Course: 5.3 将百分比写成分数

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将百分比写入分数
Apparently, if you can jump 2 m on Earth, you can jump 12 m on the moon. What percent of the height of a jump on Earth is the height of a jump on the moon?
::显然,如果你能在地球上跳2米,你可以在月球上跳12米。在地球上跳高的几个百分点是月球跳高的几个百分点?

In this concept, you will learn to write percent as fractions and fractions as percent.
::在这个概念中,你将学习以分数和分数来写百分比,以百分数和分数来写百分比。

Percents as Fractions
::百分比作为分数

Percent can be written as ratios with a denominator of 100 or they can be written as decimals. Well, if they can be written as a ratio with a denominator of 100, then those ratios can be simplified as you would simplify any fraction. Likewise, any fraction can be written as a percent using reverse operations.
::百分位数可以以百分位数表示,也可以以十进制表示。如果百分位数可以以百分位数表示,那么这些比例可以简化,因为您可以简化任何分位数。同样,任何分位数也可以使用反向操作以百分位数表示。

To write a percent as a fraction rewrite it as a fraction with a denominator of 100. Then reduce the fraction to its simplest form .
::将一个百分数写成一个分数, 重写成一个分数, 分数为100, 然后将分数减为最简单的形式。

Let’s look at an example.
::让我们举个例子。

Write 22% as a fraction.
::将22%作为一个分数写出来。

First, write this as a fraction with a dominator of 100.
::首先,写成一个分数,由100位主导者组成。

$\begin{aligned} 22 % = \frac{22}{100} \end{aligned}$
$\begin{align*}22\% = \frac{22}{100}\end{align*}$

Next, simplify.
::下一个,简化。

$\begin{aligned} \frac{22}{100} = \frac{11}{50} \end{aligned}$
$\begin{align*}\frac{22}{100} = \frac{11}{50}\end{align*}$

The answer is $\begin{align*}\frac{11}{50}\end{align*}$ .
::22100=1150 答案是1150

To convert a fraction to a percent, first, you need to be sure that the fraction is being compared to a quantity of 100.
::要将分数转换为百分比, 首先, 您需要确定该分数是否与100的分数相对应。

Let’s look at one.
::让我们看一看。

$\begin{aligned} \frac{28}{100} = ? % \end{aligned}$
$\begin{align*}\frac{28}{100} = ? \%\end{align*}$

This means that you have 28 out of 100.
::也就是说,100人中就有28人

Next, this fraction is being compared to 100, so you can simply change it to a percent.
::接下来,这个分数将比作100, 这样你就可以简单地将其改变为1%。

$\begin{aligned} \frac{28}{100} = 28 % \end{aligned}$
$\begin{align*}\frac{28}{100} = 28\% \end{align*}$

Here is another one.
::28100=28% 这里还有一个

Convert $\begin{align*}\frac{3}{5}\end{align*}$ into a percent.
::将35成百分之35变成百分之三十五

First, this fraction is not being compared to 100. It is being compared to 5. You have 3 out of 5. To convert this fraction to a percent, you need to rewrite it as an equal ratio out of 100. You can use proportions to do this. Write this ratio compared to a second ratio out of 100.
::首先,没有将这一分数比作100,而是比作5,5,5,3。要将这一分数转换为1%,您需要将这一分数重写成100的相等比例。您可以使用比例来做到这一点。写下这个比例,而100的第二个比例是100。

$\begin{aligned} \frac{3}{5} = \frac{?}{100} \end{aligned}$
$\begin{align*}\frac{3}{5} = \frac{?}{100}\end{align*}$

Next, use multiplication to create equal ratios or a proportion .
::其次,使用乘法来创造相等比率或比例。

$\begin{aligned} \begin{array}{rcl} 5 \times 200 & = & 100 \\ 3 \times 20 & = & 60 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 5 \times 200 &=& 100 \\ 3 \times 20 &=& 60 \end{array}\end{align*}$

Next, put these together.
::接下来,把这些放在一起。

$\begin{aligned} \frac{3}{5} = \frac{60}{100} \end{aligned}$
$\begin{align*}\frac{3}{5} = \frac{60}{100}\end{align*}$

Then, change the fraction to a percent.
::然后,将分数改变为百分之一。

$\begin{aligned} \frac{60}{100} = 60 % \end{aligned}$
$\begin{align*}\frac{60}{100} = 60\%\end{align*}$

The answer is 60%.
::答案是60%。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about the lunar jump.
::早些时候,有人给了你一个关于月球跳跃的问题。

