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Pre-Algebra - 4.5 Day 2: More 2-Step Equations Practice

Added Jan 07, 2021 •

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TWO Steps (check first - if you can simplify one side of the equation by combining LIKE Terms - if possible) 1) How to you eliminate the Constant? (set it to ZERO by using the Additive Inverse) 2) How to you eliminate the Coefficient? (set to ONE by using the Multiplicative Inverse)

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I don't like the hardest type of ones you got to do two-step equations it's like everyone always says going to move things over for no sew on two step equations when you have an equation always look think of that will sign like a wall look at this right here if I have a wall this 22 is by itself that means I don't really care about it I'll deal with it later before you move Wings over or start doing things to move see if you can simplify you want to see this that's only thing that really matters right now 3 x / 2 + 4 x do I have any like terms I can combine and that's pretty much what we have here I'll look that's a fraction that's not a fraction let's make this into a fraction and deal with it then Sao 3 x / 2 4 x / 1 treat it like a fracture I got 3 / 3x is over to I got four exes over one treated like a fraction make common denominators common denominator is to this doesn't really change x / 2 + and I want to make a fraction over to right here so how does one become two I * 2 I got it so that's not an ex at the time that's why they change it to the Dot 4 x x 2 4X x 2 4 x 2 8x 8 2/2 is the same thing as 4 x / 1 and notice this Lonesome 22 whatever it's by itself I didn't do anything to this side that's the hardest part A lot of these problems realize I don't need to do anything to this at all I did was make a new version of Forex my new version of Forex is 8x over 2 because I didn't really change the value of the number I did nothing I don't do anything that's what makes this hard to realize I didn't need to do anything there so right here now I combine like terms I'm just like adding fractions 3 x / 2 + 8 silver to treat it like it was a regular fraction oh my denominators are the same so I add my numerators together let's rewrite that right there so then we go 3x Plus 8X / 2 and again all I'm doing is rewriting I'm not changing anything of value and when you add your number is like terms three I got three X's just imagine three Lego blocks of the same size plus eight more how many do I have I got 11 X / 2 equals 22 all I did was clean this side up I didn't do anything to change the value I'm just changing the way it looks cleaning it up simplifying 11x / 2 equals 22 something different 11x divided by 2 equals 22 well I got to get X by itself now that I can't do anything more on this side is simplified let's start getting X by itself so 11x divided by 2 equals 22 will let's do the opposite 11 x / 2 * 2 / 2 x 2 cancelled now I change the value what you doing one side when you change the value you got to do to the other side the same amount so * 2 x 2 I should have did a separate line my fault so 11x * 2 / 2 just look at this 11x * 2 is 2222 / 211 * 2 in / to cancel each other out and save yourself some time if you see that so then we end up with 11 X equals 22 * 244 what a lotta guys type this in and you left it like this remember your whole goal is not to get just the x-term it's just to get x 1 x we have 11 x is right here what is One X worth that's 11 times x so we should / x 11 x / 11 up that wasn't there before what you do on one side because I change the value I got to do the other side only do things to both sides when you change values if you don't change values just change the way it looks that's the beginning of algebra looking did I change the value if you check value did I change the value or did I simplify then you just leave it so let's finish 11 / 11 that's one so we're left with x 44 divided by 11 4 I did more work that I needed but this is just to show you including all the little Mental Math now this right here the same thing very similar but before I could do anything that 380 let's combine all all his exes are fractions that's a to that's a 6 that's a four what is the common denominator 12 so all of these I need to change into a brand-new fraction for 12 and I'm just going to do some men from Mass to try and do that right there and because I'm just changing the way this side looks not the value it still equal to 380 so let's look at this so we got X over to become something over 12 what did I do to the two to make a 12 x 6 so as a multiply this by 6/6 I'm not changing the value I'm just changing the way it looks so I don't need to do anything to this side that's where the biggest mistake first comes in a place a lot of guys think I got my X changing how it looks not the value I made a brand-new equal fraction 6X / 12 is the same thing as x / 2 change the way it looks not the value same thing right 5x / 6 mm x 2 mm x 2 a 2 Hour 2 as a one I didn't change your body just change the way it looks so that's a 10x / 12 * 3 * 3 3x so now I'm able to combine all my terms together 6 + 3 is 9 9 + 10 is 9 these are all X's 19x / 12 equals 380 I can get egg lights off so