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.