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Math 7 - Module 2A - Practice Test Questions

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so here's our first problem I'm going to get something like this let's go -5 - 12 + 18 - 7 it's going to be 4 pictures and this is the only problem with only integers every other problems going to have mixed numbers fractions with those fractions are going to be common denominators and all that so make it simple for the right here one way you have to do it one method that you are forced to do is the number line if you do not do the number line the most points you can get out of four cuz every question is four points I'm Braiding on a a b c d f I don't like a 4.0 is in a so every question is graded from 8 f that's what the points are worth the most you can get is a 3.5 3.5 if do not use the number line but if he showed other two methods and you got a good work most you're going to get is most you're going to get us 2.5 doesn't mean you're going to get it you can alright first things first for all these problems to make it nice for you change it to Edition all Edition because if we have all addition problems that means we can we can pretty much so why she should get up turn on your camera stop laying down grassy I turn on your cameras participation grade everyday automatic zero and four cameras off even if you're participating I don't care about the chat but I do care about the chat naked paying attention so first things first change all of it to Edition cuz if it's Edition that means you can mix these up or group of any way we want using the commutative and associative properties but that's a method that is the method but first let's change it to an addition problem so we got -5 let's change it remember subtraction is adding the opposite so we change the time action to adding and the opposite of the number what's the opposite of 12 opposite of 12 with a heads for putting something negative 12 thank you for paying attention one person this is already Edition we don't need to change a dishes to track Edition already so it's + 18 so everybody who has their camera off I'm about to send you to the waiting room and you can stay there forever unless you're already in the class Fredo is in the class he's fine unless you're here it's called you got to have your camera on those are the only people don't need to turn it on cuz you're sucking up my Wi-Fi Ellen subtraction becomes addition so subtraction is adding the opposite of 7 -7 if you like someone was already first nobody talked in the computer everything is Edition we can rearrange but stop let's stop now I'm going to give 1.1 if you can't do anything else I will give you one point for every single that you change correctly to Edition so that that say if you can't do anything else all you can do is change it to Edition you're going to get 1.4 problems at least get something hey something is better than nothing when you have addition you could do the number let's do the number line first now you could do any method for the other one but on the first one you are required to show two methods and one of them is the number line to let's do the number line so look at all numbers that are going everywhere so it's just look at it cuz he had to think where would you start your year zero from cuz we're going to -5 and then look at this or adding a negative number so we're going left then we're adding a positive number so we're going right + 18 and then we're going back left so you got to think we're mostly doing our work on the negative number side so we should have a lot of space on the negative side and then we start at 0 so like I said where are we right here so we have more space on the negative side that right there let me know cuz if you're doing your number line in your graphic let you know you're not paying attention this at least gives me a quote after work so that helps me saying they're getting it so we start at zero and we go to -5 that's the only one where we go to the number unexplained in a second so we got a negative five -5 it says right here that's the only one we regarding the number so this next number lot of people don't pay attention don't understand his number bigger than -12 but no only the first number you go from 0 to number after that you go that many spaces make the sign tells you are you going to the left or the right and since it's negative we're going to the left we're going to the left left 12 units you got to think understand how a number line works 0 negative 125 but we're going left -6 understanding how that works I don't want to do 12 little lines understanding homecoming up awesome timing up and adding adding good Sabrett -17 and why am I adding look at this right here after we do this first prom we're going to do a little bit more notes just straight up notes not an example but look at this right here I'm adding two numbers that are negative remember same sign keep the sign and add the absolute values together 5 + 1217 and we keep the will do a review on that don't worry too much write that down later next one we're adding 18 that means we're going that's a positive number that means we're going to the right we land on one good 18 spaces to the right if here to hear is 17 that means when I go back to zero in a 17 space is that means I got to go over one so I'm we're at 1 now and then we got to go left so if we go left what time do we end up on left 747 units so we're at 1 when left 7 think about that so we are at 