this is 19x / 12 think about it like that you can do with us one step let me rewrite this part right here this one makes it a lot less work so 19x / 12 can also be written as 19/12 * X equals 380 why do I do this so this is a shortcut you can read this as 19 / 12 or I divide 12 first and then x 19 going the other way it doesn't matter which one you do my whole goal is to make the numbers the coefficient in front of x variable into 1 how do you make 19/12 into 1 one thing you can do is multiply by the reciprocal of the latest multiply by the reciprocal if I X they let me write another line so let me do this let's multiply by the reciprocal which is 12 / 19 look at this now here's the thing I do not need to multiply 12 + 19 + 19 + 12 cuz I know this could be the same number over the same number 12 * 19 will end up being the same number as 18 * 12/4 * 5 is 25 times 4 is 28 commutative property same number instead of having 19/12 by * 12 or 19 I have a 1 Now One X here's the hard part realizing hey I just changed the value of my ex I went from 19/12 x 2 1X I changed the value so now and this is what you doing one side by changing the value I got to do the exact same thing to keep it balanced and equal and once I figure that out so x 1 x equals well let's go I don't know what I want to do first going to divide first I'm going to divide first when you have a fraction multiplied by another number we could do one of two things first I can * 12 and then divide the results by 19 or if I see it's a multiple of each other I could divide by the denominator and then the result * 12 I think that's going to be easier cuz I want to deal with smaller numbers so I'm going to go 9380 / 19 19 goes in the rear of that two times right 20 and then 20 times and then I got 20 times the 12 240 So my answer is x equals to 40 yeah same thing like a lot of guys got do not leave it as a fraction if you can simplify a lot eat some of you guys went 4560 / 19 cuz you didn't want a divided by 19 you might think you would be on a test Mark 1/2 wrong because that fraction can be simplified to 240 / 1 fractions always got to be simplified so I'm going to go back and go over all the homework problems now which is all this is like the hardest As It Gets all right Alright sorry lot of people that's the thing about starting now from now on really it's like did you finish and it's a lot of stuff and you might forget to put back something so I'll look at the chat later responses for problem to do so let's see free I will do 2323 have them write it down so I'm going back 2325 3135 39 + 40 alright these are the problems I'm going to do if there's any other problems you don't see that you want me to go over put it on here again I don't care about your answers cuz I gave you the answers for all of these I just want to see if you know how to do these that's the main thing for this right here alright summer start with 23 I am 70 R17 so 17 let's look at this right here so we got 4D -18 equals -34 a lot of the stuff for most people a boof up on is the arithmetic watch funny adding subtracting multiplying dividing that's where almost everybody messes up and my main thing first if I was going to braid this as a question did you understand what you get rid of first did move things did you say this is what this the number I need to eliminate this the number I need to clear as long as I see there's like you did the right step assist arithmetic kind of got messed up self I would grade you easily on that to give you partial credit that tells me you at least know what to do you just didn't do it right and that's okay we all mess up a multiplying adding subtracting dividing so Facebook where your variable is and again think about the equal sign as a wall look at where your variable is and always first check can I clean the side up can I simplify it for D- notice I don't care I didn't say anything about this I don't care about what's on the side is this site has the variable 40 - 18 there are no like terms there's nothing I can combine I just leave it so now if I can't do anything identify where your variables at that's what you want to get by itself what then you ask a question what is keeping my D from B 1D I got 40 in I want 1D One Direction so I want One Direction 1D 44 oz in my way but what else is in the way this - 18 so that's in the way of me getting this whole answer my D my variable isolated your main goal is just to get one variable so get rid of the coefficient so here steps to do this stuff 1 simplify simplify and here's a thing if possible side with variable so it's a check if possible is the key phrase for this side doesn't have the verb I don't care about it so simplify is possible side with variable 40 - 18 get a check is there anything else if I if you answer no move on if you answer yes simplify cuz when you do the next step would be first eliminate the cause or clear I use both word eliminate / clear out the constant after you do that you got a new expression a new equation next thing you do lemonade clear wealthcare eliminate clear out the constant you want to make it equal to 020 I'll explain that in a second. Scooted over which is different on the next one you want to eliminate slash clear out the coefficient 1 that is there a butt