#### MATH & GEOMETRY Vocabulary and Terminology in English

Hi. Welcome to www.engvid.com. I’m Adam. In today’s video I’m going

to look at some math. Now, I know this is an English site, don’t

worry, I’m not actually going to do any math. Philosophy and English major, so math not

my favourite, but I will give you some math terminology, words that you need

if you’re going to do math. Now, a lot of you might be engineers or you

might be students who came from another country to an English-speaking country, and you go to

math class and you know the math, but you’re not sure of the wording. 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. Okay? We’re going to start

with the very basics. You know all these

functions already. 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. So, you know the four basic functions: “addition”,

“subtraction”, “multiplication”, and “division”. What you need to know is

ways to say an equation. Right? You know an equation. “1 + 1=2”, that’s an equation. “x2 + y3=znth”, that’s also an equation which

I’m not even going to get into. So, let’s start with addition. The way to talk about addition. You can say: “1 plus 1”, “plus”, of course

is “+” symbol, that’s the plus symbol. “1 plus 1 equals 2.” 2 means the total, is

also called the “sum”. Now, you can also say:

“The sum of 1 and 1 is 2.” You can also just say, without

this part: “1 and 1 is 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. Everybody will understand

you’re making… You’re doing addition. Sorry. Doing addition,

not making. If you add 1 and 1, you get 2. Okay? So: “add” and “get”, other words

you can use to express the equation. Now, if you’re doing math problems,

math problems are word problems. I know a lot of you have a hard time understanding

the question because of the words, so different ways to look at these functions using

different words, different verbs especially. If we look at subtraction:

“10 minus 5 equals 5”. “5”, the answer is also

called the “difference”. For addition it’s the “sum”, for

subtraction it’s “difference”. “10, subtract 5 gives you 5.” Or: “10 deduct”-means take away-“5”,

we can also say: “Take 5 away”… Oh, I forgot a word here. Sorry. “Take 5 away from

10, you get”, okay? “10 subtract 5”, you can

say: “gives you 5”, sorry, I had to

think about that. Math, not my specialty. So: “Take 5 away from 5, you get 5”,

“Take 5 away from 5, you’re left with”, “left with” means what remains. Okay, so again, different ways

to say the exact same thing. So if you see different math problems in different

language you can understand what they’re saying. Okay? Multiplication. “5 times 5”, that’s:

“5 times 5 equals 25”. “25” is the “product”, the answer

to the multiplication, the product. “5 multiplied by 5”,

don’t forget the “by”. “5 multiplied by 5 is 25”, “is”,

“gives you”, “gets”, etc. Then we go to division. “9 divided by 3 equals 3”, “3”, the

answer is called the “quotient”. This is a “q”. I don’t have a very pretty

“q”, but it’s a “q”. “Quotient”. Okay? “3 goes into… 3 goes

into 9 three times”, so you can reverse the

order of the equation. Here, when… In addition, subtraction,

multiplication… Well, actually addition and multiplication

you can reverse the order and it says the same thing. Here you have to reverse the order:

“goes into” as opposed to “divided by”, so pay attention to the

prepositions as well. Gives you… Sorry. “3 goes into 9 three

times”, there’s your answer. “10 divided by 4”, now, sometimes

you get an uneven number. So: “10 divided by 4” gives you 2 with

a remainder of 2, so: “2 remainder 2”. Sometimes it’ll be “2R2”,

you might see it like that. Okay? So these are the basic

functions you have to look at. Now we’re going to get into a little

bit more complicated math things. We’re going to look at fractions, exponents,

we’re going to look at some geometry issues, things like that. Okay, so now we’re going

to look at something else. We’re going to look at fractions,

exponents, and decimals. Again, all of you know these things even from

high school, even before high school, primary school math some of this stuff. A “fraction” is basically a partial

number; it’s not a whole number. It’s a part of, that’s why

it’s called a fraction. You have two parts to this fraction, you have

the “numerator”, “nu-mer-a-tor”, and then you have the bottom part which is the

“denominator”, “de-nom-in-at-or”. Numerator, denominator. 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. We just need to know the words. What you might have some

trouble with is pronunciation. 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”. Now, keep in mind that even native English

speakers have a hard time pronouncing this, so if you find it

difficult don’t worry. In context people

will understand you. If you say: “Five

twelfs”, okay, I get it. If you say: “Five twelfth-th-th”, I’ll get

it, I’ll know what you’re trying to say. “Five sixths”, this one’s

even worse, “xths”. “Sixths”, just say it as close as you can,

you’ll be understood because people know you’re talking about fractions. Okay? On the other side we can

