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Math 7 - Lesson 12

Added Apr 22, 2021 •

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How is Multiplication related to Division? Identify the Dividend, Divisor, and Quotient. How are the Dividend and Divisor related to Numerator and Denominator? How is division related to fractions?

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e x 7 there is no twin there is just there is not a twin but there is something similar to three times seven so they'd have to walk around the classroom and for all right who has something that's like mine three times what is light well that's one that this equals 21 but what else equals 21 so you would have to find 7 x 3 person and then there are more all right so that right there is to show the commutative property so I'm going to do a quick review of the commutative property right here the commutative property come you don't need to write this down but you should if you want commute property and look at this three times 7 equal 117 * 3 which one of us will do the same thing all it is is there flip so multiplication it doesn't matter what or do you multiply in just like Edition so that's a comedian Bree and her thing you got to be specific of multiplication multiplayer keishin you can I don't care if that's okay that's it out all right now let's connect that with what we learned already the commutative property of addition commutative property of addition I'm just going shorthand it does it's just lazy 5 minutes all right so the community property of addition said 3 + 7 equals 7 + 3 3 + 7 is 10/7 + 3 is 10 3 times 7/7 times 321 equals 20 10 equals 10 there different ones Edition ones multiplication now we also learned last module that there is no such thing as commutative property of subtraction let's go what is 7 - 3 7 - 3 what is 3 - 7 negative 4 so 10 equals 10 but -4 does not equal 4 so that's why there is no subtraction community property so there's this attraction it doesn't exist for some prank same thing for division we're going to go over to Vision in the second but we learned we'd learn so we learn how to change a subtraction problem into an addition problem so let's do a quick review of module 2A so this is why people messed up on so you guys thought you cannot you can change subtraction to addition low so the change subtraction into addition let's do this Mark 7 - 3 subtraction to a but notice this comes first we don't do anything with the first number subtraction becomes Edition but it's called adding the opposite to subtraction becomes Edition what is the opposite of 3 a lot of people forgot to write down the negative side so you can just make a addition it needs to be adding the opposite that's where people messed up 7 - 3 is 4/7 + -3 is 4 that's why now it's Edition we can flip it around -3 + 7 addition can be flipped around commutative property only for addition only for multiplication we're going to show later on that it does not work for division so let's get back to this looking at the title of this right here so there are two people walking around or would have been have a related division equation what is the related division equation for this 3 * 7 three times 72017 * 3 is 21 they're both they're both equivalent but they don't mean the same thing okay so remember the first number says how many times a number is repeated so we have three sevens right that's what multiplication means but it also means repeated addition 7 + 7 + 7 repeated this year 7 is repeated 7 * what's 7 * 3 seven groups of three that's why we don't like writing repeated addition we short made a short and just did multiplication but they're both equal to 21 which is true you are right so now look at this though Co there are equal to 21 but look at the topic division of integers there would be two people if this was a regular class normal time I'd happy you have to find two more people but those two people that these are the only ways to multiply to get 3 * 7/7 * 3 that's only get 21 but what about division so that's why we're doing this today I lie to you guys freak out over to visit it is not hard isn't all right you need to finish that thought you were correct forget the Asian don't that's why you get stuck using divisions division division is the same it's the same thing as multiplication just written differently let's look at this no going back so you were connecting you were connecting addition and subtraction addition and subtraction are connected subtraction just adding the opposite it's just the trash is a shorter way of writing adding negative numbers oh okay let's go do it now then so let's look at this 21 / 3 a lot of guys freak out forget that this is where algebra comes in so when you going to get the next year or the year after so instead of seeing as 21 / 3 look at it like this three times what number gets me 21 3 times what is 21 able to do that instead of same thing go instead of looking at it is 21 / 3 equals 7 anytime you're stuck with the vision think multiplication ignore the quote ignore the big number you're saying / 3 forget / 3 3 * the answer gets me 21 the opposite 7 you're correct yes 7 so then 21 / 7 you got to think what number times 7 gets me 21 just think the other way around but you earlier somebody said earlier you threw a negative so this right here is the basic equation you have your basic family right here but you have so think about this 3 * 7/7 * 3/3 pretty much almost exactly the same your siblings but these right here they're not equal to 21 but they're connected connected by one step stool like cousin your first cousin is either is from your mom or dad side that's your first cousin second cousin which are like cousins of cousins you're not directly related you might not be blood related to them but you still call him a cousin cuz they're related to your cousin but they're not your cousin second cousin so so this right here would be a first cousin cuz they're connected directly but let's look at my second cousin's not directly plated but similar so the first one we're going to write down is let's go instead of 3 * 7 we got I'm going to right over here this should have been a bigger butt yes go find Millsap so slightly different instead of 3 * 7 + -3 * 7 what is -3 * 7 what is a chatter so much that it out here go ahead what is it lalalala lalalala you made the best mistake so 80 I said it earlier what did I say about 80% of their mistakes 80% of your math mistakes are adding subtracting multiplying dividing that is 8 a lot of guys freak out and say all I got the wrong answer so you got the wrong answer why don't you look at your mistake -21 that's what I want you guys to do use the example of The Tortoise and the Hare I use example of The Tortoise and the Hare this is not a race this is about getting math is about getting it right you saw a -3 and 7 and went straight to 4 I understand why you did that look at this right here -3 and 70 subtract you get for but you went so fast you skip how are they connected in the middle multiplication you had if it was a distance between you have been perfectly right but slow it down just a little bit or see everything and you would have gotten it right and you saw the 21 after so but that's the whole thing are you guys thinking about checking your answer and looking it over and things that I do it right now he's just like I won't be done in math is not about a race it's about getting it right so watch -3 * 7 negative 21 what's another way to write -3 * 7 looking like modeling let's the next one I put that under here so I'm going to and notice all we did was Flip Flip the negative and positive signs the negative is now on the staff appositive noun the three and it's still good correctly stole -21 but was there another way to write -3 * 7 well we'll get to that multiplying a multiplying is there another way to write as multiplication as multiplication we got -3 * 7 equals 21 -7 * 3 + 21 please multiplication have another way of writing multiplication that's so so we're doing all this cuz we need to see all the different that's a freak so many ways so many ways something I said I can't do this I quit but it's not so anyway it's just written differently that's what you guys need to understand so good one person gave me an example here with this one you can give me the next one watch -3 * 7 is the same thing as 7 * -3 that's negative 21 so what do you think this got so what's this one direct your right yes you're right 3 * -7 the commutative property remember multiplication has nothing well there is the positive negative aspect but when we multiply we can switch the order around it does not matter so which one's better that's a personal choice do you like vanilla or chocolate or cookies and cream that's a personal choice I hate chocolate mints I used to like it I used to like it I can't eat it anymore it's disgusting I like I like the little the chocolate the little Andes chocolate mints those are tasty but when you make a ice cream flavor out of it and now I can't do it I like I don't know I like it at a restaurant when they get when they put it on the thing and all I told him to take it out and see thank you for submitting your mouth hat off all right let's get all of this so alright so we got to there is look at this I got a -3 and I got an egg 7 with a positive 7 and a positive 3 look at this I got a positive 3 and a positive 7 does anybody know the last one go ahead what do the fish later does anybody know the last version of a multiplication of 7 and 2/3 that we have enlisted I think we got several times throughout here go ahead -7 equals what ? -7 * -3 all the different so go back to last week's lesson lesson 11 what is it just 21 find the negative positive remember the process of combining is Edition but when it says positive positive not a addition good but good yes fix the terms let's learn the Lexile with Wonder vocabulary so good so negative times negative becomes a positive so we don't need to write the plus sign cuz when it's not there we assume that it's automatically positive that's the whole thing about me it's like a language it's when I decided in high school to take Spanish 1 the Espanol no sdn that's what I would always say como como como te llamas read me Professor with always yell at me you got to pronounce or I'm taking a class I hate you color yeah I didn't learn that the exit but that's the whole thing of what makes math lucky we got all these little different ways of writing it out so positive 21 and we don't need to write a positive sign all of the things good all you guys or -3 * -7 equals positive 21 all right all right I'm going to give you a second so you guys I'm going to give you the first one all right so just to save space you don't need to write this next half for this next one cuz these are the same thing like Mathias said all it is it's the same thing it's just what we do so we don't want this life or the next one so I'm going to give you this one right here we're going to go or time six fill in the three here and fill in only the three version all right I don't need this path so and space it out cuz we're going to add stuff right here to it space it out so I'm going to give you two minutes let me bust 4 * 6 is 24 great lot of people. That lets check your work 6 times for 24 so flipping it why do you guys wrote flipping it no use the math term when you switch the order of numbers the commutative property of multiplication and then division the store 24 / 4 + 24 / 6 and they're just the opposite of each other on opposite cuz that would be negative there just the other number all right so let's go with this right here so I hear so let's match it up so let's go -4 * 6 equals what good you said you didn't know it and then missing right here -6 * 4 equals -24 what's the only difference from this one to this the negative on the floor good and look what happened to wear answer became negative to look at this what's the difference between this one all we did was switch the negative look at that right there and what's the difference between this one and this one we switch the negative from the 4 to the 6 and the positive from the 6th to the four and then the last one which is right one of them it doesn't matter we don't need both of them so -4 * -6 both of them are negative Aldi's right here near me positive 24c good good positive I like it now we have the related to switched one but I don't want to write that down so now if someone said that Division 1 