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Math 7 - Module 2B - Lesson 16 and test review problems

Added May 16, 2021 •

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right here is a practice for your test I'm not going to give you both you're going to get one or the other new numbers of this right here so convert decimals to fractions so easiest thing is understanding place value if you understand place values these problems become super easy if you don't understand place value it makes it a lot harder all these people I will retake rolling up fit don't want to shut the front and shouldn't have did everything go all right place value let's say I had 7842 I know your place values the seven is in the thousand thousand spot it is in your hundred spot hundred 4 but that's not a for that that's why it's actually 40 44 * 10 is 40 That's in the 40 spot eight is in your hundred eight times a hundred 807 is your thousand 7 * a thousand seven thousand and finally we got your One your one spot ones tens hundred thousand but we have a decimal and back of the decimal that positions that are to your first position is your tents all it is is between your s you put a th instead of tens tents behind right here tenths hundredths dread you put a th hundred thousand ten thousand if you know how it that's all you got to do to change it to a fraction you put your number over that number let's read it let's do this this last position is the only one we care about so we got ten hundred thousand this is work right here identifying the position that tenths hundred thousand this right here is ten thousand that's your worth telling me what position that last number is in and what do you do after that you make a fraction over that number so that would be the next it will not show it the notes will not show that you do the bottom first so it's going to be over 10,000 that's the first thing you do the second thing you do is you put the number on top what number you put on top 100 to know you don't put that whole thing the zeros are there as placeholders for debt for the decimal so if you cover up is just 24 we don't read it at 00204 we just read it as 424 ten thousands so 20 and look at this read this decimal correctly 24 and thousands how do you read this fraction correctly 24 10000 when you have a base 10 for Dena my base 10 is anything with the one in the front and zeros in the back 10 100 1000 million a billion 6 trillion well not 6 trillion 1 trillion I messed up right there and it has to be but that's not a base 10 because it has a 6 in front but one trillion is a basin what is a 1 in front of 10,000 is a base 10 because it's a 10 100 and you read it 24 10000 they're the same thing and that's that right there identifying but if you don't know the name spots here's another way to do it put a one down same just like I put a one down and for every decimal place you want to put a zero this number is your turn on the hey look at that that's 10,000 again so you put a one down and for every decimal place you could have Durham bag that's how you make a fraction 24 / 10000 now if you do this or this with this you're only getting half credit two points out of four remember if your fraction be simplified it's an unsaid Ruel you have to simplify your fraction so 24 and a 10,000 I can divide top and bottom by 4 if I divided by 4 and up with the new fraction that is 6 2500 but I can simplify this fraction Again by dividing by 2 6 / 2 I get a 3 mm 500 / 2 1250 fractions must be certified and this is your correct answer this is mathematically correct but not your final answer so you got to show some work to get to your final simplified fraction this one not a problem I don't think so you just got to follow a little process he's your answer is going to be a mixed number because the decimal is just 08 so you gotta remember this whole numbers 3 is a whole number so your answer has to have a 3 so if you have a number a whole number in front of your decimal you need to bring it down bring it out you know it's part answer because the decimal is the fraction I don't care about the 3 cuz that's part is like my mixed numbers answer I'm not going to change anything with the three it is my decimal that is my fracture if you read this correctly tenths hundredths your work right here is honey so your fraction is 8 over 100 simplify that fraction I could / 4 if I divided by 4/8 divided by 4 is to 100 / 4 is 25 my final answer 3 2/25 you have a fraction mixed number still we converted the decimal into a fraction. Bring her home number the work is easier than this or somebody I say easier yes or no this one right here if you do the work you're going to get your answer but this one right here you need to remember to bring down your whole number most you guys on your homework did not do that you just gave me the decimal into a fraction part you just gave me the 220 v but it's not 220 v do you have to have the three in front so I'm going to take away a bunch of points so this one even though