1 we're going to go -7 spaces and Let's ignore that right now let's go back to the rules of addition we're adding one + -701 + -7 I'm adding a positive and a negative number so when the signs are different we keep the sign of the longer Arrow if I'm going to draw an arrow for this pink this pink right here it's give me 7 units long to the left if I compare that to an arrow that's one unit long meaning here to here that's the one you know where we always keep the sign of the longer Arrow which is negative well nut in this case the negative set now what do we do after that we take the absolute values and subtract larger - smaller 7 - 1 7 - 1 is good and negative good if that's what's up we go here and we right here -6 so this is how you would use the number line to show your work and if you need to you could do every little Mark you know one two three four five 6 in 07 you could do every little taken there but this is the bare minimum I need to see on the number line all right all right now I don't give a I only give two and a half points because on this first problem remember I'm requiring requiring you to do it two ways one has to get the number line if you don't do the number line and you do to other methods maxpoint you're going to get is 3 and 1/2 but before that lets go back with a note so couple things so let's go through the adding and subtracting rule if you're adding two numbers with the same sign A positive plus a positive or A negative plus a negative remember are the same sign keep the sign am I always left off this last one for those you guys are learning right now yeah they're the same sign you keep this I so if I'm adding two positive is positive negative negative but what do you do after this part while you guys are pendant you then add this is dead now forget it this kind of useless then add the absolute values together like in this case this person right here I'm adding two negative numbers -5 1/12 I know my answer is going to be negative so I keep same sign keep the sign then I just add them together what's 5 + 12 17 so negative 17 that's why were there so same sign design it's a science that's the next one we got two different times a positive plus a negative or a negative plus a positive you know we keep the sign of longer vector remember Vector just means Arrow which one would be the longer if you drew each one of these and draw an arrow representing each separately which one's the longer ones you keep the sign of the longer back there Ben Subs larger absolute ABS is an S absolute value minus shorter absolute or smaller absolute value this can buy with -17 -17 + 18 + negative plus a positive 8 would be 18 is longer than 17 and 18 is positive or answers positive we just subtract 18 - 17 1 wind it up right there and look at this last one so we're at 1 and then there's our next Answer 1 + -7 + negative plus a positive positive that one first week of s the negative is the bigger Arrow so we know the answer is negative and then subtract 7 - 1/6 but it's negative so rules of adding soundtrack that's pretty much what we will expect you guys on a number line or going left to right let's do the left to right one so we can understand that so message number two is just use going left to right and using these rules rewrite this let me rewrite the addition problem left to right there's no real name it's just on left or right left to right one number at a time so negative 5 + -12 + 18 + -7 all we're doing is literally just calling this thing two numbers at a time left or right negative plus a negative same sign keep the sign so this right here same time Heap sign and we just add so it's negative 17 -17 plus 18 plus -7 one number at a time it's right here next step -17 + 18 different sign keep sign longer vector longer Arrow remember Vector arrow is positive so we know it's going to be positive so I'm going to put a positive sign in parentheses just to remind us that it's positive in this case and then all we do is subtract 18 - 7 one positive one plus a negative 7 now we're adding a positive number plus a negative number this right here we keep sign of longer Vector keep sign of longer vector this case if we drew an arrow A1 arrow and  -7 Arrow the negative 7 arrow is longer so we keep the sign of that so we know the answer is negative and then we subtract forget that has Megan we just look at it throw away all the time is now 7 and this is the one that we subtract a bigger - 7 - 1/6 look at this right here same answer I'm going to tell you this number one on your test on Friday if you do two methods can you get different answers you did something wrong on one of them it should be the same answer if you're doing the same problems why so you should get the same answer you're just doing the work differently there's no name for this yes would this be another method do it just to left or right someone said on the last month do we do I have to write all this keeps up know know if I was going to do this on the that's just for notes that's that's notes right there and a hair let's go side to side left to right against Legacy so -5 + -12 + 18 + -7 and then -17 + 18 + -7 next step is a 1 + -7 and then negative 6 yeah one number at a time so that's another method going left or right you got means you're doing and I each step is just like a brand new problems you create so that right there is just no. You do not need to show all of those little you know you just do that right there I'm just putting that for your notes so why do guys when