say, like, this is a half. Right? 1 over 2, so a half. We can say it in

“decimals” as well. “Decimals” are the point form. So, this is “0.5”, I hope you

can see this point here. We don’t say: “Zero decimal five”, we don’t

say: “Zero period five”, always “point”. Okay? “Zero point five”. Now: “Zero point thirty-three”, no, because

this is not a number, this is a partial number, just like a fraction, it’s less than

one so it’s not “thirty-three”, it’s “zero point three, three”. And as many numbers as you have: “Zero point

three, three, seven, eight, nine, ten”. Well, no “ten”, “one, zero”. Okay? So, and the thing, and you can

go as many decimal places as you want. So this is a whole number,

this is the decimal. One, two, three, four, five, six decimal places,

that’s what we talk about after the decimal point. Okay? Now, this is the 10th or

one-tenth, everything that’s here. So if you have “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, but we don’t usually talk in these terms beyond the third because

it gets a little bit too complicated. Now, three… Where does this number…? First of all:

“3/100”, so first of all it’s here… Oh, no, it’s not,

that’s thousandths. It’s over here. Okay? So, “3 hundredths”,

“3 hundredths”. Now, if you just say: “zz”, like in “pizza”,

“3 hundredths”, close enough, then, again, people will understand you. When you’re talking about sports, for example,

and they say there’s like point-five seconds left on the clock, so he… The guy, basketball, he shoots it, he scores

with a tenth of a second left in the game. So you understand? They’re talking

about 0.1 second. Okay. Next we have “exponents”. X with a small “2” or a small

“3” or whatever number. So this whole thing is called… 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”. So, the whole thing is the

“exponent”, “base”, and “power”. Now, when we talk about: “X to the power

of 2”, we don’t say: “to the power of 2”. When the number is 2, we say:

“squared”, so: “X squared”. When we talk about

“3”, we say: “cubed”. 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. Different shapes, of course, but “area” is

measured with “x2” or whatever the measurement is squared, and the volume

is measured with “cubed”. Okay? Now, once you get past the third-four, five,

six-there’s two ways you can say it, 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”. Now, sometimes you might see… You might hear this

expression: “The nth power”. “The nth power” means unlimited, it goes on

forever, or infinite, 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. Now, if you’re going the opposite direction,

instead of squaring the number you want to find the “root” of the number. So, 3 squared equals 9. Okay? The square root of 9 is 3. How many times does 3 go into 9? 3 times, etc. “Square root”, finding out how many

times the number goes into itself. X2, multiplying the number

by itself two times. Okay. So far so good, but

we’re not done yet. We still have to look at shapes and

what to do with them, and angles. A lot more interesting stuff coming up.

One sec. Okay, so actually we’re going to look at a

couple more symbols and words before we go on to other more

complicated things. I wanted to just squeeze these in because

they’re a little bit simple, but still need to understand them. “Average” and “mean”, now, “average” and “mean” are

synonyms, they essentially mean the same thing. We use “mean” more with math. We use “average” more with other

things, like everyday things as well. But they mean the same thing. So when you’re looking for the average or

the mean, you’re taking all the values… So in this case we have one, two, three, four

values, you add them up, you take the total and then divide it by the number

of values you started with. So the… We have four values, the total 20 divided

by 4, and the average of these values is 5. Okay? So that’s “average” or “mean”. Now, on the other hand, you want to

sometimes look for the “median”. Now, some… In some situations you don’t want the mean

or the average because the extremes, the top or the bottom are so far apart that the average

will not give you a right idea of what’s going on with whatever values you’re looking

at, so what you want is the “median”. The “median” is more like the middle number

that has an equal number of values above it and an equal number

of values below it. So that’s a little bit more representative

of the situation you’re looking at. Okay, so now we’re going

to look at these symbols. We got this one, this one, this

one, and this one – four of them. Now, this one, when you have the bigger size

open and then it goes to the smaller size means y is larger than x. Larger, smaller, right? So, y is larger than x, y is

greater than x, y is more than x. Don’t forget the “than” because,

again, you have a comparative here. And if you turn it around, y is

smaller than, y is less than x. Now, sometimes you might see these symbols

with a line underneath, in which case: y is greater than or equal to x.