You know that you can jump 2 m on the earth and 12 m on the moon. You are trying to find the percent of the height on earth compared to the height on the moon.
::你知道,你可以在地球上跳2米,在月球上跳12米。你试图找到与月球高度相比,地球高度的百分率。

First, write a fraction to represent this problem.
::首先,写一个部分来代表这个问题。

$\begin{aligned} \frac{E a r t h}{M o o n} = \frac{2}{12} \end{aligned}$
$\begin{align*}\frac{Earth}{Moon} = \frac{2}{12}\end{align*}$
::地球月文=212

Next, write this as a proportion with a denominator of 100. Start by writing the fraction with $\begin{align*}x\end{align*}$ as the unknown numerator out of 100.
::下一步,写成此比例, 以 100 分母为分母, 开始以 x 为 100 中未知的分子数来写入分数。

$\begin{aligned} \frac{2}{12} = \frac{x}{100} \end{aligned}$
$\begin{align*}\frac{2}{12} = \frac{x}{100}\end{align*}$
::212=x100

Next, cross multiply to solve for the unknown variable.
::下一步,交叉乘以解答未知变量。

$\begin{aligned} 2 (100) = 12 (x) \end{aligned}$
$\begin{align*}2(100) = 12(x)\end{align*}$
::2(100)=12(x)

Then, solve for “ $\begin{align*}x\end{align*}$ ” by dividing both sides of the equation by 12.
::然后,通过将方程两侧除以12来解决“x”问题。

$\begin{aligned} \begin{array}{rcl} 2 (100) & = & 12 (x) \\ 200 & = & 12 x \\ \frac{200}{12} & = & \frac{12 x}{12} \\ x & = & 16.67 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 2(100) &=& 12(x) \\ 200 &=& 12x \\ \frac{200}{12} &=& \frac{12x}{12} \\ x &=& 16.67 \end{array}\end{align*}$
::2(100)=12(x)200=12x20012=12x12x=16.67

The answer is 16.67.
::答案是16.67。

The jump on earth is 16.67% of the jump you can make on the moon.
::地球跳跃是月球跳跃的16.67%

Example 2
::例2

Jack’s baseball team won 9 out of 12 games. What percent of the games played did the team win? What percent did of the games played did the team lose?
::杰克的棒球队赢得了12场比赛中的9场比赛中的9场比赛。比赛中有多少场比赛赢得了球队的胜利? 比赛中有多少场比赛输了?

First, write the number of games won as a fraction.
::首先,将赢出的游戏数作为一个分数写入。

$\begin{aligned} \frac{9}{12} \end{aligned}$
$\begin{align*}\frac{9}{12}\end{align*}$

Next, write this as a proportion with a denominator of 100. Start by writing the fraction with $\begin{align*}x\end{align*}$ as the unknown numerator out of 100.
::下一步,写成此比例, 以 100 分母为分母, 开始以 x 为 100 中未知的分子数来写入分数。

$\begin{aligned} \frac{9}{12} = \frac{x}{100} \end{aligned}$
$\begin{align*}\frac{9}{12} = \frac{x}{100}\end{align*}$
::912=100

Then, cross multiply to solve for the unknown variable.
::然后,交叉乘以解答未知变量。

$\begin{aligned} 9 (100) = 12 x \end{aligned}$
$\begin{align*}9(100) = 12x\end{align*}$
::9(100)=12x

Then, solve for “ $\begin{align*}x\end{align*}$ ” by dividing both sides of the equation by 12.
::然后,通过将方程两侧除以12来解决“x”问题。

$\begin{aligned} \begin{array}{rcl} 9 (100) & = & 12 (x) \\ 900 & = & 12 x \\ \frac{900}{12} & = & \frac{12 x}{12} \\ x & = & 75 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 9(100) &=& 12(x) \\ 900 &=& 12x \\ \frac{900}{12} &=& \frac{12x}{12} \\ x &=& 75 \end{array}\end{align*}$
::9(100)=12(x)900=12x90012=12x90012=12x1212x=75

The answer is 75.
::答案是75

The team wins 75% of the time.
::团队赢得75%的时间。

The team then loses 25% of the time.
::然后团队损失了25%的时间

Example 3
::例3

Write $\begin{align*}\frac{44}{100}\end{align*}$ as a percent.
::写44100的百分率。

First, remember that a percent means that the denominator is 100. Since this fraction is already out of 100, you can convert it to a percent.
::首先,记住1%意味着分母为100, 因为这个分母已经超过100, 您可以将其转换为1% 。

$\begin{aligned} \frac{44}{100} = 44 % \end{aligned}$
$\begin{align*}\frac{44}{100} = 44\%\end{align*}$