the work is less is easier to lose points if you don't remember to bring at 3 so that's part of your notes so you're going to get one of the others just going to get a straight-up decimal or a whole number decimal convert decimal fraction or not you're just going to get one but these are notes two different types now this section down here is two parts you're only going to get one fraction and you're going to have to change a fraction to a decimal I'm going to suggest for the first one changing a fraction that's what we do the one we learned last lesson division long division divide first but I showed you last numbers what's the division for all of these Bishop will be the last one then we'll go back to the office so this is like a test I'm looking at it I can do more work and simplify that I can't survive that I can Superfly that but this was easier to divide so I'm going to do this one first division long division and I'mma tell you all of you all of these I'm going to start with long division just for party no matter what no matter what all fractions can become decimals and all of them can be done doing long division some do this one here first I'm going to go 40 divided by 3 divided by 40 340 doesn't go in at 3 so that says 0 Let's put a decimal place now three doesn't he doesn't go in the 30 that's still a zero I'm going to put another zero right there how many forties or 30727 * 4 is 28 with a zero 280 and then let subtract we get 20 bring down a zero how many 40s are in 2 L 5 boom done long division lighting guys think is super hard it's not because I had zero that makes it super easy now that's long division right there you everyone here thinks long division is thinking it's that's what's called long division said yeah cuz it doesn't have to be long division just means you're doing the long number by number by number work let's do long division for this one up here 3 / 14 that looks pretty easy so 14 on the outs and that's what you notice how I'm setting it up so you can use that his mouth the numerator is always on the inside so there is not a 14 and 3 so it's a zero bring down with another girl comedy for teens are in 32 2 * 14 28 and find someone up there in the chat said man I am multiplying do my work too fast cuz I've done this over and over and over again that's the only reason why I know your mental math skills your arithmetic you guys got a practice that and I'll go play those stupid  games they're not stupid if you plan against somebody like that one but you guys were racing people on where you answer math questions make a car go faster cuz the graphics are goofy and stupid by but you know if they're there more advanced ones somebody something about you made nice looking ones where you answer questions to make your character go faster or give yourself boost but that's a hard damage control. I'm not going to play that game anymore but let's keep on doing it 30 - 28 that's a two we got to still the remainder bring it down 2014 goes in a 21 time so subtract six string down to zero how many fourteeners are in 60 so I don't want to do the work here my math isn't good so I do my calculation that I can't do my head 14 is close to 1515 * 4 is 67 go 14 x 4 that is 56 I subtract I get for bring down a zero weight let me put that I forgot to put my for right there don't forget that 14 goes into 4014 * 4 was too much so I'm going to try 314 * 3 that is a 12 that's 42 that is still too much so that mean 214 * 2 is 28 and I subtract that is 12 bring down a zero 14 times what gets 101 if I'm at 14 times 4 is 56 why don't I go 14 * 814 * 8 that's thirty-two carrying a 3 100 + 12 yeah good good observation let me finish this and we'll go so that's 8 and then I get 112 and then now I get 880 but it doesn't look like it's going to end so if it if you get five numbers I'm not going to give you anything more that'll stop but if its after 5 numbers you done your work this does anybody remember what it's called when it doesn't end not unless but close non terminating is the term so all you have to do is put a... Say goes on forever if you can't finish so... So goes on forever but let's look at this we're going to compare the this one goes on forever and look at this one this look harder because people look at that for this one first this one was smaller number but man look at that Mental Math had to do multiplying numbers with zeros is always easy dividing numbers geros always easy to look at this one it's here we change it to a decimal super easy super quick now call WeChat what's another way to change it into a decimal so this one right here we so one of the reasons why you cannot change a fraction into a decimal a second way is because that right there so this is part a always do part a long division first I would always do long division first 4 parte cuz that'll help you do Part B in a bit we're almost done so well we still got to finish the lesson if it's here if you got this is all non terminating decimal you got to write a sentence out if there's two ways