Okay? Y is greater than or equal to x,

y is less than or equal to… Sorry, y is greater… Less than or equal to x. And now, this one you have… Basically you have the equal sign,

but then you have a squiggly line. This means it’s approximately equal to, so

it’s an approximation, not exactly equal. And then you have the equal sign with a strike

through, and in this case it’s just not equal. Okay, pretty

straightforward stuff. Let’s move on to some other

more complicated things. Okay, let’s look at

some more math stuff. We’re going to look at shapes. Okay? So, first of all we’re going to start with

our “rectangle”, means the two sides… All four sides are

not the same length. You have the “width”,

you have the “length”. Okay? Now, when you add a “height” or a “depth”, both okay,

depending on what you’re looking at, then you… First of all, you’ve

created a box. So, a rectangle is two-dimensional,

a box is three-dimensional. Width, length, height

or depth, both okay. Now, when you measure

these, when you measure… Like, basically you want to measure the

inside space, then you’re measuring the area. So you do length times width, and then

the answer is whatever the number is. So let’s say you have two feet by four feet,

so you have eight, and then the measure… If you’re measuring in metres, in feet, in

inches, in kilometres, whatever, and then you have the square. So, whatever 20 metres square,

20 square metres, etc. With… When you add the third dimension now you’re

measuring volume and you’re using the 3, the exponent 3 instead

of the exponent 2. Okay? Now, other shapes. We have a “square”, all

four sides are equal. When you put in the extra measure, the

extra side, then you have a depth to it, then you have a “cube”.

Okay? So… And, again, another way to think about this: This

is two-dimensional, that’s why it’s squared; this is

three-dimensional, cubed. Okay. A “circle” or a “sphere”. Now, I can’t draw a sphere because I’m not a

very good artist, like if I do like this… You know, like a moon,

like a ball is a sphere. The flat shape is the circle. If you want to measure the outside

of the circle then you’re looking… You’re trying to measure

the “circumference”. Sorry, I forgot to mention, if you want to

measure the outside area of the rectangle, you’re measuring the

“perimeter”, same for square. For a circle you’re measuring

the circumference. If you want to measure the volume of a sphere

then you’re starting to get into things like “radius”, so our radius is from the centre

to one side, that’s half the distance from side to side. If you want to go the full distance,

then you have the “diameter”. “Radius”, “diameter”, full length, basically

cutting it in half, equal points. So that’s the circle. Then you start… If you want to get into the actual measurements

then you start having to look at “pi”. Okay? Just that’s how it’s

spelled, “pi”, from the… I think Greek, if I’m not

mistaken, the letter. Now, we’re getting

into “triangles”. We’re going to look at triangles again in

a minute, but for now the two-dimensional triangle. Now, three-dimensional you can have a “pyramid”,

you can have the base and then you have the sides coming up to an apex. “Apex” means top point of something, or you

can have a “prism” where you have the extra side on this side. Okay? So, triangle,

pyramid, prism. But then we have other shapes like “oval”,

this is like a “cone”, like an ice cream cone. And there’s a bunch of other shapes, there’s

a “rhombus”, there’s a “diamond”, there’s a “hectagon”, there’s an

“octagon”, all kinds of shapes. If you’re not sure, basically you

can punch in the word you want… Just get a math book or Google “shapes”, and

you’ll see all the different shapes that are available to you, both two-dimensional

and three-dimensional. Okay? There’s too many of

them to list here. These are the basics, we’re

going to work with these. We’re not done yet, though. There’s still some more

math stuff to come. We’re going to look at the different types

of triangles and the different angles that each of them will have. Okay? Okay, almost done, don’t worry. I know you’re loving this math

stuff, but we’re almost done. We’re going to look at some

triangles and some angles next. Okay? So there are different

types of triangles. “Isosceles”, “isosceles triangle”

has two equal sides and one… Two equal length sides, and one that’s different,

and “equilateral” has all three sides equal length. By the way, just so you know, “lateral” means

side, “equi” is equal or even, so “equilateral”. So, equilateral, all

three sides are even. And then when you have all three sides different

length, we call this a “scalene”, “scalene” triangle. Now, the… For example, the isosceles or the scalene,

or really any much either of these two can also be a “right

angle triangle”. A “right angle” is this square

here, it means 90 degrees. When you have a 90 degree angle and you want

to measure its area, you have to use this line directly opposite to the right angle,

and this line is called the “hypotenuse”. “Hypotenuse”, okay? You use that to calculate. Now, when we’re talking about triangles,

or really any shape, like we can… A rectangle in a box, in a rhombus, etc., we

have angles and when you’re talking about… When we talk about angles

we’re talking about degrees. So, a circle is 360 degrees. Now, if I have just a straight line, that’s

