I'm Adam.

我是亞當

In today's video I'm going to look at some math.

在今天的視頻中，我將看一些數學知識。

Now, I know this is an English site, don't worry, I'm not actually going to do any math.

現在，我知道這是一個英語網站，別擔心，我其實不會做任何數學。

Philosophy and English major, so math not my favourite, but I will give you some math

哲學和英語專業，所以數學不是我的最愛，但我會給你一些數學。

terminology, words that you need if you're going to do math.

術語，單詞，你需要 如果你要做數學。

Now, a lot of you might be engineers or you might be students who came from another country

現在，你們中的很多人可能是工程師，也可能是來自其他國家的學生。

to an English-speaking country, and you go to math class and you know the math, but you're

到一個英語國家，你去上數學課，你知道數學，但你是

not sure of the wording.

不知道措辭。

Okay?

好嗎？

So this is what we're looking at, terminology, only the words that you need to go into a

所以這就是我們要看的，術語，只有你需要進入的詞，才是

math class or to do some math on your own.

數學課或自己做一些數學題。

Okay?

好嗎？

We're going to start with the very basics.

我們要從最基本的開始。

You know all these functions already.

這些功能你都已經知道了。

I'm just going to give you some ways to talk about them, and then we'll move on to some

我只是給大家講一些關於它們的方法，然後我們再繼續講一些。

other functions and other parts.

其他功能和其他部分。

So, you know the four basic functions: "addition", "subtraction", "multiplication", and "division".

所以，你知道四個基本功能。"加法"、"減法"、"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說法方法。

Right? You know an equation.

對吧？你知道一個方程式。

"1 + 1 = 2", that's an equation.

"1+1=2"，這是一個方程式。

"x2 + y3 = znth",

"x2+y3=znth"。

that's also an equation which I'm not even going to get into.

這也是一個方程式，我甚至不打算進入。

So, let's start with addition.

那麼，我們就從加法開始。

The way to talk about addition.

談到加法的方式。

You can say: "1 plus 1", "plus", of course is "+" symbol, that's the plus symbol.

你可以說："1加1"。"1加1"，"加"，當然是 "+"號，就是加號。

"1 plus 1 equals 2."

"1加1等於2"

2 means the total, is also called the "sum".

2是指總數，也叫 "和"。

Now, you can also say: "The sum of 1 and 1 is 2."

現在，你也可以說："1和1的總和是2。"1和1的總和是2."

You can also just say, without this part: "1 and 1 is 2."

你也可以直接說，沒有這部分，"1和1是2"。"1和1是2"

So you don't need the plus, you don't need the equal; you can use "and" and "is", but

所以你不需要加號，不需要等號，你可以用 "和"、"是"，但

it means the same thing.

它的意思是一樣的。

Everybody will understand you're making...

大家都會明白你在做...

You're doing addition.

你在做加法。

Sorry. Doing addition, not making.

抱歉，我是在做加法，不是在做。是做加法，不是做。

If you add 1 and 1, you get 2.

如果你把1和1相加，就會得到2。

Okay? So: "add" and "get", other words you can use to express the equation.

好嗎？那麼，"加 "和 "得"，"加 "和 "得"，你可以用其他詞來表達這個等式。

Now, if you're doing math problems, math problems are word problems.

現在做數學題的話，數學題就是文字題。

I know a lot of you have a hard time understanding the question because of the words, so different

我知道你們很多人很難理解這道題，因為文字，所以不同

ways to look at these functions using different words, different verbs especially.

用不同的詞、不同的動詞，特別是用不同的詞來看這些函數的方法。

If we look at subtraction: "10 minus 5 equals 5".

如果我們看減法。"10減5等於5"。

"5", the answer is also called the "difference".

"5"，答案也叫 "差"。

For addition it's the "sum", for subtraction it's "difference".

對於加法是 "和"，對於減法是 "差"。

"10, subtract 5 gives you 5."

"10，減去5就得到5。"

Or: "10 deduct"-means take away-"5", we can also say: "Take 5 away"...

或："十扣"--意思是拿走--"五"，我們也可以說。"拿走5"...