you can write it out of the sentence or show work mathematically if you see that right there I said I think the sentence is easier but it's no longer will answer so 2nd way not possible because decimal is non terminating meaning it doesn't end the whole thing is if you're going to change a fraction to decimal you need to know what the best secure we have to have it said we had that know a place to put it over something over what number that's what that last number is houses it's over 10000 but look at this right now and Tony tens hundreds thousands ten thousands hundred thousands so it's this number over a hundred thousand right no because I know I can go to another number if I go to another number that means it's over a million but then I know it's going to keep on going 10 million so what number do I put it over because I'm always going to have another number coming that's why I can't write another method as terminating but there's another answer and it's actually pretty quick and we're going to do it this and come back to another way to do that's call this be one I'm going to do be to in a second it's not 62 it's be too I'm at there's only one way to do this look so 3/40 I'm going to break it apart into prime factorization so prime factorize so let's go instead of four let's go to * 2 * 20 right that's two times two times I got put another two in the front remember that was the first time if you can write your denominator as a combination of twos and fives only choose and 5 you can do a second message what do you do if you can write it as Susan five you want to try each one of these factors into a 10 2 times what makes a 10 2 * 5 makes a 10 but you do down here you got to do up here to * 2 * 5 makes a 10 5 * 2 makes a 10 so if you look at this two times five nights at ten ten ten ten ten X when is a hundred a hundred times 10 is a thousand thousand times 10 over 10,000 now let's go to the numbers up let's look at this 5 times 5 is 25 this is what we're going to do today I'm going to give you an expression with like five to six numbers at the so you can multiply 3 * 5 and then that number * 5 but this is what we're going to do today I'm giving you a heads-up so this is instead of multiplying left or right this 5 * 2 is a 10 anything * 10 is easy cuz all I got to do is put a zero and back and one times whatever that number is in front let's look at this less than 5 * 5 is 25 and 3 * 5 is 7 575 x 10 750 750 over 10,000 and 0 and back 75 thousand hey look at this 10 hundred thousand if you know your positions 10 * 100000 all you need to do is fit in your numerator into this starting from the back so but we can't have an X in front of a number so we put a 0 there .07 5 I'm just you every little step so you could change any fraction into a decimal 2 ways only if your denominator and breaks apart into two and then you just do the work and you know is she may and then you write it over that whatever base 10 and you just do it as a decimal that look at this up here we're going to redo this one so this one had a second method and you got to do it this one didn't and you had to write a sentence if you knew it's not terminating that's all you to do but if we follow this right here three over instead of 14 let's write it as 2 * 7 you're done why do guys think it's easier to write a sentence what is this your denominator when you break it apart has to be twos and five only but look at this you can Circle the snow and just do this not a 2 or 5 so not possible is a possum or not it's not possible cuz that's a 2 or 5 it's not a tour for it needs to be true or false but you just got to do so here's the thing just seen that nonterminating you know you can't do it a second way but writing that out is actually longer then just prime factorize in it which means you got to actually do something different yes we'll have examples and I can support and look how easy it's not a chore fiso second method is not possible the denominator be 205 let's let's do long division and we can see it not possible just the answer and I'm just telling you what it is right now so 7 / 30 330 doesn't go 270 but Thirty goes in a 70 thank you two times the job we subtract 10 we got to put a 0 bring it down and makes a hundred thirty how many 30s are in 103 that makes 90 but when we subtract we get a 10 we already had a 10 to begin with up here what will happen if I put a 0 bring it down we get 100 * 3 that's 90 again it'll notice if you need to do it a couple times and see that it's repeating it's going to be 0.23 3 3... It goes on even though it's not terminating and you on this one you can't leave it as a... So how do you know when to make a... you need to give me at least five numbers if it doesn't get you an answer by five numbers you go... Nonterminating but this is different than that one and only one sense even though it's an entremet it repeats if you have a repeating decimal remember you put a line over the number that's being repeated but if you put it over here you do not get full credit