The answer is 44%.
::答案是44%。

Example 4
::例4

Write $\begin{align*}\frac{1}{2}\end{align*}$ as a percent.
::写12成百分比。

First, this fraction is not being compared to 100. It is being compared to 2. You need to rewrite it as an equal ratio out of 100. You can use proportions to do this. Write this ratio compared to a second ratio out of 100.
::首先,没有将这一分数与100作比较,而是与2作比较,需要将其重写成100中之和的相等比例。您可以使用比例来做到这一点。写下这个比例,而100中只有第二比例。

$\begin{aligned} \frac{1}{2} = \frac{?}{100} \end{aligned}$
$\begin{align*}\frac{1}{2} = \frac{?}{100}\end{align*}$

Next, use multiplication to create equal ratios or a proportion.
::其次,使用乘法来创造相等比率或比例。

$\begin{aligned} \begin{array}{rcl} 2 \times 50 & = & 100 \\ 1 \times 50 & = & 50 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 2 \times 50 &=& 100 \\ 1 \times 50 &=& 50 \\ \end{array}\end{align*}$

Next, put these together.
::接下来,把这些放在一起。

$\begin{aligned} \frac{1}{2} = \frac{50}{100} \end{aligned}$
$\begin{align*}\frac{1}{2} = \frac{50}{100}\end{align*}$

Then, change the fraction to a percent.
::然后,将分数改变为百分之一。

$\begin{aligned} \frac{50}{100} = 50 % \end{aligned}$
$\begin{align*}\frac{50}{100} = 50\%\end{align*}$

The answer is 50%.
::答案是50%。

Example 5
::例5

Write $\begin{align*}\frac{5}{7}\end{align*}$ as a percent.
::57 以百分比表示写作。

First, write this as a proportion with a denominator of 100. Start by writing the fraction with $\begin{align*}x\end{align*}$ as the unknown numerator out of 100.
::首先,写成此比例, 以 100 分母为分母, 开始以 x 作为100 中未知的分子数。

$\begin{aligned} \frac{5}{7} = \frac{x}{100} \end{aligned}$
$\begin{align*}\frac{5}{7} = \frac{x}{100}\end{align*}$
::57=100(57=100)

Next, cross multiply to solve for the unknown variable.
::下一步,交叉乘以解答未知变量。

$\begin{aligned} 5 (100) = 7 (x) \end{aligned}$
$\begin{align*}5(100) = 7(x)\end{align*}$
::5(100)=7(x)

Then, solve for “ $\begin{align*}x\end{align*}$ ” by dividing both sides of the equation by 7.
::然后,通过将方程两侧除以7来解决“x”问题。

$\begin{aligned} \begin{array}{rcl} 5 (100) & = & 7 (x) \\ 500 & = & 7 x \\ \frac{500}{7} & = & \frac{7 x}{7} \\ x & = & 71.4 \end{array} \end{aligned}$
$\begin{align*}\begin{array}{rcl} 5(100) &=& 7(x) \\ 500 &=& 7x \\ \frac{500}{7} &=& \frac{7x}{7} \\ x &=& 71.4 \end{array}\end{align*}$
::5(100)=7(x)500=7x50007=7x7x7x=71.4

The answer is 71.4%.
::答案是71.4%。

Review
::回顾

Write the following percent values as fractions in simplest form.
::以最简单的形式作为分数写入以下百分比值。

1. $\begin{align*}16\%\end{align*}$

2. $\begin{align*}40\%\end{align*}$

3. $\begin{align*}2\%\end{align*}$

4. $\begin{align*}4\%\end{align*}$

5. $\begin{align*}45\%\end{align*}$

6. $\begin{align*}20\%\end{align*}$

7. $\begin{align*}18\%\end{align*}$

8. $\begin{align*}10\%\end{align*}$

Write the following fractions as a percent. Round to the nearest whole percentage point.
::将以下分数写成百分比。圆到最近的整百分点。

9. $\begin{align*}\frac{2}{3}\end{align*}$

10. $\begin{align*}\frac{23}{30}\end{align*}$

11. $\begin{align*}\frac{4}{75}\end{align*}$

12. $\begin{align*}\frac{21}{2}\end{align*}$

13. $\begin{align*}\frac{4}{5}\end{align*}$

14. $\begin{align*}\frac{6}{10}\end{align*}$

15. $\begin{align*}\frac{3}{25}\end{align*}$

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

将百分比写入分数

Percents as Fractions ::百分比作为分数

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

Percents as Fractions
::百分比作为分数

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