Oh, I forgot a word here. Sorry.

哦，我忘了一個詞在這裡。對不起，我忘了一個詞。

"Take 5 away from 10, you get", okay?

"十拿九穩"，你懂嗎？

"10 subtract 5", you can say: "gives you 5",

"10減去5"，你可以說。"給你5"。

sorry, I had to think about that.

對不起，我不得不考慮這個問題。

Math, not my specialty.

數學，不是我的專長。

So: "Take 5 away from 5, you get 5", "Take 5 away from 5, you're left with",

所以，"從5中取5，你得到5"。"從5中拿走5，你就得到5"，"從5中拿走5，你就剩下"。

"left with" means what remains.

"剩下的 "是指剩下的東西。

Okay, so again, different ways to say the exact same thing.

好吧，所以再次，不同的方式說完全相同的事情。

So if you see different math problems in different language you can understand what they're saying.

所以，如果你看到不同語言的數學題，你就能明白他們在說什麼。

Okay?

好嗎？

Multiplication.

乘法。

"5 times 5", that's: "5 times 5 equals 25".

"5乘以5"，就是。"5乘以5等於25"。

"25" is the "product", the answer to the multiplication, the product.

"25 "是 "積"，是乘法的答案，是積。

"5 multiplied by 5", don't forget the "by".

"5乘以5"，別忘了 "以"。

"5 multiplied by 5 is 25", "is", "gives you", "gets", etc.

"5乘以5是25"，"是"，"給你"，"得到 "等。

Then we go to division.

然後我們再去分工。

"9 divided by 3 equals 3", "3", the answer is called the "quotient".

"9除以3等於3"，"3"，答案叫做 "商"。

This is a "q".

這是一個 "q"。

I don't have a very pretty "q", but it's a "q".

我的 "q "不是很好看，但它是一個 "q"。

"Quotient".

"商數"。

Okay?

好嗎？

"3 goes into... 3 goes into 9 three times",

"3進..."3進9，3次"。

so you can reverse the order of the equation.

所以你可以把等式的順序倒過來。

Here, when...

在這裡，當...

In addition, subtraction, multiplication...

加法、減法、乘法... ...

Well, actually addition and multiplication you can reverse the order and it says the

嗯，其實加法和乘法你可以把順序反過來，上面寫著

same thing.

同樣的事情。

Here you have to reverse the order: "goes into" as opposed to "divided by",

這裡你要把順序顛倒過來。"進入 "與 "除以 "的順序相反。

so pay attention to the prepositions as well.

所以也要注意介詞。

Gives you...

給你...

Sorry. "3 goes into 9 three times", there's your answer.

對不起，"3進入9的三次"，這就是你的答案。"3進入9的三次"，這就是你的答案。

"10 divided by 4", now, sometimes you get an uneven number.

"10除以4"，現在，有時你會得到一個不均勻的數字。

So: "10 divided by 4" gives you 2 with a remainder of 2, so: "2 remainder 2".

所以："10除以4 "得2，有餘數為2，所以"10除以4 "得到2，餘數為2，所以："2除以2"。

Sometimes it'll be "2R2", you might see it like that.

有時會是 "2R2"，你可能會看到這樣。

Okay?

好嗎？

So these are the basic functions you have to look at.

所以這些是你必須要看的基本功能。

Now we're going to get into a little bit more complicated math things.

現在我們要進入更復雜一點的數學事情。

We're going to look at fractions, exponents, we're going to look at some geometry issues,

我們要看分數，指數，我們要看一些幾何問題。

things like that.

這樣的事情。

Okay, so now we're going to look at something else.

好了，現在我們要去看看別的東西。

We're going to look at fractions, exponents, and decimals.

我們要研究分數、指數和小數。

Again, all of you know these things even from high school, even before high school, primary

同樣，這些東西你們都知道，甚至從高中開始，甚至在高中之前，小學就知道了

school math some of this stuff.

學校數學這一些東西。

A "fraction" is basically a partial number; it's not a whole number.

"分數 "基本上是一個部分數，它不是一個整數。

It's a part of, that's why it's called a fraction.

