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Positive and Negative Numbers - I
成绩单
算术和分数，阳性和负数。在此视频中，我们将讨论如何添加和减去正面和
negative numbers. Now, this is a very basic topic.
Again, if you are proficient in this topic, do not feel compelled to watch this entire video.
This is a video designed to get people comfortable with this topic, if it is unfamiliar or they have some uncertainty with the topic. 所以无论您开始的任何地方，我都会假设您精通两个基本情况，如何添加两个正整数，或 how to subtract two positive integers when they're in the form, bigger minus smaller. First thing I'll say is, if you need practice with this, practice every day.
精通两位数和减法非常重要。能够这样做，作为精神数学，将使测试更顺畅。 Now the good news is, if you can do these two things, you can do anything else. This entire topic is very easy, if you know these two things. 有很多方法可以讨论这种材料。让我们从减法开始。
所以me mathematicians would say subtraction doesn't really exist. What does that mean? Well, subtraction of any number can be re-written as the addition of a number of the opposite sign. 因此，一些数学家会说这个添加实际上是真正的形式。所以，让我们确保我们理解这一点。
可以重新编写任何数量的减法作为添加多个相反的符号，这里是四个不同的减法实例。 我们有一个积极的积极，负面减去一个积极的积极态度。积极减去阴性，阴性减去消极。 在所有四种情况下，我们可以重写减法作为添加许多相反的标志。
在我们减去正面的情况下，这与添加负面相同。 In the cases where we are subtracting a negative, that's the same as adding a positive. 我们会注意到我们得到一些简化，但在每种情况下都不是简化。
For example, in the first one, it looks like we were better off where we started. We were better off without changing it to addition. In the third one, it looks like we clearly made things better off by changing it to the addition of two positive numbers. 在第四个，注意现在它添加了。它的换向，所以我们可以在周围切换订单。
当我们周围切换订单时，我们可以将其重新写入减法，这更容易。 所以, sometimes this is really an important move for simplification, but not always. You don't always have to re-write subtraction as addition, but it can be a very good simplifying trick to have up your sleeve. Notice in particular, for the case (positive)- (negative), this trick will always simplify it.
它将永远变为积极的+积极，这是我认为你知道如何做的基本事物之一。 现在，让我们来看看那个棘手的双负病例，它可以出现在形式（负） - （正面），或以形式（负）+（否定）。 The big idea is we can always factor out a negative sign. Now, what does this mean, exactly?
Let's look at that first one, (-46)- 37. We can factor out a negative sign. 如果我们要考虑一个负片，那么内部的一切都变得积极。所以，它只变为46 + 37，添加两个正数。 所以你执行此外，然后只是在总和前粘在否定。您可能想在页面上尝试这些其他人。
Pause the video here, try these others and then you can compare your answers to mine. Here are the answers. One other case folks find tricky is the case (small positive)- (big positive), which also shows up as (small positive) + (big negative). 在这里，大思想正在向反向减法顺序的负面符号进行处理。
那么，这是什么意思？假设我有23〜64，通过因素出一个负面的标志， 那么我得到的是反向顺序的减法，64-23。嗯，现在这更大的减去了，我们可以做， 这是基本技能之一。这样减法，然后只需粘在它面前的负符号即可。
Let's look at another one. 26- 63, factor out the negative and we a get a negative in front of the reversed order subtraction. 63- 26, perform the subtraction, and stick a negative sign in front of it. 这里有更多，你可能想在这里暂停视频并自己练习这些。
Here are the answers I get. Very important that you're able to do things like this. 这对精神数学来说是非常好的做法，能够在你的脑海中做到这一点。这些想法允许您更改任何添加或减法 两个阳性的总和，或较大减去较小的差异。在这里，我刚刚讨论了整数的简单性，但所有这些同样的想法都会 对于正面和负数的小数和分数也是如此。
核心技能是添加两个阳性，或更大的积极减去较小的正面。 从这里，如果我们正在做积极的负负面，我们可以将其改变为积极加上积极。 If we have the double negative case, we can factor out a negative sign, and whenever we have smaller minus bigger.
