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.