at 1 that's understanding what a constant and coefficient is that's why I understand terms and what the terms are constant is a number by itself with no variable connected to it make that a zero the coefficient is a number in front of a variable you want to make that into a 1 and that's the main that's pretty much those in the steps of how easy it is the hard part is this the calculations we always mess up on those cuz we rushed through it all right so let's look at it so we can simplify everything one check step to clear out the constant how do you make a -18 in zero you find the additive inverse what's the additive inverse A+ 18 I'll look at I made the negative 18 -18 + 18 becomes a 0 I change the volume I -18 into a zero so that tells me what I do one side I got to do to the other because I changed the value of it that's how you know you got to do something other side I change the value so I got to add a teen to keep it balanced -3 4 + 18 we're adding two numbers together and if the signs are different we just subtract and keep the sign of the bigger integer that's bigger than the bigger absolute value 34 is bigger than 80 and 34 is a negative so this is going to be a negative answer still and when the signs are different all you do is subtract and make that into a 2 in this in one 14 - 8 that is a 6 to -1 one -16 and you bring down the four dimensions for the let's rewrite that 4D + 0 equals -16 40 + 0 we can clean that up hey start over at the can I clean 40 pazura guess it's just 44d equals -16 I don't have a constant I have a coefficient I want to get rid of that four times. So what's the opposite you / 4 Let's do an extra step I don't want to mix up your notes for the equal -16 so now I divided by 4 what you doing what before I finally 4D / 4 4 / 4 is one I change the value what you change a value that means I got to do the same thing to the other side Sephora / 4 I'll do one extra step that beat A1 4/4 is 1 1 D equals -16 / 4 -4 d equals -4 you do not need to write the number 1 if you left your answer is this I would still give you full credit but know that 1D is the same thing as just d and these are the three steps you pretty much need to follow I'm going to keep on putting it over here so let's do 19 19 and 21 or a 1920 123 I'll do 1919 Saint concept but instead now let's get 19 h / 9 - 3 equals 2 here's the side with the variable let me and you don't it by Somerset do I need to draw the wall now you know but I put it visual aid just to say this is my left side this is my right side my variable is on the left side so I don't care there's no variable here I just deal with it when I need to first off can I simplify the side with the variable h / 9 / 9 - 3 no I can't. No terms are like to combine second thing eliminate clear out the constant 2-0 how do I make -3 in a row you add the opposite to it which is a plus 3 -3 + 3 I got a zero show in this space I changed the value when I change the value that means I got to do the same thing to the other side to keep it balanced so I got to add 3 over here 2 + 3 I have five and then I just bring this down cuz someone said how come I didn't add 3 to the h / 9 it's combining like terms this is a variable is it that's a constant a variable and a constant cannot be combined you can just rewrite it as a simplified expression so that's why I bring it down h / 9 8 divided by 9 plus 0 equals five I can clean that up I'm going to get h / 9 equals 5 someone just wrote do I have to write 2 + 0 you know you could have went straight from here to this line this line is just for you to see the the zero make Missouri but yes you could actually scribble that's why I'm out in Just Go with this one right here good I can skip that part yes you can this is just for notes now let me read this correctly H divided by 9 equals 5 forget the letter H some number divided by 9 equals 5 What number divided by 9 equals 5 and that's pretty much what it is but how do you show the work so undo a divided by 9 i x 9 Let's do an extra line of work so now I want to clear out the coefficient and make the coefficient if you want I want a 1 so instead * * 9/1 so look at this right here H * 9 which is 9h 9 * 1199 / 9 is one instead of not instead of h / 9 I have 1 h I changed the value by multiplying by 9 so you got to realize what you doing one side you got to do the other this is the next biggest mistake for ladia guys you forget to put the same thing to the other side so I can multiply this side by which equals 45 gauge equals 45 again for some reason why guys freak out when you have a variable over a number I'm going to do this part I'm going to start here and I'm do this again from here this part instead of h / 9 I'm going to go 1/9 H is technically there is a one right here so I just pulled the H out cuz it's 1/9 * h equals 5 if I have a having a fraction is actually easier than having a variable over from that easier to just the better visual for a lot of people that's how do I make 1/9 into a one I multiply by the reciprocal let me rewrite this line over H equals 5 what's the reciprocal of 1/9 + 9/1 * 9/1 what I do on one side I do to the other 9/1 * 1/9 + 9/9 I have a 1 age now or Justin H 9/1 * 5 45 / 1 which is best 45 which one do you like better that's up to you to