We can factor out a negative sign, reverse the order subtraction, and then what's inside bigger minus smaller that's something we can do.
阅读完整成绩单
This is a video designed to get people comfortable with this topic, if it is unfamiliar or they have some uncertainty with the topic. 所以无论您开始的任何地方，我都会假设您精通两个基本情况，如何添加两个正整数，或 how to subtract two positive integers when they're in the form, bigger minus smaller. First thing I'll say is, if you need practice with this, practice every day.
精通两位数和减法非常重要。能够这样做，作为精神数学，将使测试更顺畅。 Now the good news is, if you can do these two things, you can do anything else. This entire topic is very easy, if you know these two things. 有很多方法可以讨论这种材料。让我们从减法开始。
所以me mathematicians would say subtraction doesn't really exist. What does that mean? Well, subtraction of any number can be re-written as the addition of a number of the opposite sign. 因此，一些数学家会说这个添加实际上是真正的形式。所以，让我们确保我们理解这一点。
可以重新编写任何数量的减法作为添加多个相反的符号，这里是四个不同的减法实例。 我们有一个积极的积极，负面减去一个积极的积极态度。积极减去阴性，阴性减去消极。 在所有四种情况下，我们可以重写减法作为添加许多相反的标志。
在我们减去正面的情况下，这与添加负面相同。 In the cases where we are subtracting a negative, that's the same as adding a positive. 我们会注意到我们得到一些简化，但在每种情况下都不是简化。
For example, in the first one, it looks like we were better off where we started. We were better off without changing it to addition. In the third one, it looks like we clearly made things better off by changing it to the addition of two positive numbers. 在第四个，注意现在它添加了。它的换向，所以我们可以在周围切换订单。
当我们周围切换订单时，我们可以将其重新写入减法，这更容易。 所以, sometimes this is really an important move for simplification, but not always. You don't always have to re-write subtraction as addition, but it can be a very good simplifying trick to have up your sleeve. Notice in particular, for the case (positive)- (negative), this trick will always simplify it.
它将永远变为积极的+积极，这是我认为你知道如何做的基本事物之一。 现在，让我们来看看那个棘手的双负病例，它可以出现在形式（负） - （正面），或以形式（负）+（否定）。 The big idea is we can always factor out a negative sign. Now, what does this mean, exactly?
Let's look at that first one, (-46)- 37. We can factor out a negative sign. 如果我们要考虑一个负片，那么内部的一切都变得积极。所以，它只变为46 + 37，添加两个正数。 所以你执行此外，然后只是在总和前粘在否定。您可能想在页面上尝试这些其他人。
Pause the video here, try these others and then you can compare your answers to mine. Here are the answers. One other case folks find tricky is the case (small positive)- (big positive), which also shows up as (small positive) + (big negative). 在这里，大思想正在向反向减法顺序的负面符号进行处理。
那么，这是什么意思？假设我有23〜64，通过因素出一个负面的标志， 那么我得到的是反向顺序的减法，64-23。嗯，现在这更大的减去了，我们可以做， 这是基本技能之一。这样减法，然后只需粘在它面前的负符号即可。
Let's look at another one. 26- 63, factor out the negative and we a get a negative in front of the reversed order subtraction. 63- 26, perform the subtraction, and stick a negative sign in front of it. 这里有更多，你可能想在这里暂停视频并自己练习这些。
Here are the answers I get. Very important that you're able to do things like this. 这对精神数学来说是非常好的做法，能够在你的脑海中做到这一点。这些想法允许您更改任何添加或减法 两个阳性的总和，或较大减去较小的差异。在这里，我刚刚讨论了整数的简单性，但所有这些同样的想法都会 对于正面和负数的小数和分数也是如此。
核心技能是添加两个阳性，或更大的积极减去较小的正面。 从这里，如果我们正在做积极的负负面，我们可以将其改变为积极加上积极。 If we have the double negative case, we can factor out a negative sign, and whenever we have smaller minus bigger.
We can factor out a negative sign, reverse the order subtraction, and then what's inside bigger minus smaller that's something we can do.