all right let's write the division so this one right here -4 * 6 equals -24 look at this all it is we take the app sister and we / the other number we take our Aunt it's not equal it's not equal to draw an arrow not equal I almost wrote equals naughty we're going to change it with the vision so we take our answer and now instead of being the answer it becomes part of the expression the equation so negative 24 / and choose one of the numbers 3 / X the network south 2224 / -4 and then let's do the other one positive 6 cuz it's just the other one a -24 divided by 6 no look at it what are the two numbers are multiplied all all you have to undo division is to look at your answer and connect it with one of the other numbers and the answers the other number let's go do this one right here so it still negative 24 and let's what's line it up listen right here so -24 / 4 equals look at this all it is is the other number let's go the other one 24 / Let's go negative 6 it's the other number division is just looking for the other number you * list of division as multiplication and after a while you start seeing the same numbers you do it over and over again and you don't even care about multiplication or division you just do because of The Hobbit this is what I do remember every time you set up a division you always take the answer the multiplication problem start out with that so 24 and you / one of the other numbers in your answer is always the other one we're just looking for a pattern here 34 divided by -4 no yeah CC we delivered it we did -24 / new but now we got 24 divided by -4 which is -24 divided by -6 other number -4 good now we're going to answer some questions when I look at some powders but let's look first to let's look at these numbers Let's ignore the division positive times positive because this we got two positive numbers right here answers positive we got to neg we multiply positive we got a negative times a positive and we could have did positive times a negative with the other way around got a negative answer now let's look at our division with / positive numbers we divided by a positive and a negative that's my fault I'm just like they're divided by a negative and a negative divided by negative negative / positive negative / positive negative divided by negative positive divided by negative look at the results that's we're looking for patterns so let's see so right here let's look at it list example so right here when we're talkin about example the quotient list examples of division problems that produced a quotient that is a negative number a quotient is the answer to a division problem much like product is the answer to a multiplication problem that's a product that's a product this is a quotient this is a quotient yes next page show quotient so I'm going to bring up some vocabulary words dividend and divisor in a division problem it is dividend did it end / / bore. equal to the quotient like I was going on with this finish this up so the quotient is the answer to a division problem the first numbers called the dividend II numbers call the divisor and someone in the other class I just want to hit it off we can right there we can write division as a fraction but that's the whole thing so let's finish this up you what so they were they make money when they form an emo band are they going to be living outside right now my potentials move on dividend and divisor John hear dividend / divisor equals a quotient is always a quotient it's the answer to a division problem about someone brought up earlier that we can write the vision as a fraction so it's numerator over denominator yeah cuz I need you guys to see how all this stuff connects look at this right here dividend / divisor that's down here dividend and divisor and quotient the answer to a division problem is the quotient but someone in the last class said we can write division fractions right we learned that as we did the fractions first now we're going back to go back and do a division so we call it numerator divided by denominator and that's the thing cuz when you set it up as a fraction numerator or denominator So Eun to know that it's also div ID n over divisor yeah cuz the whole thing is vocabulary these are synonyms but depending on what we're talking about fraction it should be called numerator and denominator but when we write it as division it should be called dividend and divisor but they're related they're connected to the best thing I could think of when you go to like 7-Eleven and you tell someone to buy you a soda you said go buy me a can of Coke if if you go if someone if your cousin's going to the 7-Eleven you want to stay home and play fortnite or something and you but they're both coach cuz if they said you said give me a kind of hope that's all day but the whole thing is a bottle of Coke in a can of Coke is still is the same product but that little bit of difference so in a fraction the parts are called numerator and denominator but when it's division the parts are called dividend and divisor but they are pretty much the same problem same thing I don't use the word product is that means multiplication so they're the same thing so vocabulary is key when you guys take those the reading STAAR test the state task pass to get in testing in the college they're going to ask you those things that's where you're getting mixed up in so watch out so let's go through this go back to hear look at all our division include these right here look at all are examples of division list all the examples of division that produce the quotient that's a negative number we are so good so good that's your first one right there so all the division problems that produced a quotient that's negative -24 / 6 equals negative 4 and let's go with this one -24 / 4 equals -6 and then let's look at this 24 divided by -6 equals -4 and then we got another one 24 divided by -4 equals -6 these are the four different variations where the answer to a division problem negative reviews of the four combinations and let's look at it if the quotient is the answer to a division problem is a negative number what must be true about the sign of the dividend and divisor look at our dividend and divisor dividend and divisor they both get us- for but