Period 6: Grade 7 Mathematics: Adding & Subtracting Rational Numbers

[00:00:10]Okay.

[00:00:13]Yeah, I got everything all situated.

[00:00:18]Perfect. Perfect side out. So, okay.

[00:00:32]So first up, if you're dealing with denominators like this, you need to you need to ask yourself what is the so what is the most common denominator because yeah.

[00:00:59]So, yeah, we're dealing with five, four, and eight.

[00:01:07]I'm going to take some notes, too, on here.

[00:01:12]Well, not exactly on here, but I'll give us hints as to as to which as to which goes where. So we're doing both with five, four, and eight. So So what do I think? Okay. So when I think this to myself, I norally ask, what number does all three numbers go into? So first I think of four is the smallest number. So four.

[00:01:55]So we got four 8 16 20 24 28 32 40.

[00:02:11]So 40.

[00:02:14]Yeah. So 40 goes into fours.

[00:02:26]40 goes into four. Then I think of fives.

[00:02:30]So fives like five 10 15 20 25 30 35 40.

[00:02:36]40 goes into fives.

[00:02:40]We're going to test and see if 40 is the correct number.

[00:02:44]and then I think eight which is the last number. So we got 8 16 24 32 40 easily.

[00:02:54]So the most common denominator here is 40.

[00:02:58]So so what we do to one side we always do to the other side. So we're going to do 40. So 40.

[00:03:12]So what do I think of when I'm subtracting numbers? So when I'm multiplying different numbers at the same time. So 40.

[00:03:26]So 4 fths is 80% of 40. So what's 80% of 40?

[00:03:34]32.

[00:03:36]Okay. for 32 and then we're going to add 30 and what do we get?

[00:03:48]62 and then I Okay, so then I subtract 35 because 7 / 8 is 87. So 35 and then I simplify the first number we leave the bottom number always.

[00:04:08]So that would give us 62 - 35 which is 27 27 27 over 40.

[00:04:21]And then we're doing this to the next set. The next set of three numbers. Next set of three numbers. Yeah.

[00:04:32]Same three.

[00:04:40]So this so far this one I'll leave it as eight. So we're going to use a denominator of eight.

[00:04:52]Okay. So both two and four go into eight. Correct. So which means 6 - 2 + 12.

[00:05:07]So what's 8 * 2? 16. 16 - half of 8 four.

[00:05:17]Um 16 - 4 12.

[00:05:24]Hi. Can I bring the board closer to the camera? Yes.

[00:05:31]Oh.

[00:05:36]Yeah.

[00:05:38]Yeah. We're just doing the warm warm up.

[00:05:46]But 6 - 2 is 4, right? 4.

[00:05:52]4 + 12 16 / 8 2.

[00:06:03]What is enter draw? Enter draw. What?

[00:06:10]I do not say withdraw this more rational numbers.

[00:06:18]Okay, we're going to do the same thing to the next two.

[00:06:27]Yes, I do not know why it's taking us so long to do our actual warm up.

[00:06:37]I know I'm being kind of crazy right now, but yes.

[00:06:43]So, two could go into 14, but four can't because even though 14 is an even number, we get 13 and a half.

[00:06:54]Yeah, 13 and a three and a half. Good video. Yeah, this is seventh grade math. Yeah, I know.

[00:07:04]So, so we're going to multiply both sides by two.

[00:07:11]Okay, hold up. So, we're going to check this both 14, 4, and two, but 28.

[00:07:23]So, 2 can go into 28 14 times.

[00:07:29]So, correct.

[00:07:32]And then I do four. Four can go into 28 seven times.

[00:07:41]So check from that. And then 14 can go into 28 two times. Correct. So yeah, he was asking about calculus, I think. But you were doing fractions for a warm up, right? Um, this is actually grade seven math.

[00:08:04]not calculus.

[00:08:06]Although one person asked me to do calculus on Tik Tok, so and and I was like, I'm not going to teach calculus because it's a college class and this is a grade 7 through 11 academy or whatever.