它是一部分，所以叫分數。

You have two parts to this fraction, you have the "numerator", "nu-mer-a-tor", and then

這個分數有兩個部分，你有 "分子"，"nu-mer-a-tor"，然後是

you have the bottom part which is the "denominator", "de-nom-in-at-or".

你有最下面的部分，這是 "分母"，"de-nom-in-at-or"。

Numerator, denominator.

分子，分母。

Now, the thing to know about fractions, now, how to add them, how to multiply them, that's

現在，關於分數，現在要知道的是，如何加法，如何乘法，這是

a math lesson, we don't need to know that.

一堂數學課，我們不需要知道。

We just need to know the words.

我們只需要知道這些話。

What you might have some trouble with is pronunciation.

你可能會有一些問題，就是發音。

So: "5 over 12", we don't say: "5 over 12", we say: "Five twelfths",

所以說："5比12"，我們不說："5比12"，我們不說： "5比12"，我們說："5比12"，我們說："5個12"。

"fths", so you have a lot of consonants here.

"fths"，所以你這裡有很多輔音。

"Twelfths".

"十二分"。

Now, keep in mind that even native English speakers have a hard time pronouncing this,

現在，請記住，即使是以英語為母語的人也很難發這個音。

so if you find it difficult don't worry.

所以，如果你覺得困難，不要擔心。

In context people will understand you.

在上下文中，人們會理解你。

If you say: "Five twelfs", okay, I get it.

如果你說："5個12"，好吧，我明白了。

If you say: "Five twelfth-th-th", I'll get it, I'll know what you're trying to say.

如果你說，"五十二三"，我就會明白，我就知道你想說什麼。"12月5日"，我會明白的，我知道你想說什麼。

"Five sixths", this one's even worse, "xths".

"六分之五"，這個更慘，是 "四分之三"。

"Sixths", just say it as close as you can, you'll be understood because people know you're

"六分"，你就儘量說得近一點，就會被人理解，因為人家知道你是個。

talking about fractions.

談到分數。

Okay?

好嗎？

On the other side we can say, like, this is a half.

另一邊我們可以說，比如，這是一個半。

Right?

對吧？

1 over 2, so a half.

1比2，所以半。

We can say it in "decimals" as well.

我們也可以用 "小數 "來說。

"Decimals" are the point form.

"小數 "是點陣。

So, this is "0.5", I hope you can see this point here.

所以，這就是 "0.5"，希望大家在這裡能夠明白這個道理。

We don't say: "Zero decimal five", we don't say: "Zero period five", always "point".

我們不說："小數點後5位"，我們不說："小數點後5位"。"零點五期"，總是 "點"。

Okay? "Zero point five".

好嗎？ - "零點五"。"零點五"。

Now: "Zero point thirty-three", no, because this is not a number, this is a partial number,

現在的。"零點33"，不，因為這不是一個數字，這是一個部分數字。

just like a fraction, it's less than one so it's not "thirty-three",

就像一個分數，它小於一，所以它不是 "三十三"。

it's "zero point three, three".

是 "零點三，三"。

And as many numbers as you have: "Zero point three, three, seven, eight, nine, ten".

還有你有多少數字就有多少數字。"零點三，三，七，八，九，十"。

Well, no "ten", "one, zero".

嗯，沒有 "這個"，"一，零"。

Okay? So, and the thing, and you can go as many decimal places as you want.

好嗎？ 所以，和事情，所以，和事情，你可以去 許多小數位，只要你想。

So this is a whole number, this is the decimal.

所以這是一個整數，這是小數。

One, two, three, four, five, six decimal places, that's what we talk about after the decimal point.

一、二、三、四、五、六位小數，這就是我們所說的小數點後的情況。

Okay?

好嗎？

Now, this is the 10th or one-tenth, everything that's here.

現在，這是第十或十分之一，這裡的一切。

So if you have "0.3", you have "three-tenths" of whatever it is you're talking about,

所以，如果你有 "0.3"，你有 "十分之三"，不管你說的是什麼。

"one hundredth", "one thousandth", and then we go on from there, but we don't usually talk

"百分之一"，"千分之一"，然後我們繼續從那裡開始，但我們通常不會談論。

in these terms beyond the third because it gets a little bit too complicated.

