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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.

  • 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.