personal choice we do 21 same concept with the variables on the other side now yep under the under the problem that we do how do you get + 3 - 3 so what's our what's the next step what's the first thing you want do you want to get rid of the constant the constant so this is 3 let's look at it first step is always get rid of the one that always but you don't have to do it but it's the best way the safest way is to get rid of the constant c h / 9 - 3 equals to I don't care about the side without the variable my whole goal is to get H by itself here's the H I want to get that by itself that's connected to the nine but there's also this negative three in the way so that is actually a coefficient that's how I wrote it down here one night H2 coefficient of one night coefficient is the last thing you want to get rid of you want to get rid of the constant first so how get rid of a -3 what do you do want to change the constant to a zero that's not a zero that's a negative 3 how do you make -3 into 0 you add three that's where the play three came from so I added three to -3 to make it a zero pair let's write that that's his girl right now that's a zero but because I made this into a zero I change the value what you doing once Equus all you had to do to the other so that means I got to go to plus 3 so now here's my new expression h / 9 + 0 is equal to 5 I kept it balanced as long as it's equal I can do anything I want work-wise and so what's 8/9 + 0 8 / 9 but now instead of equal to 2 is equal to 5 because I had to keep it balanced let me do it on the next one the next one is very similar a kind of do it algebra tile ish so 21 we got 20 equals m / 5 + 12 all right I'm going to try and do a bunch of algebra tiles so I'm just going to do the little circles set of writing in his 20 let's go write it as that's why I P what to do with this algebra tiles stuff so I got 20 red coins and look at this is 7 / 5 + 12 * 12 points let's go all right and I'm going to leave this as m / 5 for now cuz that's a variable that I divided by 5 so so it's balanced this equal says this is equal to this hey look this shares something with this this how many is another color let's let's go with this this right here is the same as this right there so if I because it sequel a seesaw and these are weights on a scale it's not moving anywhere and I don't want to move anything cuz if I dip one side it's no longer the same but can't I throw both of these away and it's still equal cuz there staying the same weight I got 12 here and I got 12 here so I threw the 12 away how do you throw something away in Matthew subtract it so let's go do that lets - 12 if I mine is 12 that means I eliminate this 12 - 12 become 0 look at this if I subtract 12 away with was 2468 what's 20 - 12/8 but then I can't forget I got to bring this M5 down cuz it's m / 5 + 12 but now it's 0 so let me read it cuz it's ugly looking so this 12in is 20 because they're like terms on the other side what's in common so now I have this new equation 8 equals m / 5 + 0 but I don't need this plus 0/8 equals divided by 5 so some number divided by 5 equals 8 what is that what number divided by 5 equals 8 and how do you show the work she had a thing do this let me rewrite it hey equals one fifth of a number m one fifth of a equals 8 8 divided by 5 equals 8 same thing how do I change my coefficient into a one so first let's go back and review first make your constant into a 0 on the side of the variable so that constant was 12 how do I make it easier on sbtrkt well so now it says 0 now that I have that I need to make my coefficient the number connected to the variable in 201 so m / 5 is the same thing as 1/5 x m how do I change as 1/5 into a one let me rewrite it I * 5/1 the reciprocal what you doing so instead of 1/5 5/1 * 1/5 I have one now 5/5 heads do an extra step 5/5 M which equals 1 M I change 1/5 into a 1A change the value what you doing one side you got to do to the other so how did I make 1/5 into a 1A * 5 over 1 so that means on this side and then I * 5/1 which is just 40/1 which equals 40 40 equals m more steps than I need but I'm showing you every little intricate detail that was 21 let's do 23 now almost lost my list there maintain so here are the steps again simplify if possible this is a check step one we don't always do we do knot always usually start with step 2 but you always got to check first can you clean up what the side with the variable meaning combining like terms did you do that you got to do that then next thing clear out the constant 2-0 make that constant into a 0 what you do that your new equation what's up so then after that coefficient the one so let's go look at number 23 46 - 8X equals -18 here's my variable this side doesn't have the rainbow so I don't care about that you want to imagine that there was a wall this is the World War II German that's alright Germany is separating the East and West Germany country back in the East and West Germany there's a wall we cannot see the other side but we just know it needs to stay balanced so we looked at this site with the variable 46 - 8X can we clean it up is there any terms that are alive that you can buy no cuz this is a constant and this is a variable that's a coefficient so it means there's eight variables -8 variable deal with the constant first on this right here when the concert is in front you got to helps to do this put a plus sign in front to remind you that it's a positive 46 text goal because we can't clean everything up make our constant into a zero sub before I move on type it in the chat so I know you're paying attention how do you make the + 46 into a 0 what do you have to thank you one person paying attention to people 3 for all right everyone. The same thing that's good enough at least you guys are paying attention everyone else is not so we subtract good because look at this right here 46 - 46 that's a zero now I turn this 46 into a I change the value if I change the value you got to go to the other side of the wall of the equal sign and do the same thing so let's subtract 46 so this right here look at this I made a zero this has nothing to combine with so you just bring it down -8x and this is the next place where most mistakes arithmetic -18 - 46 that's how we did the number lines when we did the beginning so you got to think I'm at user I'm at -18 subtract -18 acre 46 close this way that means the numbers are getting higher I'm adding but if you remember the rule the other thing was if my signs are the same and I'm adding and subtracting signs are the same all I do is add my numbers together and I keep the signs when the signs of the same keep the sign and add them 8 + 6 is 14. 1826 -6 4 you got to think if I'm at -18 and I go 46 faces this way just you can tell hopefully that you're adding your in your digits together and it's still negative not positive that's what we use the number line adding subtracting when that's okay someone said shouldn't be positive it's a negative a negative but are we multiplying and dividing know we're adding and subtracting you got to know the difference is right there so that's another mistake good for bringing that up so now let's rewrite this -8x equals -64 + -8 x x how do you undo it instead of -8 * x -8x divided by -8 what you doing okay I change the value -8 divided by -8 8 / negative to positive 8/8 is a one I have One X now I just change the value I change the value on one side and need to change the value on the other side negative divided by negative is positive so that goes away 64 / 8 8 when x equals 8 that's fine but x equals 8 is the better notice how much less work I didn't show every little step lot of the stuff that I showed was that the mental math the hardest part is remember always making this am I keeping everything equal that's why set did I change the value or not that is the hardest thing overall making sure and understanding what is equal did I keep it equal that I change the value so I got to oh I didn't change the value so I just do my work I'm simplifying all right next one that was 23 -7 equal key / -5 - 1 can I simplify this can I clean the combine like terms P / -5 - 1 can I come by so what do I do good Soma set plus one thank you go to the steps first get rid of the constant here's our constant let's make this into a 0 so I add one I change the value of this part right here so I got to go back to this this now I care about the side cuz I got to keep it balanced -1 + 1 0 I don't have to write my 0 down I'm just bringing this down. Over -5 but let me clean this up -7 + 1 mi signs are different and you're different you subtract and keep the number of the bigger integer with the bigger digit so 7 - 1 which is 6 but because the seven is a negative negative 6 all right we look at this we have a brand-new no constant P divided by -5 equals negative 6 how do I get rid of a divided by -5 is to show the extra step right here which is important divided by 5 divided by -5 times it by -5 -5 / -5 that's a positive one these go away but I change the volume SP now but I don't want side to the other and that's here's another mistake I put a -5 next to it what am I supposed to do I multiply some people would see this as -6 when is five best mistake of subtracting and adding instead of multiplying so negative times negative is positive 6 x 5:30 -5 divided by -5 that's a that goes away leaves me with just p p equals 30 31 3131 the decimal ones so so 31 we got six 1e equals 1.07 equal with a plus c I messed up I caught myself I caught myself. is mastery even though I almost made a mistake it's okay so what you guys don't get my get freaked out if you make a mistake and always make you see me mess up a lot but unable to correct it that's the difference of being able to correct it so I mess up I fixed it so can you so 1.6 e plus what equals 9 I first I need you guys remember this cares if it's a decimal you do the same thing step one what's that has the variables outside that means I don't care about the nine right now you always want to double-check first this is number 29 number 31 problem 31 6.1 + 1.07 that's what's up with the variable I don't care about the variable then covered up first ask yourself can you simplify this can can I combine this variable to 6.1 variable with this constant of 1.07 no then you go to Next Step get rid of the constant who cares that it's a decimal you use the same process so how do I make this constant into a 0 what do I have to do what operation do I have to do to make this + 107 go away thank you you