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比率和税率
成绩单
Ratios and rates. Rates are ratios.
在分子和分母中不同单位的任何比率称为速率。
为了解决大多数涉及各种率的问题，我们必须做的就是建立形式比率=比率的等式。
We just match the units on each side. Remember that such an equation, fraction equals fraction or ratio equals ratio, 被称为比例。如果你不熟悉它，那可能是一个好主意 look at the video Operations with Proportions. What you can do and can't do with a proportion mathematically.
That video is in the fraction module. Rates are often expressed as so many units per units. 例如，所有这些都是税率。其中许多来自科学。 最后两种是特殊类型，每小时60分钟，或每次革命360度。这些是单位转换的例子。
So these would be examples of things you would actually be expected to know. The other one's you would not be expected to know. But you would be expected to know that there are 16 minutes in an hour. And you could write this as a ratio. We would set this given rate equal to a fraction with the same units in the numerator and the denominator.
所以问题本身都会给你一个利率。例如，蓝速之一。 Or you would know yourself something about the units and the way that the units are related. 您将其设置为比例。然后您将其设置为等于另一边的比率 that matches the same units in the numerator and in the denominator.
这是一个练习问题。暂停视频，然后我们会谈谈这个问题。 Okay, so this problem gives us a rate. It gives us the rate of 8 grams per hour. So that has grams in the numerator and hours in the denominator. So we're going to set this equal to a fraction on the other side that also has grams in the numerator and hours in the denominator.
We're gonna have 30 grams in the numerator and then we're just gonna have a variable. I'll call it H, in the denominator. 这是未知的小时数。我要简化的第一步是我会将双方划分为2。 So I'm gonna divide the 8 by 2, and divide the 30 by 2. If that operation is an unfamiliar operation.
If you're kind of shocked by that, or didn't know that that was a possible thing to do with proportions, I highly recommend 你回去观看视频，以比例的操作。同样，该视频在分数模块中。 此时，我们将跨越繁殖，然后将其自行划分，我们将划分为4.我们在4小时内得到H = 15。
Write this as a mixed numeral, 3 and three-quarters hours. We're asked when, which is actually a clock time. So we started at noon. Three hours later would be 3 PM 3 quarters of an hour is 45 minutes. So that means, it's completely melted at 3:45 pm. Here's another practice problem.
暂停视频，我们将讨论这一点。大黄蜂的翅膀襟翼8秒内的1440次。 So, that's essentially a ratio. We could say it's 1440 flaps per 8 seconds. 多少次拍打一会儿吗?嗯,冷杉st of all, let's simplify that a little bit.
1440 flaps in 8 seconds, I'm gonna divide by 2. That gets me down to 720 over 4. That I'm gonna divide by 2 again. That gets me down to 360 over 2, and then, I'm gonna divide again, and that's gonna get me down to 180 over 1. So, there are 180 flaps in one second.
Well, we want the flaps in a minute, so clearly, what we're gonna have to do is multiply by 60 seconds, because there's 60 seconds in a minute. 因此，襟翼总数将是180次。我们实际上并不需要一个计算器。 让我们这么想这个。让我们删除那些0，让事情变得更简单。
如果我们正在做18次6.思考这一点的方式，18是（10 + 8）。 好吧，我可以做6次10，那是60岁。我可以做6次8，那是48。 我可以添加那两个，那是108.所以现在我们只是加入两个零，所以 我们得到的是10,800的产品。
And that is the number of flaps in a minute. Here's another practice problem. 暂停视频，然后我们会谈谈这个。好的，这很棘手。 We have a couple rates. We have the 20 grams per centimeter.
我们每克50美元。然后我们有这个初步的起始金额， starting volume, which is 2 centimeters cubed. So first thing I'm gonna do is I'm gonna start there, 我要乘以那些外出，然后我得到8立方厘米。好吧，我想乘以一个速度，所以那些立方厘米取消。
So I'm gonna multiply it by that first rate, 20 grams per cubic centimeter. That way the cubic centimeters will cancel. 然后我会用克留下来。现在我想乘以一些东西，所以克取消。 如果我现在乘以50美元每克,克cancel and I'll be left with units of dollar.
And that's what we're looking for. We're looking for the price. So, I'll point out here. This is actually very easy now because 20 times 50 is just 1,000 times 8 is 8,000, so that would be worth $8,000. In summary, when you see a problem with rates, remember you can set up proportions.