basically like the diameter of a circle. If you think of this as a circle, this is the

diameter, so it’s 180 degrees for a straight line. So we have 360, 180,

and then we have 90. So when you have a line, when you have a square,

when you have a straight line and another straight line directly on top of

it making a square, a right angle, we call this a

“perpendicular” line. This line is standing

perpendicular to this line. Okay? We’re going to get back

to that in a second. Now, let’s look at

some other angles. If you have an angle that

is less than 90 degrees… Okay? I hope you can sort of

see it in this diagram. Less than 90 degrees it’s

an “acute angle”, “acute”. Not “cute”, “acute”. Angle, sorry, not a good one. If you have… If you have an angle that is more than 90 degrees

we call this an “obtuse”, “obtuse angle”. And then if you have an angle that’s more

than 180, so for example if I’m measuring thing angle, it’s more than 180

degrees, that’s a “reflex angle”. So you have all these different

angles to work with. Again, very important for those of you who

are doing geometry and whatnot to know the names of these angles. Now, here we have a perpendicular line, means

straight at 90 degrees or at a right angle to another line. If it’s not at a 90 degree angle,

then it’s on a “diagonal”. So, diagonal is less or more than 90 degrees,

it depends which way you’re looking at it. Now, one last thing here, if

you’re looking at graphs… Like, I’m not going to get into the details

of the math here, but these two lines, they intersect at this point, this is, like, usually

the zero point base, whatever, at this point they intersect, cross. Now, generally this is the “x axis”, this is the

“y axis”, and in this graph you have two axes. Singular: “axis”,

plural: “axes”. Okay? So you know these lines. And finally we have

“parallel lines”. Parallel lines are two lines that go in

the same direction, but will never meet. Okay? So there’s an equal distance between them, and that

equal distance between them continues forever. They’re running along the same direction,

the same track apart from each other, they will never meet. Okay, so I think we’ve covered

basically everything on this here. Now, before I finish, I

just want to say one thing: I have just scratched the

surface of math in this lesson. I know math is huge, it’s a huge field, I

don’t pretend to know even a bit about it, but I wanted to give this

to you as a starting point. From here you can go on and do whatever

math you do, whatever specialty you have. If you need to get into more… Like in more depth, more detailed math, you’re

going to have to look that up on your own because, again, I’m not going to be

very helpful with the math part of it. When you go to the forum at www.engvid.com to ask

questions, please don’t ask me any math questions. You can ask me about words. Don’t ask me to do any equations

or anything like that. Calculus, forget it; algebra,

geometry, trigonometry, whatever. Here are your basics. Okay? If you have any questions, though, of course

do come to the engVid forum and ask them. There’s also going to be a quiz where you

can practice with some of these words. If you like this video, and I hope you did,

please subscribe to my YouTube channel. And again, I hope you enjoyed

it and I’ll see you again soon. Bye-bye.

perfect math vocabulary

The lesson was great, Adam. But I have to admit that I'm quite disappointed in myself. I remember I was bad at math at school but after this I noticed that I remember almost nothing about it. HAHAHAHAHAHAHA.

Should've put a little more effort to my studies back then….

it was amazing. I think you are one of the best.

It is very important to me. thank you for your video.

Hi Adam , this is a great video, now I've learnt something new

Great lesson,

Thanks

I can not find enough words to

fullyexpress my appreciation for your incredible instruction. Your explanation of the English words used in Math captured my attention for the entire time. Thanks toyourvideo, I am more confident that a firm understanding of Math "language" helps us with the actual "operations" that need to be performed.As a person who loves language, I can honestly say again that I sincerely impressed with your presentation. Thank you for sharing this lesson with us here on YouTube.

Great one, thanks a lot!

Omg this is so helping me because i get a material for my prrsentation about it. Thanks a lot sir 💕

you are best of the best /this video helped me so much

Thanks a lot ! It's a very very helpful video

Thank teacher.

video would be perfect, if not one thing… Noone has noticed it's "hundreDths not hundreths". Look up in dictionary if you dont trust me

Thank you, Adam! You did great job here! From time to time, I get different questions about some Math stuff from my students. This video is super helpful.

I'M TÜRKISH ♥

Thank you Adam you are doing great job

Thanks

Thank you Very Dear Teacher

Thanks very much, Adam! I love your video and that's very helpful to me !

Thank you! I often watch math and physics lessons in English on Khan Academy channel and it's necessary to understand the math terminology for the best understanding of teaching material. But still it's difficult to me to watch and understand some physics lessons, because some physics terms cannot be translated word-for-word, for example, the term "cross sectional area".