在這些條款中，超越第三種，因為它變得有點太複雜了。

Now, three...

現在，三...

Where does this number...? First of all: "3/100", so first of all it's here...

這個數字在哪裡...首先："3/100"，所以首先是在這裡... ...

Oh, no, it's not, that's thousandths.

哦，不，不是，那是千分之一。

It's over here.

它在這裡。

Okay? So, "3 hundredths", "3 hundredths".

好嗎？所以，"百分之三"，"百分之三"。

Now, if you just say: "zz", like in "pizza", "3 hundredths", close enough, then, again,

現在，如果你只是說。"zz"，就像 "披薩 "中的 "三百分之一"，足夠接近，然後，再來一次。

people will understand you.

人們會理解你。

When you're talking about sports, for example, and they say there's like point-five seconds

當你在談論體育，例如， 他們說有像點五秒，

left on the clock, so he...

剩下的時間，所以他... ...

The guy, basketball, he shoots it, he scores with a tenth of a second left in the game.

那個人，籃球，他投籃，他在比賽還剩十分之一秒的時候就得分了。

So you understand?

所以你明白了嗎？

They're talking about 0.1 second.

他們說的是0.1秒。

Okay.

好吧，我知道了

Next we have "exponents".

接下來我們有 "指數"。

X with a small "2" or a small "3" or whatever number.

X用小 "2 "或小 "3 "或任何數字。

So this whole thing is called...

所以這整個事情叫做...

The "2" is actually called the exponent, the x or whatever number is called the base, and

這個 "2 "其實叫指數，x或什麼數字叫基數，而

we can also refer to this as "the power".

我們也可以將其稱為 "權力"。

So, the whole thing is the "exponent", "base", and "power".

所以，整個就是 "指數"、"基數"、"動力"。

Now, when we talk about: "X to the power of 2", we don't say: "to the power of 2".

現在，當我們談論，"X的2次方"，我們不會說："到2的倍數"。

When the number is 2, we say: "squared", so: "X squared".

當數字是2時，我們說。"平方"，所以："X的平方"。

When we talk about "3", we say: "cubed".

當我們說到 "3 "的時候，我們說。"立方"。

Okay?

好嗎？

So we're going to look in a second, and we're going to look at measuring area of a shape

所以我們馬上要看一下，我們要看一下形狀的面積測量。

or measuring the volume of a shape.

或測量形狀的體積。

Different shapes, of course, but "area" is measured with "x2" or whatever the measurement

當然，形狀不同，但 "面積 "是用 "x2 "或其他什麼測量方法來測量的。

is squared, and the volume is measured with "cubed".

是平方，體積用 "立方 "來衡量。

Okay?

好嗎？

Now, once you get past the third-four, five, six-there's two ways you can say it, you can say:

現在，一旦你過了三四五六，有兩種說法，你可以說。

"X to the 4th power", if this is a "4": "X to the 4th power",

"X到第4次冪"，如果這是一個 "4"。"X到第4次方"。

or "X to the power of 4".

或 "X的4次方"。

Now, sometimes you might see...

現在，有時你可能會看到...

You might hear this expression: "The nth power".

你可能會聽到這樣的表述："第N個權力"。

"The nth power" means unlimited, it goes on forever, or infinite, we don't know where

"第n次冪 "的意思是無限的，它一直持續下去，或者是無限的，我們不知道在哪裡。

it ends but this is actually an expression used in regular English as well, and we'll

結尾，但這其實也是常規英語中使用的表達方式，我們會用

talk about that another time.

下次再談吧

Now, if you're going the opposite direction, instead of squaring the number you want to

現在，如果你要往相反的方向走，而不是把你想要的數字平方化，你要

find the "root" of the number.

找到數字的 "根"。

So, 3 squared equals 9.

所以，3的平方等於9。

Okay?

好嗎？

The square root of 9 is 3.

9的平方根是3。

How many times does 3 go into 9?

3進入9的次數是多少？

3 times, etc.

3次，等等。

"Square root", finding out how many times the number goes into itself.

