer is 33.3%.
::p100=0.333100xp100=0.333x100p=33.3 答案是33.3%。

Therefore, Donna’s original picture represents 33.3% of the final framed picture.
::因此,唐娜的原始图片占最终图象的33.3%。

Example 2
::例2

33 is what percent of 50?
::33%是50的几率?

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 33 = \frac{p}{100} \times 50 \end{aligned}$
$\begin{align*}33 = \frac{p}{100} \times 50\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 50.
::33=p100x50 下一步,通过将两边除以50来解决 p100 的值。

$\begin{aligned} \begin{array}{rcl} 33 & = & \frac{50 p}{100} \\ \frac{33}{50} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.66 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 33 &=& \frac{50p}{100}\\ \frac{33}{50} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.66 \end{array}\end{align*}$
::33=50p1003350=p100p100=0.66

Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::然后,解决p, 百分率通过乘以双方100。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.66 \\ 100 \times \frac{p}{100} & = & 0.66 \times 100 \\ p & = & 66 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.66\\ 100 \times \frac{p}{100} &=& 0.66 \times 100\\ p &=& 66 \end{array}\end{align*}$ The answer is 66%.
::p100=0.66100×p100=0.66×100p=66 答案是66%。

Therefore, 33 is 66% of 50.
::因此,33是50的66%。

Example 3
::例3

18 is what percent of 20?
::18是20的多少? 18是20的多少?

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 18 = \frac{p}{100} \times 20 \end{aligned}$
$\begin{align*}18 = \frac{p}{100} \times 20\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 20.
::18=p100x20 下一步,通过将两边除以20来解析 p100 的值。

$\begin{aligned} \begin{array}{rcl} 18 & = & \frac{20 p}{100} \\ \frac{18}{20} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.9 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 18 &=& \frac{20p}{100}\\ \frac{18}{20} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.9 \end{array}\end{align*}$ Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::18=20p1001820=p100p100=0.9 然后 p, 以将两边乘以100 来解答百分比。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.9 \\ 100 \times \frac{p}{100} & = & 0.9 \times 100 \\ p & = & 90 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.9\\ 100 \times \frac{p}{100} &=& 0.9 \times 100\\ p &=& 90 \end{array}\end{align*}$
::p100=0.9100×p100=0.9×100p=90

The answer is 90%.
::答案是90%。

Therefore, 18 is 90% of 20.
::因此,18是20的90%。

Example 4
::例4

5 is what percent of 300?
::300的5%是多少?

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 5 = \frac{p}{100} \times 300 \end{aligned}$
$\begin{align*}5 = \frac{p}{100} \times 300\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 300.
::5=p100x300 下一步,通过将两边除以300来解析 p100 的值。

$\begin{aligned} \begin{array}{rcl} 5 & = & \frac{300 p}{100} \\ \frac{5}{300} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.0167 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 5 &=& \frac{300p}{100}\\ \frac{5}{300} &=& \frac{p}{100}\\ \frac{p}{100} &=& 0.0167 \end{array}\end{align*}$
::5=300p1005300=p100p100=0.0167

Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::然后,解决p, 百分率通过乘以双方100。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.0167 \\ 100 \times \frac{p}{100} & = & 0.0167 \times 100 \\ p & = & 1.67 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.0167\\ 100 \times \frac{p}{100} &=& 0.0167 \times 100\\ p &=& 1.67 \end{array}\end{align*}$ The answer is 1.67%.
::p100=0.0167100×p100=0.0167×100p=0.167×100p=1.67 答案是1.67%。

Therefore, 5 is 1.67% of 300.
::因此,5是300的1.67%。

Example 5
::例5

60 is what percent of 400?
::400的60%是多少?

First, set up the percent equation to solve for $\begin{align*}p\end{align*}$ .
::首先,设置百分比方程式解决p。

$\begin{aligned} 60 = \frac{p}{100} \times 400 \end{aligned}$
$\begin{align*}60 = \frac{p}{100} \times 400\end{align*}$
Next, solve for the value of $\begin{align*}\frac{p}{100}\end{align*}$ by dividing both sides by 400.
::60=p100x400 下一个,通过将两边除以400来解析 p100 值的 p100 。

$\begin{aligned} \begin{array}{rcl} 60 & = & \frac{400 p}{100} \\ \frac{60}{400} & = & \frac{p}{100} \\ \frac{p}{100} & = & 0.15 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 60 &=& \frac{400p}{100}\\ \frac{60}{400} &=& \frac{p}{100}\\\ \frac{p}{100} &=& 0.15 \end{array}\end{align*}$
::60=400p10060400p100p100=0.15

Then, solve for $\begin{align*}p\end{align*}$ , the percent by multiplying both sides by 100.
::然后,解决p, 百分率通过乘以双方100。

$\begin{aligned} \begin{array}{rcl} \frac{p}{100} & = & 0.15 \\ 100 \times \frac{p}{100} & = & 0.15 \times 100 \\ p & = & 15 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \frac{p}{100} &=& 0.15\\ 100 \times \frac{p}{100} &=& 0.15 \times 100\\ p &=& 15 \end{array}\end{align*}$ The answer is 15%.
::p100=0.15100×p100=0.15×100p=15 答案是15%。

Therefore, 60 is 15% of 400.
::因此,60是400的15%。

Review
::回顾

Solve each percent problem by using the percent equation. You may round when necessary. Round your answers to the nearest whole percentage point.
::通过使用百分比方程式来解决每个百分比的问题。您可以在必要的时候圆圆。将答案四舍五入到最近的整个百分点。

What percent of 600 is 82?
::六百分之八十二是多少?

What percent of 18 is 17?
::18分中哪分是17分?

150 is what percent of 175?
::175的150%是多少?

200 is what percent of 450?
::200是450的多少?

34 is what percent of 70?
::34是70的几率?

12 is what percent of 88?
::百分之12是八十八的百分之十二吗?

15 is what percent of 90?
::15是90的百分之十五吗?

230 is what percent of 600?
::600的230是多少?

334 is what percent of 1000?
::千分之334是多少?

2 is what percent of 8?
::2%是8的百分之二吗?

55 is what percent of 1800?
::1800年的55%是多少?

61 is what percent of 80?
::61%是80的几率?

33 is what percent of 90?
::33%是90的几率?

78 is what percent of 156?
::156的78%是多少?

19 is what percent of 31?
::百分之19是31的百分之19吗?

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

章节大纲

常规

使用百分数来查找百分比

Percent Equation ::百分比等量

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

Percent Equation
::百分比等量

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