Good job man……

Do calculus please.

Thank you so much! I love this lesson. I'm Russian I learn English and I'm so happy because I understand this video

Explained in a simple way, Thank you

very very helpful thank you very much

Thank you so much, Adam!

I’m here so I can get bored to sleep

You are great teacher.

I can speak English a little. But I try every day for learn it.

Thank you!

More video please, if you want.

Perfect video! Thank you so much!

thanks

mental

very useful lesson.

Verry Good

Now Math is so cool

I ❤ math.

Thank you ! I am from Kazakhstan , of course i dont know english huge but i enjoy this lesson!!!!I love you Mister… You´re so nice to teach and I wish to watch more videos from you…. I have 2 teacher who are so smarter by Math Profe Julio and you…. Go bless you…

thank u very much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Youre a life savior i just moved in to new country, i know math pretty good, but i didnt knew any of the english terms. This video helped a lot thanks man!

Very helpful! You are a great teacher! Thank you very much🙏🏻

Thank you for the lesson, Adam

I ♡ maths thanks 🙂

Your English is easier to understand and I love this video it can help me a lot, I'm really really thank you from hear 🙏🙏🙏

What a good teacher! Moreover you really taught about non-native speaker! It's so great to have the transcription.

U just saved my life

Wow, just what I was looking for, amazing demonstration sir 👍✅➕➖➗✖️💲

Thanks a lot. Your explanation was very helpful. Actually maths are very difficult to explain in any native language, but you did it great.

Hello, Adam! I just watched this video and loved it. I really appreciate all of the information you explained.

I’m a math teacher and I’m learning english also so you can imagine your video was to me. You really did a great job. Just can sayTHANK YOU, Adam!

By the way, I’m from 🇳🇮

Nice! but there is an error on the calculation of average.this is not -4 but rather : 4 .so it gives 20 : 4 = 5

Thank you so much….it is very useful video…..

thank my new teacher. Although ı havent a good english ı understood very well.

Thank you , that was helpful

It's a very good vedeo . I have benefited well

Useful. Just to know. TY.

Great explanation!

Come on nobody likes math !!!😯😯😯😯😯😯😯😯😯

He’s vere good Maths teacher

Teacher Adam is suberb teacher ever. Thank you

best best

What a very useful video Adam! I love you bro, regards from Colombia.

Thank you very much for this lesson!

That lesson is very useful.thanks a lot.

Hi. Can you give me transcript about the lesson fraction, exponent, decimal from this video?

respect from india thank you so much

thank you !! you saved my day !

Good 👍👍👍👍👍❤️❤️❤️❤️❤️

tanks Adam

Thanks a lot sir…

Gracias es muy claro.

amazed by the lesson…super

I enjoyed the video! Thank you!

Lots of love and respect to you sir

Such a shame I cannot subscribe twice.

wow the best teacher.

You have not explained factors. Basically I need to prepare for GMAT exam and some of the terminology of Basic maths is confusing.

That's enough stuff to start with, you're right. Many thanks.

your cone is upside down..,bdw, with decimals, can i say zero dot five insted of zero point five?? thx, Sir!

Hello Adam… Excellent class about Math elements. You made me remember my classes at University with my English teacher when I studied Engineering. Some concepts, I had forgotten them, for example "nth power" or "reflex angle"… A nice memory

ADAMSIN 😂😂😂

ADAMIN KARESİ (SQUARE OF ADAM)

How to say 2.3.4.5= 120 please?

Hello Adam, How do you say Arithmetic?

Boring

Guys. I have a doubt . Shall we write 62.56 as 62.3??

I really love your lessons thank you

Excellent Adam! Thank you so much.

ty

super lesson math and geometry

How to read this..

1×1=1

Help me plz

Thx for the lesson..

thanks for this useful of information of basic mathematics language

Just what I needed. Thank you.

Hi Adam, I learnt all these terminology in Portuguese, but i did not know how to say them in English, therefore your explanation helped me so much. I am really glad. Thanks

nice lesson

thank you very much. I will go to college and study math this fall, but I don't know any vocabulary about math because the vocabulary about math is too much. I can't remember…T T…I think I will watch this video more times.

Your level of English:

– read this – intermediate

– like – upper intermediate

– subscribe – advanced

10:40 what about Cube Root? How do you say it in your regular English, just Cube root?

what you taught is exactly what I need right now.

Thank you!

woooow great that's great

Ironically enough