you based on your understanding why we're doing that now the next method is just using the commutative and associative property I'll let's go through here commutative and associative property commute and I'm going to answer a question before someone asks you if you are not going to have to do a problem where you have to justify your answer you no remember you do your work in you right now why you didn't know that's not now give me the chance property addition Community Project Music to reorder numbers like 4 + 5 equals 5 + 4y is that important will do that in a second. did a property addition this means we regroup numbers 4 + 5 + 6 equals 4 + 5 + 6 we usually you know reorganize it combine both of these ideas together we flip it and then regroup it I had my choice I would flip this 5 and 6 so I go 4 + 6 + 10 + 10 + 5 is 15 he's your way to add so it's about changing the order and regrouping it to me and it is versus the associative and let's let's regroup this hot right here so let's rewrite the sub again if all you can do is write change subtraction to addition I'm going to give you a point but let's do more than that so that's write it as an addition -5 + -12 + 18 + -7 + how would I reorder it and group it at the same time pic of this if I have my numbers group with the same sign all I do is add them together and I keep the sign in this case I'm going to say this I would group all my negative numbers together and I was RuPaul my positive numbers so and at the same time I'm going to write it slightly different to copy this down understand why I'm doing it if I gave you a problem rice that 43 + 29 you wouldn't it would be like this yes I wouldn't know no what would you do other things other than you would stop them on top of each other right that's how we do our work we line up our one we line up our tents and then we add our ones at 12 do we keep Jupiter's at Ed we carry over so in this case I would rewrite it like that so let me group all my negatives together I'm going to go negative so let's change color the order but I'm proving them at the same time in one step so this is a combination of associative and commutative so I'm rearranging it and drooping it so I'm still going to do -5 + -12 and then I'm going to flip this around and I'm going to remove the negative 7 we're here so I'm grouping all my negative numbers not only did I flip these two numbers around but I group to the YouTube I want I'm stacking them on top of each other I'm at and then look at this this 18 is positive 18 is left on its own + 18 but look at this I could combine these right here if it's the same sign all I do is keep the sign add the numbers 5 + 277 + 7 is 14 carrier one one and one makes two negative 24 hey we didn't get that up here there's no negative -24 + 18 there's my new problem one little step I just combined it all I got straight up Francis right here right now which is the bigger number 24th we keep the sign we know it's going to be negative and all we do is subtract 24 - 18 look at this this is why we use the commutative property and associative property we group our numbers boom and they don't have what's left over boom answers right there it's a it's like a short cut not really it's working but it's compared to this let me zoom out the doll Forum all three of these methods so you can do a combination some people get stuck somewhere and then they always end up on a number line so you can do it with that something out there's another problem will do that to get a number line number line and going left to right is pretty much the same thing it's like counting with your fingers will you doing one number at a time or as this right here the commutative property and associative property which we hope to do practically get you to this is the message we would like you to get to the end but for now this is all you know stick with it but if you do both of these great but I'm number one you're going to do this one and one of these other two the two methods to get full points but if all you can do is show addition to get 1.5 whatever's else is between this right here they're technically the same thing this is like counting with your fingers one number at a time is this you just trying to group things together say sometimes there's some work right that's like the first Prime let's do one problem cuz you another one make sure you this the one down here. Let's go using associative are using commutative and associative properties but you can she come by all these methods what you guys don't get I'm making you guys do them separately on number one but you could actually do like combination I'll show that on another one in the second but visit so let me do it another problem to make sure you guys are do this so try this next one on your own let me speak this up so let's go 8 - -13 + -7 -12 just do one way just do one way to make sure you could at least get the answer choose any man that you want I don't care zoom in what's up okay do we copy this one down and try and do it on your own is it all just seems like the last one yes I'm just trying to give you a problem your you're capable remember when I said I do have a question though so you see how you wrote the problem with that like right now whatever you what is used to be possible like this do it like there's no number line as a way of doing it as credit well you can if you just go left to right sure but I would always change it to edition first the first one remember you only change the fraction subtraction