始终记得确保分子和分母的单位匹配。
阅读完整成绩单
We just match the units on each side. Remember that such an equation, fraction equals fraction or ratio equals ratio, 被称为比例。如果你不熟悉它，那可能是一个好主意 look at the video Operations with Proportions. What you can do and can't do with a proportion mathematically.
That video is in the fraction module. Rates are often expressed as so many units per units. 例如，所有这些都是税率。其中许多来自科学。 最后两种是特殊类型，每小时60分钟，或每次革命360度。这些是单位转换的例子。
So these would be examples of things you would actually be expected to know. The other one's you would not be expected to know. But you would be expected to know that there are 16 minutes in an hour. And you could write this as a ratio. We would set this given rate equal to a fraction with the same units in the numerator and the denominator.
所以问题本身都会给你一个利率。例如，蓝速之一。 Or you would know yourself something about the units and the way that the units are related. 您将其设置为比例。然后您将其设置为等于另一边的比率 that matches the same units in the numerator and in the denominator.
这是一个练习问题。暂停视频，然后我们会谈谈这个问题。 Okay, so this problem gives us a rate. It gives us the rate of 8 grams per hour. So that has grams in the numerator and hours in the denominator. So we're going to set this equal to a fraction on the other side that also has grams in the numerator and hours in the denominator.
We're gonna have 30 grams in the numerator and then we're just gonna have a variable. I'll call it H, in the denominator. 这是未知的小时数。我要简化的第一步是我会将双方划分为2。 So I'm gonna divide the 8 by 2, and divide the 30 by 2. If that operation is an unfamiliar operation.
If you're kind of shocked by that, or didn't know that that was a possible thing to do with proportions, I highly recommend 你回去观看视频，以比例的操作。同样，该视频在分数模块中。 此时，我们将跨越繁殖，然后将其自行划分，我们将划分为4.我们在4小时内得到H = 15。
Write this as a mixed numeral, 3 and three-quarters hours. We're asked when, which is actually a clock time. So we started at noon. Three hours later would be 3 PM 3 quarters of an hour is 45 minutes. So that means, it's completely melted at 3:45 pm. Here's another practice problem.
暂停视频，我们将讨论这一点。大黄蜂的翅膀襟翼8秒内的1440次。 So, that's essentially a ratio. We could say it's 1440 flaps per 8 seconds. 多少次拍打一会儿吗?嗯,冷杉st of all, let's simplify that a little bit.
1440 flaps in 8 seconds, I'm gonna divide by 2. That gets me down to 720 over 4. That I'm gonna divide by 2 again. That gets me down to 360 over 2, and then, I'm gonna divide again, and that's gonna get me down to 180 over 1. So, there are 180 flaps in one second.
Well, we want the flaps in a minute, so clearly, what we're gonna have to do is multiply by 60 seconds, because there's 60 seconds in a minute. 因此，襟翼总数将是180次。我们实际上并不需要一个计算器。 让我们这么想这个。让我们删除那些0，让事情变得更简单。
如果我们正在做18次6.思考这一点的方式，18是（10 + 8）。 好吧，我可以做6次10，那是60岁。我可以做6次8，那是48。 我可以添加那两个，那是108.所以现在我们只是加入两个零，所以 我们得到的是10,800的产品。
And that is the number of flaps in a minute. Here's another practice problem. 暂停视频，然后我们会谈谈这个。好的，这很棘手。 We have a couple rates. We have the 20 grams per centimeter.
我们每克50美元。然后我们有这个初步的起始金额， starting volume, which is 2 centimeters cubed. So first thing I'm gonna do is I'm gonna start there, 我要乘以那些外出，然后我得到8立方厘米。好吧，我想乘以一个速度，所以那些立方厘米取消。
So I'm gonna multiply it by that first rate, 20 grams per cubic centimeter. That way the cubic centimeters will cancel. 然后我会用克留下来。现在我想乘以一些东西，所以克取消。 如果我现在乘以50美元每克,克cancel and I'll be left with units of dollar.
And that's what we're looking for. We're looking for the price. So, I'll point out here. This is actually very easy now because 20 times 50 is just 1,000 times 8 is 8,000, so that would be worth $8,000. In summary, when you see a problem with rates, remember you can set up proportions.
始终记得确保分子和分母的单位匹配。