look at it look at the dividend and divisor dividend and divisor but look the same negative what's a fact you can say about the signs of the dividend and divisor if the answer to our the quotient the answer to a division problem is what can you say what's a fact you can say about the two numbers be divided by their numbers sure but if they're negative what's the fact you can say about the sign say it again their numbers but what's special about the bet so fat you are that's one fast well are these numbers the same call your bill you're going there I'm taking a bill to get trying to get you to the answer. So someone said the signs are flipped what is this both of these equal both of these equal -4 but the signs are flipped is equal -6 but the signs are flipped but what's special about not just flip one is positive one negative they're not the same so if your answer is negative can you ever have the same sign no sew right here if the potion is negative what must be true about that the signs for the Disney there's no short way of writing this dividend and but we can shorthand and divisor are not the same we'll get there that's the next one are not the same 11 number is positive thank you for letting me know and the other number is neg so if your answer to a division problem is negative they both have different signs This Is the End all right let's look at this one right here I know you guys are still raining but missing along so out of all our division problems including the ones inside the square rectangle thing list all the problems that produced a quotient that's positive so you should have for their awesome list all the quotients that are positive get super Sim all right I'm a list it too so we got 24 / or 24 / 6 -20 4 divided by -4 -24 divided by -6 equals this the other number look at all our quotients that are positive now let's look at our divisor and dividend because this they both get a six pack what's what's what's a fact we can say all look same signs what's the name of this they're both you go to for let's look at that same sign same sign positive positive same sign negative and negative so if the quotient is positive the answer to a division problem is positive what must be true about the signs of the dividend and divisor what does the thing say list the examples of division problems that produce an answer that's all positive cuz all the negative ones are up here all the positive ones are done here so if all your these are positive the signs are the same when I see the signs are the same you have positive X pause or negative times negative thank you now these right here so look at this look how simple the rules for dividing two numbers not 3.5 not a million 2 numbers there's going to be a shortcut I'll do a shortcut but we're just going to do with $2 for now when you're dividing when the answer to a division problem is negative when the quotient is negative a quotient is negative if the divisor and dividend have blank find so the answer is negative good if they have opposite signs if the answer is positive they both have the same that's their main goal for today to realize that the sign the spine issue for multiplying and dividing is the exact same thing think about it positive times positive negative times negative positive divided by positive negative divided by negative positive answer same time if we multiply or divide by opposite signs get a negative answer first things first always deal with the negative then just divide the numbers sign then negative always deal with the sign first if you can alright let me read this page and move on to the next one yeah and we got 7 minutes all right let's look at this it said is the ocean of two integers always an integer so when we divide two integers do you always get a nice little whole number and this is where we're going to prove that division is not commutative we can flip it used work space below to create oceans and integers what just do one and we're going to I'm going to use pretty much what we had here let's go use the let's go -24 / 6 verses 6 divided by -24 and how do we prove that it's not commutative make it into a fraction so this one right here -20 4 divided by 6 can be written as -24 / 6 forget that is positive or negative take away that negative sign that's a fraction bigger in one whole unit so let's look at this right here 6 divided by -24 Sophie write it as a fraction 6 divided by -24 6 out of 24 pieces does not even have one whole unit so this is less than a fraction is less than 1 where's this is bigger than one if we take the negatives off always deal with the sign first notice positive / negative or answer is going to be a negative the quotient is going to be negative and then you just divide the numbers if you can 24 / 6 for this right here 6 / 24 we can do that but we can do the sign first positive / negative negative I'm going to jump ahead and just simplify the fraction 1/4 -4 vs 1/4 ones a fraction 1 is no when you divide integers the ocean is not always and in kedar meaning you don't always get an integer sometimes it's a fraction of somebody said decimal point of Justice decimals that's another lesson where we will change fractions to decimals and decimals to fractions later on so save that you're jumping too far ahead alright I want you guys to do A & B quickly -14 / 714 / -7 you should be done like now even a tortoise should be now sacerdote work so just answer -14 / 7:14 -7 and everyone's thank you thank you for letting me know yes -2 good job everybody so leave this negative / positive negative I'm due to sign for sporty / 7 2 positive / negative I always Define first get in the habit of doing that I think you should to 14 / 7 2 but this right here it's in a presence does anybody remember PEMDAS inside the parentheses first so what's 14 / 7 so does the negative outside but the inside is a to does anybody remember what you do with something outside the parentheses you multiply what's a negative times two -2 that right there that little bit of parentheses freaks out a lot of people so what's in front of her ECU X after you finish the inside and that's pretty

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Math 7 - Lesson 12

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