is the only thing we change what is the number State pause good question all right I getting a lot of answers so I'm going to give like another 15 seconds wrap it up zero let's check it out so first always be safe this is where a lot cuz you guys are trying to come by. first things first change it to a dish in once you change it to Edition then you can choose whatever method you want it makes it a lot safer 8 subtraction becomes Edition notice I'm only changing subtraction you're adding the opposite what is the opposite of -13 good 13 this is already Edition so I keep it you do not change anything that's already Edition and that's that's not a minus that's a negative where is this right here that's a subtraction change it to addition what's the opposite of 12 good -12 and not look at this this one is group for us so this is an extra step what you don't need another line for but you got to realize hey look my positive numbers already grouped in the front my negative numbers are grouped in the back I can because it's a day add whatever order I want now my positives with my positives my negatives is my negative and since it's the same sign we keep the sign and we add 8 + 30 that's where somebody wrote down 24 not 2421 we only change the subtraction numbers anything that subtraction first number stays the same notice 8:30 positive do we change a positive number is it some traction is there a subtraction sign in front of it no sew good good question to ask but this right here look at this what's the traction right and that's a negative 13th so these are great questions right here watch out you need to ask yourself is this subtraction or is it negative we only change subtraction they got to watch this is a - -13 + -7 - 12 reading this right here for a lot of people that are doing that the coding thing medical coding be understanding that some symbols are red differently in the same sentence the sentence right here 8 - -13 + -7 - 12 notice that minus a negative use the same sign but I read it differently that's Lexa right there math Lexile very important so watch out for that so that is literally it sounds simple but that is the hardest thing about doing some traction from where you get negative and minus mixed up watch out for that watch out for that watch out for that put that in your nose is it minus or is it negative and we are only changing - Rollie changing - but we change the traction into Edition you got to remember the number that follows it we need to change it to the opposite subtraction is adding the opposite so we change subtraction to adding what is the opposite of negative 13 13 but this right here were adding and -7 we don't care about when it's adding we leave it we don't change anything when it Saturday but then this right here is mine 12 subtraction subtraction becomes addition of the opposite what is the opposite of 12 negative opposite of 12 fraction is adding the opposite and when we everything to adding we could add in whatever order we want it doesn't matter anymore what was great about this is that that's why I put the pink in there are positive numbers are in the front or negative numbers are in the back we could just are positive numbers together remember this right here we have the same sign we keep the sign then just add the absolute values O positive and positive we know still be positive and then we just do 8 + 13 21 I like this for adding two negative numbers together if they're the same sign we keep the sign we know it's going to be negative and then we just add the numbers together 7 + 12 19 and look at this down to just two numbers a positive number and a negative number going back to the rules and we just got two numbers and their difference I just imagined you'd your two separate arrows on a number line or two different number line we have a 21 error and -19 are all but which one's longer 21 by how many 21 is longer than 19 by two or three which one is it so that's how you do your answer it when you're down to two numbers your is up all right which ones bigger the pot the negative deposit swenor answers going to be positive I'm going to put the positive sign here and then all you do is subtract but just think all right so I can pair my arrows which ones bigger than 21 but how many to that's pretty much subtraction so it's a bigger by to deposit to adjust to you don't need that pause sign but all you do is subtract or just think, needs a bigger by 2 so watch out a lot of guys give me different answers cuz you guys it was a sign most 80% of our mistakes is adding subtracting multiplying dividing but usually that involves just messing up the signs so watch out for that that's what we did all these little steps right here and that's how you can do a number line to see the number line really quick so let's always start at the addition problem don't start the subtraction do the addition problem so we start at zero we go to H let's say this is we add 13 from here if I'm adding I'd go to the right 13 faces 13 spaces I'm at 21 and then I subtract 7 If I subtract 7 was that 14 14 and then I subtract 12 more if I go from 14 to 12 down I'm over two good job same answer a number line is just a visual thing to check your work Sammy has like to do the number line for fine go ahead I'm not going to say no but you know so I like a GroupMe where's the Gathering left right this did this just happen to be going left to right and grouping them at the same time so this is a combination right here notice I didn't really go