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Hi. Welcome to www. engvid. com. I'm Adam. In today's video I'm going to look at some math.
大家好。欢迎来到英格威英语学习网。今天的视频我们来学习一些数学词汇。
Now, I know this is an English site, don't worry, I'm not actually going to do any math.
我知道这是一个英文网站，别担心，我不会讲任何数学计算。
Philosophy and English major, so math not my favourite,
我学的是哲学和英语专业，所以数学不是我的最爱，
but I will give you some math terminology, words that you need if you're going to do math.
但我会给你们一些数学术语，学数学需要知道的词。
Now, a lot of you might be engineers or you might be students who came from another country to an English-speaking country,
你们中的很多人可能是另一个国家的工程师或者是学生，来到了一个说英语的国家，
and you go to math class and you know the math, but you're not sure of the wording.
你去上数学课，你知道数学，但你不知道有关的英语词汇。
Okay? So this is what we're looking at, terminology, only the words that you need to go into a math class or to do some math on your own.
这就是我们要学的，术语，是你们上数学课或自己做数学题时需要用到的词汇。
Okay? We're going to start with the very basics. You know all these functions already.
我们从最基本的开始。这些函数你都已经知道了。
I'm just going to give you some ways to talk about them, and then we'll move on to some other functions and other parts.
我会给你们一些方法来谈论它们，然后我们会继续讲一些其他的函数和其他部分。
So, you know the four basic functions: "addition","subtraction", "multiplication", and "division".
你知道四个基本的运算：“加法”、“减法”、“乘法”和“除法”。
What you need to know is ways to say an equation.
你需要知道的是方程的表达方式。
Right? You know an equation. "1 + 1 = 2", that's an equation.
你知道方程是什么。"1 + 1 = 2"这是一个方程。
"x2 + y3 = znth", that's also an equation which I'm not even going to get into.
“x2 + y3 = znth”也是方程，这个方程我就不讲了。
So, let's start with addition. The way to talk about addition.
我们从加法开始。讨论加法的方式。
You can say: "1 plus 1", "plus", of course is "+" symbol, that's the plus symbol.
你可以说："1 + 1"，"+"，当然是"+"符号，那是"+"符号。
"1 plus 1 equals 2. "2 means the total, isalso called the "sum".
1加1等于2。2表示和，也称"sum"。
Now, you can also say: "The sum of 1 and 1 is 2".
你也可以说："The sum of 1 and 1 is 2"。
You can also just say, without this part: "1 and 1 is 2."
你也可以说，不加这个：“1加1等于2。”
So you don't need the plus, you don't need the equal; you can use "and" and "is", but it means the same thing.
所以你不需要加号，不需要等号；你可以用“and”和“is”，但意思是一样的。
Everybody will understand you're making. You're doing addition. Sorry. Doing addition, not making.
每个人都会明白你在做什么。你在做加法。对不起。是“addition”不是“making”。
If you add 1 and 1, you get 2. Okay? So: "add" and "get", other words you can use to express the equation.
如果你把1和1相加，就得到2。所以：“add”和“get”，换句话说，你可以用它们来表达这个等式。
Now, if you're doing math problems, math problems are word problems.
如果你在做数学题，问题就是单词的问题。
I know a lot of you have a hard time understanding the question because of the words,
我知道你们很多人很难理解这些问题是因为不懂这些词汇。
so different ways to look at these functions using different words, different verbs especially.
用不同的词来看描述这些函数，尤其是不同的动词。
If we look at subtraction: "10 minus 5 equals 5". "5", the answer is also called the "difference".
如果我们看减法，10减5等于5。“5”，这个答案也叫“差”。
For addition it's the "sum", for subtraction it's "difference". "10, subtract 5 gives you 5.
加法得到的是“和”，减法得到是“差”。10减去5等于5。
"Or: "10 deduct"-means take away-"5", we can also say: "Take 5 away". Oh, I forgot a word here. Sorry.
或者用“deduct”，意思是减去，我们也可以说：“Take 5 away”。我忘了一个词，抱歉。
"Take 5 away from 10, you get", okay? "10 subtract 5", you can say: "gives you 5", sorry, I had to think about that.
“10减5等于”，“10减5”，你可以说“gives you 5”，抱歉，我得想想。
Math, not my specialty. So: "Take 5 away from 10, you get 5", "Take 5 away from 10, you're left with", "left with" means what remains.
数学不是我的强项。“Take 5 away from 10, you get 5”，“Take 5 away from 10, you're left with”。
Okay, so again, different ways to say the exact same thing.
再说一遍，这是同一件事的不同说法。
So if you see different math problems in different language you can understand what they're saying.
如果你用不同的语言看不同的数学问题，你就能明白他们在说什么。
Okay? Multiplication. "5 times 5", that's: "5 times 5 equals 25".
乘法。“5乘于5”，“5乘于5等于25”。
"25" is the "product", the answer to the multiplication, the product.