to correctly write a repeating decimal you write down what's not repeated and then what is repeated that's where you stopped at 8:23 but you got to put a line on top of only was repeated which is a 3.23 with a line over the 3 if you mess up and bring that line into the two I got to take away points cuz the line represents which repeated so unlike this one where you just put... Cuz it goes on forever but notice the numbers change if it's repeating you have to the repeating decimal short answer it is required it's one of those things weird things in math we can do so because we know it's nonterminating you could go back to this answer and be one you don't have to do both A Part B you just need to give me one version all right but this one is going to give me one of these 2nd way not possible because and you don't even need to say it's a repeating decimal you just got to say because decimal non terminating that sentence again is too long compared to the next one cuz if we do B2 7/30 write it as 7/2 * 5 * 3 but who cares it needs to be only too if you just had a circle right here not possible even if you as long as there's one number that is not a chew or five you're done not possible not to or that's a 2 or 5 that's 2 or 5 not 2 or 5 so not possible a notice the division part works so let's look at this one I hear I say that one for last even though that was the first one test taking strategies say the hardest ones last do the easier ones first and for now it's let's go look at this so if I break a part 40 what's a good 48th and all I need to do is for the 48 is 6 * 8 8 is 2 x 2 x 2 x 6 is 3 * look there's a three at 3 is not a 2 or 5 you can't do it but here's one thing that you need there's one thing you need to watch out for even though there's a 3 + 48 watch what I can do first 6 / 48 I can simplify 6 / 48 I can divide top and bottom by 6 5 / 6 6 / 6 I get a 148 / 6 I get an eighth and I could rewrite that as 1 / 2 x 2 x 2 look at that because I simplified it the three went away I don't have a 3 anymore even though I had a 3 to begin with when you simplify fractions sometimes those numbers go away so if you wrote I would give this the only time I would give partial credit is if you wrote all that you showed me the work when you showed me at 3 and you said off that's not a 2 or 5 okay I get it but you forgot that you could process out simplify the fractions and get rid of that three I'm getting rid of the three you're left with this 1 / 2 x 2 x 2 so instead of long division I'm going to do this way first so I am going to pay for each one of these you need to make it into a 10 5 * 5 * 5 so that's * 5 so 5 * 5 is 2525 * 525 that's a 10 10 x 10 is a hundred 100 * 10 1000 changing a fraction to a decimal read this fraction correctly 125000 thousand hence hundred thousand I need to have three decimal places in my answer because it's over a thousand I'll let us three spots right there 125 literally that's how easy it is to change if you can if you can all you got to do is write it over a base 10 and just read it correctly but I did the second way versus the first Wafers to Let's divide and if you're able to simplify a fraction so this is 6 / 48 but if you can simplify the fraction use the long division on the easier fraction I like I'd rather do that one so 1 / 8 we're going to get this same number just watch it does not go until 1 so that's a 08 goes into 10 one time we subtract and get it to 8 goes into 22 time we get 16 subtract we get on 440 5 * same answer to message to ways and again you can only do two ways if your denominator is made up of choose and Vibes only if you simplify in the beginning you might get a 3in mess up simplify your fraction if you can first alright so let's get on with it so we're applying properties of operations to multiply and dividing rational numbers do evaluate so using the commutative and associative properties to efficiently multiply rational numbers lesson so we already did this so the whole thing is evaluate the expression below right now let's just do it the long way one at a time which takes us forever so looking at this we get -6 * -2 that's -12 and then let's do bring this number down * -2 negative times negative is positive so that answer is positive 24 and then bring this -5 now what is 24 * 20 + 120 positive still with -120 and then bring down this three negative times negative is positive and then what is that at 3 * 12 is 36 and they put a Duramax tow positive 360 so let's try to types of strategies were used to evaluate the all right so that's one way of doing it so that's right there that's just left to right one method is left to right you just multiply one number after another I'm going to show you another one I'm going to rewrite this problem off to the side right here and I'm in a -6 * 2 * -2 * -5 * -3 pretty much the commutative property commute time you don't have to go there's a saying I'm not even going to move the numbers around I'm just going to underline that the lazy way of using the commutative