what I change it to Edition I kind of did go left to right I did these two but then I group them I went left to right but I didn't do one number at a time so this right here is a combination problem where I groups everything together and that's the thing about when you have Edition you could group all the methods together let's do ones with now that's like I said this right here on number one you got to show two ways one has to be the number line for pull credit if you don't know how to do the number line could do to other methods you get 3.5 fully correct all right let's go do some fractions but not Super Fresh and we're going to do with what's the decomposition method first and what do a number line to show no playing with it let's go to + 3/5 - 4/5 listen to the number line first understanding were fractions on a number Salida you guys can't do the decomposition cuz your own like you with fractions all right with your practice next module but understanding were fractions on a number line first ASCII so let's go Star up at 2 and 3/5 so here's zero 1 2 I did all this just so you know later this 2 3/5 I go to 2 and I got to go 3/5 more that means before 3 that's why I wrote down the number 3 know you guys are stuck what what what what is 3/5 said 3/5 of here's a number line a fraction just means I have a number line inside of a no and Latias just like where do I go to to but I got to go 3/5 more that means I'm going to the right that means my noon of my mini number line is between 2 and 3 and then the next step you guys and say well how do I cut it up look at the denominator that tells you how many pieces to cut it up so in between 2 and 3 I need to have four lines it's always one less cuz the whole number is the last line watch this I got 2/5 1/5 2/5 3/5 4/5 the whole number itself needs to be the last line that's V is look at this let's put it up here 1/5 / 2/5 3/5 4/5 and 5/5 is a whole unit one whole but you can't have one hole in front of another whole number it's because the next whole unit is the next whole unit the whole number solve 5/5 is the three even though it's one and he's looking this two plus one makes three that's where a lot of people are confused about this whole unit that's not a three people say but if we're coming little pieces ignoring just looking at one-fifth 2/5 3/5 4/5 - or whole unit would be 3 but since we started at to two plus one makes three so we are at 2 3/5 right here 2 3/5 and where subtracting let's change that addition problem 2 3/5 what's a 5 + -4/5 negative means we're going to the left the numerator how many many steps were taking whole steps whole units 3210 that's a whole unit but we're talking about fractions the numerators how many many steps were taken so we're taking for many steps to the left I'll look at this so here's what store near 123 but we need to take for so we need to take a mini step right here that means I need to cut up 122 it's a five-piece is also 1234 and the number itself is the fifth one so we are right here what where is this right here so look at this if we do the same thing 1/5 2/5 / 3/5 almost one and for what good one in 4/5 of the mistake with the number line using the number line message to the light but you forget good you got it though there's a whole number in front so we're at this fraction but we need to also pay attention to the integer so we're at 1 and 4/5 that's using the number line message. Somebody told people in the other class said I know my fraction rules and I know how to do fractions do I have to show the number line so only on the first one am I requiring you to use the number line if you want to use the number line for the rest of them that's why you got you only need to show one way or the other problems all the mixed number fraction 1 you'll need to do it one time one method you don't need to do anything I change my instructions to try to make it more clear but I'm just saying it right now so this is using the number line there's another method without using the number line this is just to show you how to get the answer to visualize it use the deconstruction decomposition the notes didn't use this word but some of the guys remembered it from last year which is great so I'm going to use it decomposition it means breaking apart break apart decompose when I perish and I get thrown under dirt I will deacon I will turn into mush in the worms will eat me and all that will be left or my calcified bones that the worms do not want to eat what was the weather like on the 2nd so let's go look at the problem of Judas probably guess or two and three fifths -4 fit into Edition 2 + 3/5 + -4/5 part 2 + 3/5 + -4/5 looking at this right here we could group the fractions together so too + 3/5 + -4/5 and all we do we have the same denominator we add and subtract the numerator I'll look at this 3 - 4 bigger arrow is the negative so 4 - 3 is one but it's negative so + -1 V now I'm going to stop for a second so like we could split mixed number part we can put it back together but only if they have the same sign this right here most common mistake that's a positive to a negative one fist when the number the fraction have different signs you can't merge them together for a mixed number can't do that and keep it apart show got to understand this right here I'm leaves another number line to illustrate it if you right here which want to change it to a tattoo into a fraction over 5 and then yeah you're more than welcome to do that but I'm not going to teach it I'll do