do the opposite what's the positive adding thank you next person subtraction so what do I subtract 1.07 and this is where people kind of messed up you forgot the rules of adding and attracting decimals imma do that off to the side in a second so + 1.07 - 1.0 + 700 0 so what that means I bring down the rest of stuff I didn't mess with 6.1 e equals that doesn't look good so let's do the work off to the side but because I have decimals yellow line up your decimals so instead of just 99.00 -1.07 now you guys with the new now it's is 900 divided by 107 line up the decimals so I got to borrow that becomes 9 - 0 is 9 8 - 1 is 7 7.93 I need to make the coefficient now into a one 6.1 how do I make that a 1 I'm skipping some work I just got a real I'm not going to rewrite this line but just know that that's like that color coded Academy by 6.1 what's 6.1 divided by 6.1 we have ourselves one yeah we have our stuff now one e but I changed the value because I change the value it's no law equal I divided that means I made less that means this site is lighter it's tilted now it's no longer balanced he needs to stay equal so I got to keep the state of equilibrium in Santana that's your vocabulary so what I do what did I do I did about it by someone all right so 1 E equals this messed up looking fraction 7.93 over 6.1 decimal over a decimal that is not fun to deal with I don't want to do that but let's do it person to make an equivalent fraction I'm going to get rid of my decimals cuz I don't want to play with my decimals what I'm going to do is get rid of at least one decimal I'm times it by 10 so this becomes 61 if I times it by 10 I move this decimal over what I do on one side you on the other what I do on one part of the fraction I do the other so I get 79.3 I could move the decimal over again but no one is good enough to divide with a fraction is another way of writing division 79.3 / 61 how about I do this cuz I can easily divide that 61 goes in a 79 one time and if I subtract I get an eighth to try to get a one or bring down this three and 61 goes into 183 how many times I'm going to tell you three times this three times 1/3 3 * 6/8 all look at that remainder of 0 Mi E equals 1.3 this problem is a combination of multiple it's not just the decimal problem let me zoom out it's a lot of problems in one let's look at stuff you've learned before we just learned this was a two step equation the steps but then we went back to was it fit or 6th grade when you guys did decimal fractions hahaha oh man we have a decimal fraction simplified decimal fraction and that's the whole thing then it went back to the idea of how do you get rid decimals in a fraction while keeping it equal how do you move decimals away so that was how to simplify a fraction a decimal fraction and then after that knowing that a fraction is another way of writing Division and simplifying it that way this is a 3 problems in one this right here is actually considered all the SAT if you grouped all your questions into five groups Group 1 is super easy this is if you can get this level one question why are you even taking it question 5 is oh my God this is so hard I can't my head's about to explode level 5 questions on the SAT and there's only so many of those most of your questions average between level 3 and level 4 level to which this is is all right it's a pretty easy question but I change the way it look to make it look hard it's not it just change the way it look they're saying are you intelligent enough to change it to something simple keep it simple and just change it each time to make it simple for yourself that's what a level two question level three means you got to do a little bit more thinking level Forest man that was hard I barely finished so sat average most of the questions are level three meaning you got to put some effort in did you get to all the level 5 questions and mighty and high hey this is it right here wonder what else they're doing all right that was number what 31 35 35 F / -4 + 20 5 equals 12.9 same type of question who first off who cares that it's a decimal that's the first thing you need to just get out of I'll just deal with it just see that I have my variable my constant I don't care about this side I just got to deal with this out with a variable cuz if I deal with this correctly and keep everything equal this side will work how do I get rid of a + 20.5 is a rhetorical question the same thing as the last question we subtract but let's keep our decimals lined up I'll look at this though 20.5 is bigger than 12.9 in my signs are going to be different so I'm going to write it up here - 20.5 + 12.9 I got a lot of faith just bear with me cuz our main goal first was to do what to make our constant 0-0 that out let's bring down the rest of our work on that side what's I so we don't forget it ask divided by -4 equals and now we clean up this side if I put it on the bottom it would have been this you would have had 12.9 - 20.5 then why do guys with freaking Man 12.9 - 25 what will we do I do if I know I'm subtracting and I know my signs are different I always put my bigger digit setup on top so I just do my calculation it says subtraction algorithm remember if my signs are different with my signs are different I'm