property right there to * 5 end and then let me rewrite the problem so I'm going to Route so that got a positive 10 right there but I'm going to move some numbers run so I got this -6 too and I'm going to move this -3 * -3 and then I had this 10 in the back x 10 why do I want to do this cuz I could do these two right here I got -6 * 9 is 6 * 10/6 * -10 negative positive 6 * 636 * 10 360 Mental Math wise super quick but noticed I did do a little bit of writing because there's so many numbers it's always smart to write down numbers that we can't hold in our head that's one way of doing it and here is the associative property associative property means like grouping them so let's get over this side I'm going to go us so she at 2 means setting them in groups so I'm going to rewrite all these numbers again but instead of just doing that I'm going to rewrite it and group them at the same time you know I do I'm going to group all my negative numbers together so I'm going to go -6 * -3 and I'm going to go again -2 time -5 I'm making that group so notice even in the group I said a little group is a 2 * 5 hey and then this leftover red headed step child is in the back the to the positive cuz if I deal with my negative Spurs hey I know what my signs going to be so look at this negative times negative positive that's 10 negative * 9 * 31818 * 10 is 180 and then * 2 hey 360 the associative property looks like it's the least amount of work looks but is it the quickest it's the least amount of writing but a lot depends on how we think for me I think this is always the slowest but for me I like the commutative property cuz I group numbers and think quicker was numbers I like the bunch together this right here I don't like that 180 is a 42 * 18 * 18 that took me a second I just had to remember I was 6 * 636 36 it still ends up being 36 * 10 ideas scissors left to right there's the commutative property. Remember I said commutative just mean if it's almost application or division it's doesn't matter you put it in any order you want it's not going to change the value and three we could go again if it's all multiplication division the associative property little groups so your group numbers together and here's the thing. You combine all these methods in two different, so you could use them all at once you could have went to x 5 2 x 5 x 10 12 * 10/128 hundred 20 * 3 cc what I did right there I combined going to Lester a method and the commutative and associative property I did this I got 12 this is mental math talking to it but I'm not going to * 2 * -2 * 5 so I'm going out of order that's commutative but at the same time these two together so that's a cam nation of going left to right using all of them left to right then I did a associative and commutative and then I finished with us right cuz that's the last number you don't have to use one of them you could use a combination of them identify the benefits of choosing one strategy versus another it's quicker on the mental math so whichever combination you use that's your benefit I'm going to leave blank because it's whatever benefits you you should learn all the methods both of us are stuck doing the Lester right to begin with right now try to learn another message I want you to come back hey which one's better some of you were going to realize none of these are well these two are better than just the first one but it's a combination of all of them together that's the best method what is sign of the product and how was the sign determined we went left to right I'm going to tell you this so you will use them how will what was the sign it was positive the sign of the answer is positive we did look at this negative times positive negative negative times negative or positive positive times negative negative negative the other 1 2 3 4 4 negative that's an even number if it's an even number of negative that's just saying in a what did we do normally the Lesser right now I'm going to say this from now on even next year when your teacher has you or what's the name of the day and let's just say that's an even amount of negative positive if it's like five negative us an odd number negative I don't know why they don't get why they don't teach it cuz they want to do two numbers of the time for practice but the better rule to remember is just count how many negatives there are let's move on to the next so you're going to do this one of your phone number to 1 in do exercise one and two on your own as quick as you can I want to give you I'm going to give you only a minute and 30 seconds go yes a minute 30 because calculations that you know how to move them around to all those stupid things super quick and writing it down on your test by doing that message that's showing me work that's work I'm going to give you questions that look like this right here get one of each one without fractions fractions is that all one more minute good thing I got three people that timed it right now good job good job well check your job yet he's got to check