that next module not going to teach that yet so we're at to wear at 2 and here's one so I'm going one 5th so we're taking many steps one two three four and this five-year remember the integer is the fifth piece I'm going down I'm subtracting 1/5 what's this one 1/5 2/5 3/5 4/5 1 end 4 V same thing same answer so this is a combination number line decomposition problem another way to do it someone this right here I'm going to stop these numbers up just like the oven so look at this 2 and 3/5 I'm going to stack them on top of each other - 4/5 do not copy this next piece. I'm just doing it off to the side so you understand again if I had 43 - 17 we would go 3 - 7/3 hour we can't do that we got to borrow so we buy pro at 10 so just becomes instead of 40 it becomes 30 and instead of 13 it becomes 1330 + 13 is 43 so we add 10 to this but like fractions adding a 10 adding a 1-hole so 3/4 - 4 Chords to can't do that so we have to borrow we borrow a one-hole from to the bar one hole that becomes one and one holds out of 5 p.m. so we got to add 5/5 to this we're going to do more of this I showed you some of you guys this is something I did this on the homework which is great let's double-check your work if you want to do this method that's up to you what will do more of this on module to be so right here looking is 3/5 plus 5/5 that becomes one and 8/5 this is not a correct mixed number you cannot have an integer and a improper fraction that always needs to be a proper fraction on a mixed number but you can write it like this when you're doing work cuz we're doing work right now 1 + 8/5 - 4/5 - 4/5 or Fist and that one just bring it down cuz we're not expect this one and 4/5 1 and 4/5 is the combination of different message right here let me see do I have another one are let's try this one on your own so we can see use all of the things we've done all the rules of adding subtraction method stuff try this problem out on your own see what you could do -8 3/7 - -3 + 5 sorry thank you that's on screen try this one on your own making sure you know what you were doing that 7 minutes so I can go over this and probably give you one more one more I would like to one more try and do this to put you can the last problem on your test involves three numbers It's a combination of mixed numbers and integers and fractions some of the guys will get three mixed numbers you guys will get to mixed numbers an integer some of you guys to get two mixed numbers and a fraction some of you guys will get a mixed number an integer and a fraction you would merge them together good you figure a way we'll do it next but let's try to finish this one first try to hurry up and do that one will see if you're right in the second Michigan for the for the two for the two and three fifths have to do that in one way right you do it one way I said it are the Sy all right I got to answer so let's try and wrap it up even if you're not done it as far as you can I am actually giving you less time than I would on the test remember on the test one of these problems you're getting 12 minutes maximum you are that's what it divides out to be hopefully they should take you guys each problem 5 minutes ish so that's more than double the time and give me for HP because you're not yes yes you could use your notes that's what these are so when you're done with all of this today organized this until like a couple pieces of paper so you can see which all right so why do you guys are breaking it up you guys use the composition of what I've been reading so let's break it apart now this right here that's a negative 8th and 370 weight first good pets thank you should we change the traction to edition first let's do that negative also remember subtraction is adding the opposite what is the opposite the opposite is 3 and 5/7 so watch out for bring message to change the first one but in the second one yes cuz that's not the Triton good we're only changing we're only changing the number after the subtraction good good question so now let's break it apart this is a -8 3-7 that means this whole thing is negative so we break it apart sand -8 + I don't know yet remember this right here at whole things negative snow yet that fraction no one messes up on the negative 8 but when you break apart a negative mixed number don't forget the fractions negative breaking apart of this right here we break your partner 3 + 5/7 would my next step be my next step would be I'd slip these two around so I group my whole number my integers with managers my fractions with my fractions said rewrite is negative + 3 + -3/7 + 5/7 property just so I group them together do I need to put the parentheses for grouping it now we do this all this negative what's 3 take your time you're going to have five minutes in a problem watch out watch out what's -8 + 3 -5 negative 5 to watch out you group the numbers together great watch out that's not 11 remember when we have different signs we keep the sign of the bigger vector and then we ate we subtract 8 - 3/5 the same concept we got five seven 807 -3 + 5 so 270 -5 with the truce right here I think about on a number line I'm at -5 and I take away. That means are for right here or is it not negative plus negative wait I'm adding I messed up adding adding goes this way so I got to go to negative for that means I got to cut it up into 7 pieces 1 2 3 4 5 6 7 is always a number so I'm going over too many steps that's my answer -4 12345 -4 5/7 alright so

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