"平方根"，找出這個數進自己的多少倍。

X2, multiplying the number by itself two times.

X2，把這個數乘以自己的2倍。

Okay.

好吧，我知道了

So far so good, but we're not done yet.

到目前為止還不錯，但我們還沒有完成。

We still have to look at shapes and what to do with them, and angles.

我們還是要看形狀，怎麼處理，還有角度。

A lot more interesting stuff coming up. One sec.

還有更多有趣的事情要發生。一秒鐘。

Okay, so actually we're going to look at a couple more symbols and words before we go

好了，所以實際上我們要看 在我們去之前，一對夫婦更多的符號和單詞。

on to other more complicated things.

到其他更復雜的事情。

I wanted to just squeeze these in because they're a little bit simple, but still need

我想把這些擠進來，因為它們有點簡單，但還是需要。

to understand them.

來了解他們。

"Average" and "mean", now, "average" and "mean" are synonyms, they essentially mean the same thing.

"平均 "和 "平均"，現在，"平均 "和 "平均 "是同義詞，它們本質上是同一個意思。

We use "mean" more with math.

我們用 "平均 "與數學的關係比較大。

We use "average" more with other things, like everyday things as well.

我們更多的是用 "平均 "來搭配其他事物，比如日常事物也是如此。

But they mean the same thing.

但他們的意思是一樣的。

So when you're looking for the average or the mean, you're taking all the values...

所以，當你在尋找平均值或均值時，你要把所有的值... ...

So in this case we have one, two, three, four values, you add them up, you take the total

所以，在這種情況下，我們有一個，兩個，三個，四個值，你把它們加起來，你把總。

and then divide it by the number of values you started with.

然後除以你開始的值的數量。

So the...

所以...

We have four values, the total 20 divided by 4, and the average of these values is 5.

我們有4個數值，總共20除以4，這些數值的平均值是5。

Okay?

好嗎？

So that's "average" or "mean".

所以這就是 "平均 "或 "平均"。

Now, on the other hand, you want to sometimes look for the "median".

現在，另一方面，你有時要尋找 "中位數"。

Now, some...

現在，有些...

In some situations you don't want the mean or the average because the extremes, the top

在某些情況下，你不想要平均數或平均值，因為極端值、頂部

or the bottom are so far apart that the average will not give you a right idea of what's going

或底部相距太遠，平均數不會給你一個正確的想法是什麼回事

on with whatever values you're looking at, so what you want is the "median".

所以你想要的是 "中位數"。

The "median" is more like the middle number that has an equal number of values above it

"中位數 "更像是一箇中間數，它上面的數值是相等的

and an equal number of values below it.

並在其下方有相同數量的數值。

So that's a little bit more representative of the situation you're looking at.

所以，你看的這種情況比較有代表性。

Okay, so now we're going to look at these symbols.

好了，現在我們來看看這些符號。

We got this one, this one, this one, and this one - four of them.

我們得到了這個，這個，這個，這個，還有這個--四個人。

Now, this one, when you have the bigger size open and then it goes to the smaller size

現在，這一個，當你有較大的尺寸打開，然後它轉到較小的尺寸。

means y is larger than x.

表示y大於x。

Larger, smaller, right?

大一點，小一點，對吧？

So, y is larger than x, y is greater than x, y is more than x.

所以，y比x大，y比x大，y比x多。

Don't forget the "than" because, again, you have a comparative here.

不要忘了 "比"，因為，你在這裡又有一個比較。

And if you turn it around, y is smaller than, y is less than x.

而如果把它轉過來，y小於，y小於x。

Now, sometimes you might see these symbols with a line underneath, in which case:

現在，有時你可能會看到這些符號下面有一條線，在這種情況下。

y is greater than or equal to x. Okay?

y大於或等於x，好嗎？

Y is greater than or equal to x, y is less than or equal to...

Y大於或等於x，y小於或等於......。

Sorry, y is greater...

對不起，Y是大...

Less than or equal to x.

小於或等於x。

And now, this one you have...

而現在，這個你有...

Basically you have the equal sign, but then you have a squiggly line.