your answer good job for finish but let's check your answer make sure you're correct alright 30 seconds all right I got a bunch more people thank you for letting me know that you're done all right is 30 seconds for me I always listen to my opinion I always try to do my multiply and divide I always do my find first and then I ignored the signs after I treat everything as positive so I got 123 negative so I got three negative I know my answer and I always go straight to the bank and here's another thing some guys don't like to save paper cuz it like I don't know how much space I'm going to need what if I use too much who cares it's paper so I'm going to put my equal sign all the way down here for my negative I know my answer is negative and now all I got this pain right here I'm going to ignore 1 * 3 that's 3 2 * 2 4 that's 3 x 4 lb of that once I grouped it I use a social I went left for a group 1 x 3 notice I got rid of the negative cuz I already have my sign here I don't do some training on my positive 1 x 3/2 X and then at 10 in the back what's 3 * 21212 * 10 120 and already got my negative sign done look at the amount of work I did not have to go one number to the next number to next timer done Samba okay some people said oh what a group all my negatives and you can do that too for me I always like tens cuz all you do is just cut off the one remember if you guys remember the rules of multiplying numbers with a base 10 just whatever your number is in front whatever the other numbers you multiply are so that's 12 just a 10 cut off how many zeros are are that's fine so someone said your group the negative together are listed at -1 times -3 times -2 some of you guys like that that's enough wrong with that and then 2 * 10 for the other one 1 * 3 * 2 + 6 but that's -6 * 2 * 1020 any different now negative 120 no different I'm only going to ask you to show what someone said do I know I'm only going to want one message just show me some work and I can see what you chose to do if you want to go left to right that's also fine with me but you got to make sure you show each step that's why that's why I like these right here you don't really need to show that many steps right number to some people oh man I forgot the fractions what you know what let's first deal with the sign first and then the fractions imma show you how to use it one too I got I got to negative but even so I'm just going to go equal and here because we don't need direct deposit to sign I'm just going to put a bus line in parentheses remind myself it's a positive answer and I'm going to treat everything as a positive number. do my fractions by fractions 1/3 * 1/2 notice they're no longer negative cuz I already have my spine down here I dealt with my sign first then I'm going to do I don't know what I'm going to do I was going to write down everything else 4 * 8 * 9 what did I do all I did was all I did was pretty much just group the fractions together and I rearrange it and I got rid of my negative signs because I know it's positive all right when you multiply fractions you just multiply 1 * 1 3 * 216 doesn't look good right there you know what I'm going to do this I'm going to regroup it as this right here I'm going to go 4 * 9 is 36 x 8 look what I did there either the 4 x 9 now I'm going to do this hey remember you can change any number into a fraction by putting it over 1 36 / 6 * 8 what's 36 / 6:36 remember fractions are another way of writing division 36 / 666 * 8 I already got my positive sign 48 I'm going to show one more way because I want to ask and someone ask you did a great way I'm giving you credit that you don't want you to people know who you are fine if you understand fractions what that means division that means / 3 that means / 2 again we already know it's positive I'm going to treat everything as a positive so one thing I'm going to do this I'm going to go 1/3 * 9 and then I'm going to go 4 * 4 * 8 x 1/2 look at this this right here that's just 9/3 and then 4 * 8 is 32 / 29 / 3 3 32 what's half of 3216 48 look at that right there shut up somebody said I did a diva either way you didn't * 4 * 8 you only took all right let's do that I'm going to shove and I actually like your method better notice right here I chose to multiply split up this person when they still did the 1/3 * 9 that just  at 3 but this person chose to do this 8 * 1/2 and then times that by for all right let's look at this that's a 3 what's half of 8 that's a full 4 * 4 12 * 4 is actually easier than 3 * 16 but you still get 48 notice didn't have to group them all together the same thing I'll talk to you and your Aunt Emily going to I get yes I'm going to ask you the one message just up to you left to right whichever one you want what terms did you combine first that's an opinion so you going to feel that part on your own and we already went over this refer to the example in the exercises do you see an easy way to determine the sign of the product first so let's put that as our notes count the amount numbers I use