25是乘积，该乘法运算的答案，乘积。
"5 multiplied by 5", don't forget the "by". "5 multiplied by 5 is 25", "is","gives you", "gets", etc.
“5乘于5”，不要忘记“by”。“5乘于5等于25”，“is”，或者用“gives you”，“gets”等等。
Then we go to division. "9 divided by 3 equals 3", "3", the answer is called the "quotient".
然后我们说除法。“9除以3等于3”，“3”，这个答案叫做“商”。
This is a "q". I don't have a very pretty "q", but it's a "q". "Quotient". Okay?
这是“q”，不太漂亮，但是是一个“q”。“商”。
"3 goes into. 3 goes into 9 three times", so you can reverse the order of the equation.
“9除以3等于3”，所以你可以颠倒方程的顺序。
Here, when. addition, subtraction, multiplication.
加法，减法，乘法。
Well, actually addition and multiplication you can reverse the order and it says the same thing.
实际上，加法和乘法数字的顺序调换，结果是一样的。
Here you have to reverse the order: "goes into" as opposed to "divided by", so pay attention to the prepositions as well.
这里则需要调换顺序：“goes into”和“divided by”意思相反，所以要注意介词。
Gives you. Sorry. "3 goes into 9 three times", there's your answer.
是“gives you”，抱歉。“9除以3等于3”，这就是答案。
"10 divided by 4", now, sometimes you get an uneven number.
“10除以4”，有时会得到一个不均匀的数。
So: "10 divided by 4" gives you 2 with a remainder of 2, so: "2 remainder 2".
“10除以4”等于2，余数是2，所以是“等于2余2。
Sometimes it'll be "2R2", you might see it like that. Okay? So these are the basic functions you have to look at.
有时会写作“2R2”，你可能会看到这种形式。好吧？这些是基本的运算。
Now we're going to get into a little bit more complicated math things.
现在我们要讲一些更复杂的数学问题。
We're going to look at fractions, exponents, we're going to look at some geometry issues, things like that.
我们会学习分数，指数，我们会学习一些几何问题，诸如此类。
Okay, so now we're going to look at something else.
现在我们来学别的内容。
We're going to look at fractions, exponents, and decimals.
我们将学习分数，指数和小数。
Again, all of you know these things even from high school, even before high school, primary school math some of this stuff.
再说一次，你们所有人从高中起都知道这些知识，甚至在高中之前就知道，有些是小学数学。
A "fraction" is basically a partial number; it's not a whole number.
“分数”基本上是一个部分的数字；它不是一个整数。
It's a part of, that's why it's called a fraction.
它是一部分，这就是为什么它被称为分数。
You have two parts to this fraction, you have the "numerator", "nu-mer-a-tor",
这个分数有两部分，分子，“nu-mer-a-tor”，
and then you have the bottom part which is the "denominator", "de-nom-in-at-or". Numerator, denominator.
然后是分母部分，分母是“de-nomin-at-or”。分子、分母。
Now, the thing to know about fractions, now, how to add them, how to multiply them, that's a math lesson, we don't need to know that.
关于分数的知识，如何相加，如何相乘，这是数学课，我们这里不讲。
We just need to know the words. What you might have some trouble with is pronunciation.
我们只需要知道这些单词。你可能在发音方面有困难。
So: "5 over 12", we don't say: "5 over 12", we say: "Five twelfths","fths", so you have a lot of consonants here. "Twelfths".
我们不说“5 over 12”，我们说：“Five twelfths”，“fths”，这里有很多辅音。“Twelfths”。
Now, keep in mind that even native English speakers have a hard time pronouncing this, so if you find it difficult don't worry.
请记住，即使母语是英语的人发这个音也有困难，所以如果你觉得很难，不要担心。
In context people will understand you. If you say: "Five twelfs", okay, I get it.
在上下文中，人们会听懂。如果你说“Five twelfs”，好的，我明白了。
If you say: "Five twelfth-th-th", I'll get it, I'll know what you're trying to say.
如果你说：“Five twelfth-th-th”，我就明白了，我知道你想说什么。
"Five sixths", this one's even worse, "xths".
“Five sixths”，这个更难读，“xths”。
"Sixths", just say it as close as you can, you'll be understood because people know you're talking about fractions.
“Sixths”，发音越接近越好，别人会理解你的意思，因为大家都知道你说的是分数。
Okay? On the other side we can say, like, this is a half.
另一边我们可以说，这是二分之一。
Right? 1 over 2, so a half. We can say it in "decimals" as well. "Decimals" are the point form.
二分之一。我们也可以用小数来表示。小数点是有小数点的形式。
So, this is "0. 5", I hope you can see this point here.
这是零点五，希望你可以看到这个点。
We don't say: "Zero decimal five", we don't say: "Zero period five", always "point". Okay? "Zero point five".
我们不说：“Zero decimal five”，我们不说：“Zero period five”，总是“点”。好吧？“Zero point five”。
Now: "Zero point thirty-three", no, because this is not a number, this is a partial number,
“0.33”，因为这不是一个数，这是一个小数，
just like a fraction, it's less than one so it's not "thirty-three", it's "zero point three, three".