subtracting these two numbers but how do you subtract put the bigger number on top so is 20.5 - 12.9 when the signs are different you subtract and because my number on top is negative I know my answer is going to be negative so I put that down and subtract 5 - 9 can't do that so I got to borrow 15 - 9 that's a 6 don't forget the decimal 9 - 2 is 1 - 1 is 0 * -7.6 it's setting it up don't just write it down set it up so you have less work to do so now I have a brand-new equation F divided by -4 was -7.6 who cares that it's a decimal look at this right here this is actually easier than the last problem ask divided by -4 4 equals -7.6 I want just f1f how do I get rid of divided by -4 * -4 what I do on once I do to the other if I'm changing the value * -4 -4 divided by -4 let me do actually cuz I got a bunch of confused faces right there I'm in a * -4 / 1 which is the same thing as multiplying by negative for Watch What Happens f * -4 negative 4 F -4 * 1 -4 look at this what's -4 / negative for positive One S and what do I do here I have my now all I got to do is clean all of this app -7.6 * -4 negative times a negative is a positive all I have to do is multiply now for time 6 24 carrier to 4 * 728 + 230 and don't forget your one decimal place s equals 30.5 39 + 41 so just like the warm-up questions we did same concept 39 so we got a decimal decimal and Route 39 is a messed-up question that is a level three question on the SAT 40.77 equals y over 5 + 2.0 for why + y / 10 man this is a messed up problem but we'll deal with it in a second first off make a decision do you want to play with this as a decimal or a fraction and it's a rhetorical question yes if you do not have a calculator it is always best to change that into fractions play math fractions is way easier than than than dealing with decimals so this right here I'll deal with it later I'm going to ignore it for now but I'm going to change to point for So This Is 4/10 this is 2 4/10 but since I got a tenth right here let me change this into an improper fraction so true in 4/10 that's 24 24/10 y + 1 y / 10 that's another place where people mess up they don't see that that's a 1y and then I got this y / 5 I like these are both over 10 let's make this over 10 5 * 2 makes 10 so I got to do it up here so that becomes a to y 2 y + 24 y + 1 y / 10 2y + 24 + 27 + 27 7 y / 10 what's up man that's a lot of work and then we get 40.77 we got a fraction and a decimal here do a two parts look at this that's 27 y / 10 equals 40.77 how about I do this I multiply both sides by 10 I'll do it I'll write it again let me do it so I don't mess up the notes for you I'm going to multiply both sides by 10 and do it this way 10 / 10 that makes a one which leaves me with 27 why but if I multiply a decimal by 10 that means I just move the decimal place over 1004 7.7 and look at this right here I could / 27 I'll do an extra line I'm showing more work than I need what's divided by 2 7 answer 27/27 or 1 1 why which is just Why I am done almost cuz I got this messed up looking fraction to deal remember fractions are another way of doing division let me do this off to the side 27 goes into 41 time I subtract 13 just bring down the seven how many 27 are in 137 I'm going to check 27 * 5 that's 35 carrier 335 so close but that's what I need 135 I subtract I get 20 set to I bring down the guy that I get a nice 27 how many 27 71 do not forget my decimal place 15.1 so a lot of people would have made this into a fraction also notice what I said always is deal with one side of the equal sign with the variable clean it up first clean it up and you get to here and you can cuss out what do I do well get rid of the 10 and you can multiply 2 by 10 and then we got this right here you got this messed up fraction but then you would have needed to see a fractions or just division but if this was a little bit harder than it should have been sure it's all right some people somebody said oh somebody said right up here so they saw four tenths as two fifths yes they combine 2 + 2 + 2/5 + 1 V you can buy in this and then you can buy it yes you could have done that lot of different things you could have done could you have turned yes turn 40.77 into a fraction to let's do that enough time I wouldn't like to do it but you can 40.77 equals unless we know that's what it's going to simplify to let's change it into go straight there 27 y / 10:40 70s hundreds and then 40 and 7 so that's 40 and 70 cents that's 104,000 for 1077 / 100 = + 270 100 why I made an equal fresh air compressor on a 07 I could get rid of the one hundreds cuz it's both the same thing 4077 equals to 170 why and then I / 270 and then you got to simplify this which is into Fun 270 / 4077 I got one here so that's 270 and then I got to borrow that becomes a 390 10 10 minutes 3 137 then I got to go bring this down how many 270s are in at 5 270 * 50305 carry a 310-1350 270 and I got the decimal places you are right here no remainders how many 270 271 15.1 so yes you could have done it that way so many different ways to do it but which one fits better for you that's the answer and that's a personal choice that's how we show all these different ways all right I'm not going to do the last one

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