the word amount not the number number of the number count the amount of negative first hey if amount of negative and it's a long way to explain something simple is there of negative numbers is odd product negative amount negative numbers is even product positive and even their same deal with the sign first got nothing to worry about yes thank you for letting me know yes we got 10 minutes left let me look at this I'll keep this just two pages right add two more pages and their space big too so we don't need to worry too much so this method right here the distributive property distributed means whatever is on the outside of parentheses gets distributed inside but we distribute the 6 so another way of writing this is -6 parentheses 5 1/3 so when there is no sign in between a parenthesis and a number it means multiply and you distribute but why do they want us to distribute to this what are they trying to say but they're also trying to say is I remember a mixed number is a whole number and a fraction I'm going to do the other way and what they want so they want us to write this 5 1/3 as 5 + 1/3 so when we distribute it looks like this -6 I'm Spa + -6 * 1/3 we can do this first part -6 * 5 negative negative 30 and this right here -6 and one-third remember this right here I'm going to do this off to the side a little bit that beat -6 / 3 cuz you can multiply any fraction with a number by changing the other number into a fraction 6 * 161 * 3 3 and its -6 / 3 + + -2 -30 + -2 negative 32 we barely dealt with the fraction if we do the other method the old way we got to change the into a improper fraction first so that becomes -6 * 16 / 3 and then this is X friend number one so we get -6 * 16/3 even though it looks like less work Mental Math what's 6 * 16 I just did the work cuz it's low it's a nice but this right here my mental math skills are not that great so first let me say it's negative I know it's negative I'm going to put my sign their first I'm going to do work. They decide 16 * 6 6 * 63660 + 396 * -96 / 3 then divide do some work off to the side 3 divided 96 and since I already know it's -3 goes into 9 three times bring Donna 63 goes into 62 * -32 even though it look like less writing it actually took me twice as long to do because I had to do some Mental Math we're about to decide this method just saves us so much time here there's another exercise in the next pay let's break this apart fall along alright break apart what do we get how does the distributive part look like good a -3 and 1/2 thank you so it's nine times a negative 3 nothing out of -3 this is a -3 and admins + 1/2 and we do the dishes you should so when you distribute inside the parentheses it means you distribute to everything inside so what that looks like it's at 9 times -3 plus and this one doesn't work out we could still do it 9 * 1/2 * -3x + -1/2. I almost messed up remember when you break mixed number the fraction is also negative I almost messed that up right there so that's not all that nice right then yeah so nice 27 + and this right here 9 * 1/2 put it over when we get a negative 9 and 1/2 but hey let's break this will changes into a mixed number 27 the how many pole units are there right here that's a -8/2 plus a negative 1/2 that's a negative for awesome -1 -27 and -4 that is -31 and then we got a fraction that has the same sign you can put it as a mixed number put it -31 and 1/2 we did we really deal with the fraction not really or minutes last page playing time so they're saying right here evaluate using the distributive property so it's up to you to decide how you want to split this up let's do this first they haven't I didn't get a chance so I'm not going to give you anything like this cuz look at this I'm going to teach it though they have an addition sign right here what's 16 * 2 I'm not going to give you anything we're has again. I think that's just messed up we don't have this so what they're saying is this they both have a Time 60 Minutes factor out of 16 in the front and then let's go naked 3/8 + 1/4 16 * -3/8 + 2/8 common denominator so we get 16 time -1 h and then when you multiply this -16 negative to that edition part so you're going to learn this some more next year I'm not going to ship them just showing you what they're expecting this one right here no cuz there's a tradition making you see that yellow I got a 16 so you simplify that first I'm not going to ask you to do that but that's just what this is asking and this one right here you got to remember to change division the multiplication of the reciprocal we got a minute I don't even know when it rang early so notice this becomes something we did you will you could you will get something like this maybe it's a mix if the division is makes it is only a division and multiplication just take it to the reciprocal and become something we already did

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Math 7 - Module 2B - Lesson 16 and test review problems

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