就像一个分数，它小于1，所以不是33，它是“0.33”。
And as many numbers as you have: "Zero point three, three, seven, eight, nine, ten".
后面有多少数都可以：“0.3378910”。
Well, no "ten", "one, zero". Okay? So, and the thing, and you can go as many decimal places as you want.
不是“10”，是“1，0”。你可以想要多少位小数就有多少位小数。
So this is a whole number, this is the decimal.
这是一个整数，这是小数。
One, two, three, four, five, six decimal places, that's what we talk about after the decimal point.
一，二，三，四，五，六位小数，这就是小数点后的数。
Okay? Now, this is the 10th or one-tenth, everything that's here. So if you have "0.3",
这是十分之一，或者说“one-tenth”。所有这些。如果你说“0.3”，
you have "three-tenths" of whatever it is you're talking about, "one hundredth", "one thousandth", and then we go on from there,
它就是“十分之三”，“百分之一”，“千分之一”，可以说更多。
but we don't usually talk in these terms beyond the third because it gets a little bit too complicated.
但超过三位时，我们通常就不会用这种表达，因为它太复杂了。
Now, three. Where does this number. First of all:"3/100", so first of all it's here.
这个数字，首先看“百分之三”，首先它在这里。
Oh, no, it's not, that's thousandths. It's over here. Okay? So, "3 hundredths","3 hundredths".
不是，那是千分之一。它在这里。“百分之三”。
Now, if you just say: "zz", like in "pizza", "3 hundredths", close enough, then, again, people will understand you.
如果你只是说：“zz”，就像在“pizza”中的发音，“百分之三”，足够接近，然后，再说一次，人们会听懂。
When you're talking about sports, for example, and they say there's like point-five seconds left on the clock, so he.
举个例子，当你在谈论体育运动的时候，他们说还剩下1.5秒，所以，
The guy, basketball, he shoots it, he scores with a tenth of a second left in the game.
那个家伙，他把篮球投了出去，他在比赛还剩十分之一秒的时候得分了。
So you understand? They're talking about 0. 1 second. Okay.
所以你明白吗？他们说的是0.1秒。好吧。
Next we have "exponents". X with a small "2" or a small "3" or whatever number. So this whole thing is called...
接下来说说指数。X带上一个小的“2”或小的“3”或任何数字。所以这整个东西叫做，
The "2" is actually called the exponent, the x or whatever number is called the base, and we can also refer to this as "the power".
“2”就叫做指数，x或者别的数字叫做底数，我们也可以称它为幂。
So, the whole thing is the "exponent", "base", and "power".
整个就是“指数”、“底数”和“幂”。
Now, when we talk about: "X to the power of 2", we don't say: "to the power of 2".
当我们说“X to the power of 2”时，我们不会说“2次方”。
When the number is 2, we say: "squared", so: "X squared". When we talk about "3", we say: "cubed".
当数字是2时，我们说：“平方”，所以是：“X的平方”。当我们谈论“3”时，我们说：“立方”。
Okay? So we're going to look in a second, and we're going to look at measuring area of a shape or measuring the volume of a shape.
我们马上来看一下，我们要测量一个形状的面积或者说一个形状的体积。
Different shapes, of course, but "area" is measured with "x2" or whatever the measurement is squared, and the volume is measured with "cubed".
当然是不同的形状，但“面积”是用“平方”或任何平方的度量单位来测量的，而“体积”是用“立方”来测量的。
Okay? Now, once you get past the third-four, five, six-there's two ways you can say it,
现在，一旦数字超过三的话——4，5，6——你有两种方式可以说，
you can say: "X to the 4th power", if this is a "4": "X to the 4th power",or "X to the power of 4".
你可以说：“X的4次方”，如果这是4就说：“X to the 4th power”或者“X to the power of 4”。
Now, sometimes you might see. You might hear this expression: "The nth power".
有时你可能会看到，你可能听过这个表达：“n次方”。
"The nth power" means unlimited, it goes on forever, or infinite,
“n次方”的意思是无限的，它是无限的，
we don't know where it ends but this is actually an expression used in regular English as well, and we'll talk about that another time.
我们不知道它在哪里结束，但这实际上也是一个在日常英语中使用的表达，我们下次再讨论它。
Now, if you're going the opposite direction, instead of squaring the number you want to find the "root" of the number.
如果是与之相反，你想要的不是数的平方而是数的“根”。
So, 3 squared equals 9. Okay? The square root of 9 is 3. How many times does 3 go into 9? 3 times, etc.
3的平方等于9。好吧？9的平方根是3。9除以3等于多少？3，等等。
"Square root", finding out how many times the number goes into itself. X2, multiplying the number by it self two times. Okay.
“平方根”，求出哪个数的平方是这个数。“X2”，将这个数自身相乘。好吧。
