Section: 查找下降百分比 | 5.11 找出下降的百分比

Section outline

Manny is looking to buy a new pair of sneakers. He really wants a designer pair, but they usually cost $165.00. Today, Manny walks past a store and notices that the shows he wants are on sale for $115.50. What is the percent of the decrease?
::曼尼想要买一双新的运动鞋。他真的想要一对设计师的鞋,但通常要花165美元。今天,曼尼走过一家商店,注意到他想要的节目以115.50美元出售。减幅的几率是多少?

In this concept, you will learn to find the percent of decrease.
::在这个概念中,你会学会找到下降的百分比。

Percent of Decrease
::下降百分比

When you have an amount decreasing, you can always calculate the percent of decrease. The percent of decrease is the percent that a value decreases. To find the percent of decrease, divide the amount of decrease by the original amount and multiply by 100. In other words:
::当数量下降时,您总是可以计算下降的%。下降的%是数值下降的%。要找到下降的%,将减少的金额除以原来的数额,再乘以100。换句话说:

$\begin{aligned} percent of decrease = \frac{amount of decrease}{original amount} \times 100 \end{aligned}$
$\begin{align*}\text{percent of decrease} = \frac{\text{amount of decrease}}{\text{original amount}} \times 100\end{align*}$
::原数×100 原数×100

Let’s look at an example where there is a percent of decrease.
::让我们看看一个下降百分比的例子。

A helicopter’s altitude went from 350 feet to 38 feet. This was a difference of 312 feet. By what percent did the altitude decrease?
::直升机的高度从350英尺下降到38英尺,相差312英尺。以什么比例的高度下降?

Use the formula to find the percent of decrease.
::使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{312}{350} \times 100 \\ percent of decrease & = & 89.14 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{312}{350} \times 100 \\ \text{percent of decrease} &=& 89.14 \% \end{array}\end{align*}$
::原原数 x 100% 原数 = 312350 × 降 = 89.14% 原数 = 312350 × 降 = 89.14%

The answer is 89.14%.
::答案是89.14%。

The helicopter has a percent of decrease in altitude by 89.14%.
::直升机的高度下降了89.14%。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Manny’s search for shoes.
::更早之前, 曼尼在寻找鞋子时,

The original price of the sneakers was $165 but Manny finds them on sale for $115.50. Manny wants to figure out the percent of the decrease.
::运动鞋的原价为165美元,但曼尼发现它们以115.50美元的价格出售。曼尼想弄清楚减价的多少。

First, find the difference.
::首先,找出差别

$\begin{aligned} 165 - 115.5 = 49.5 \end{aligned}$
$\begin{align*}165-115.5=49.5\end{align*}$

Next, use the formula to find the percent of decrease.
::接下来,使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{49.5}{165} \times 100 \\ percent of decrease & = & 30 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{49.5}{165} \times 100 \\ \text{percent of decrease} &=& 30 \% \end{array}\end{align*}$
::原数============================================================================================================100==============================100===============================================100=====================================================================================================================================================

The answer is 30%.
::答案是30%。

Therefore, the sneakers are on sale 30% off.
::因此,运动鞋售价为30%。

Example 2
::例2

What is the percent of decrease from 2500 to 400?
::从2500到400的下降比例是多少?

First, find the difference.
::首先,找出差别

$\begin{aligned} 2500 - 400 = 2100 \end{aligned}$
$\begin{align*}2500 - 400 =2100\end{align*}$

Next, use the formula to find the percent of decrease.
::接下来,使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{2100}{2500} \times 100 \\ percent of decrease & = & 84 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{2100}{2500} \times 100 \\ \text{percent of decrease} &=& 84 \% \end{array}\end{align*}$
::原原数 x 百数 = 20.002500× 百数 = 84% 原数 x 百数 = 20.002500× 100 百数 = 84% 原数 x 百数 = 20.002500× 100 百数减 = 84% 原数 x 百数 = 20.002500× 100 百数 = 84%

The answer is 84%.
::答案是84%。

Example 3
::例3

Find each percent of decrease from 80 to 30.
::找出从80到30的下降的每一个百分比。

First, find the difference.
::首先,找出差别

$\begin{aligned} 80 - 30 = 50 \end{aligned}$
$\begin{align*}80 - 30=50\end{align*}$

Next, use the formula to find the percent of decrease.
::接下来,使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{50}{80} \times 100 \\ percent of decrease & = & 62.5 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{50}{80} \times 100 \\ \text{percent of decrease} &=& 62.5 \% \end{array}\end{align*}$
::原原数 x 100% 原数 = 5080× 降 = 62.5% 原数 x 原数 = 5080× 降 = 62.5% 原数 x 原数 = 5080× 降降 = 62.5%

The answer is 62.5%.
::答案是62.5%。

Example 4
::例4

Find each percent of decrease from 90 to 40.
::找出从90到40的下降的每一个百分比。

First, find the difference.
::首先,找出差别

$\begin{aligned} 90 - 40 = 50 \end{aligned}$
$\begin{align*}90-40=50\end{align*}$

Next, use the formula to find the percent of decrease.
::接下来,使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{50}{90} \times 100 \\ percent of decrease & = & 55.6 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{50}{90} \times 100 \\ \text{percent of decrease} &=& 55.6 \% \end{array}\end{align*}$
::原原数 x 100% 原数 = 5090× 降 = 55.6% 原数 x 原数 = 5090× 降 = 55.6% 原数 = 55.6% 原数 x 原数 = 5090× 降降 = 55.6% 原数 = 55.6%

The answer is 55.6%.
::答案是55.6%。

Example 5
::例5

Find each percent of decrease from 130 to 100.
::找出从130到100的下降的每一个百分比。

First, find the difference.
::首先,找出差别

$\begin{aligned} 130 - 100 = 30 \end{aligned}$
$\begin{align*}130-100=30\end{align*}$

Next, use the formula to find the percent of decrease.
::接下来,使用公式来找到下降的百分率。

$\begin{aligned} \begin{array}{rcl} percent of decrease & = & \frac{amount of decrease}{original amount} \times 100 \\ percent of decrease & = & \frac{30}{130} \times 100 \\ percent of decrease & = & 23.1 % \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} \text{percent of decrease} &=& \frac{\text{amount of decrease}}{\text{original amount}} \times 100 \\ \text{percent of decrease} &=& \frac{30}{130} \times 100 \\ \text{percent of decrease} &=& 23.1 \% \end{array}\end{align*}$
::原原数 x 100% 原数 = 30130× 降 = 23.1% 原数 = 30130× 降 = 23.1%

The answer is 23.1%.
::答案是23.1%。

Review
::回顾

Calculate the percent of decrease. You may round to the nearest whole percent.
::计算下降的百分比。您可以圆到最近的整百分比。

From 74 to 35, a decrease of 39
::从74个减至35个,减少39个

From 576 to 476, a decrease of 100
::从576减至476,减少100

From 200 to 175, a decrease of 25
::从200减至175,减少25

From 150 to 100, a decrease of 50
::从150减至100,减少50

From 325 to 290, a decrease of 35
::从325人减至290人,减少35人

From 45 to 18, a decrease of 27
::从45个减至18个,减少27个

From 19 to 1, a decrease of 18
::从19个减至1个,减少18个

From 22 to 10
::22至10

From 34 to 20
::34至20

From 230 to 220
::230至220

From 350 to 250
::350至250

From 700 to 350
::700至350

From 130 to 7
::130至7

From 890 to 700
::890至700

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

Percent of Decrease ::下降百分比

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 of Decrease
::下降百分比

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