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• Hi. Welcome to www.engvid.com.

• 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?

• 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.

• 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...

• 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",

• 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...

• 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...

• "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

• 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...