[00:08:29]This is not math. is AI physics or frankly physic is not physics it's math not anything to do with physics okay so we're just going to go to 28 so what's 28 * 2 56 so 56 - 14 which is 7 * 2 And then 3 * 2 is 6. Like 3 * 7 is 6. 3 * 7 is 21. Okay.

[00:09:11]+ 21us 11 2 + 5. Okay.

[00:09:21]140.

[00:09:23]Okay. 140. Um.

[00:09:27]Yeah. 140. So, and now we're going to calculate it, you know, right? So, 56 - 14 is 42 + 21 is 63.

[00:09:44]63 - 140 will give us to a negative number for sure.

[00:09:49]63 - 140 that get us to 77.

[00:09:56]Yeah. Three 3 seven.

[00:10:09]Yep. It got us 77, right? I was right. So, it gives us -77 over 28.

[00:10:24]28 * 2 is 46. No. 28 * 2 36. Sorry, my bad. No worries. It's okay.

[00:10:32]I want to ask them from Shane.

[00:10:35]I'm very I'm very smart in math, but I don't know. 28 + 28 = 56.

[00:10:43]28 + 28 is 56.

[00:10:48]Okay, we have one more fraction problem before we actually start the lesson which is about adding and subtracting rational numbers.

[00:11:02]We're going over three examples, but apparently I've been through 11 minutes worth of thing live whatever and now we're already halfway through. Okay.

[00:11:16]So, the decimals are a little easy, but this stuff right here. Okay.

[00:11:24]So, this is going to go one for youide by one.

[00:11:29]So, 9 cannot go into 11.

[00:11:33]One could go into 11 11 times. 1 * 11 is 11. So, I would think of 99. So 99.

[00:11:45]So 99.

[00:11:48]Okay. So I'll check one 9 11.

[00:11:55]So we're going to one goes into 99 99 99 times. So check 9 goes into 99 11 times.

[00:12:05]So check 119. Chuck multiple mastermind is what I am.

[00:12:17]Who? What do you mean? Who?

[00:12:26]One moment.

[00:13:03]Five of the internal dysfunctions. So, okay.

[00:13:10]So, we're going to multiply 3 by 99. So, what's 3 * 99?

[00:13:16]297. So, we're going to go over to 297 - 23 * 9, which is the same thing as 230 - 23. So which is 207 + 7 * 11 is 77 which is equal to what's 297 - 207 10 + 77 89 10 + 77 is 87 87ide by 99.

[00:14:02]This is the same thing as 8 7 8 7 8 7 8 7 or Yeah, now we're starting to get to decimals.

[00:14:17]So.5 + 2.4 4 is 2.9.

[00:14:22]My 3 is.1.

[00:14:29]And now 4 - 3.1 is 0.9 plus 8.3 is 9.2.

[00:14:38]Now we're done with our warm up.

[00:14:41]This is so easy. So, now we're actually starting to get into the real.

[00:14:52]Sorry, sorry, sorry.

[00:14:54]Sorry about that.

[00:14:57]Um, okay.

[00:15:11]Hope it doesn't move. Okay.

[00:15:15]So, now we're starting to get in a bit of rational numbers.

[00:15:19]Okay.

[00:15:21]Okay.

[00:16:04]So we're multip So we're adding and subtracting rational numbers. Here's the term for it, not calculus.

[00:16:11]Many people suggested me take teaching calculus, but I do not know when I will if I will ever teach calculus and when and where I would teach calculus, but if it's in the Yeah, I might teach in the college. I don't know if it is. And it's college geometry, college algebra, um, trigonometry.

[00:16:37]That's what second period, fifth, third period's doing. It's algebra. It's algebra 2 with trigonometry.

[00:16:48]I do not know what trigonometry is, but it's some sort of college level close to calculus. So afterward 2 goes calculus.

[00:17:04]Hey Ethan, I over reacted to your comment, but I not even know which part it was, but okay.

[00:17:23]Um, do you remember me from school? Wait, what school? What do you remember me from school? Um, I do remember you, but I do not know when.

[00:17:48]So now so now I'm doing this which my class has and now we're in and a quarter till class end.

[00:18:01]I stay going three three examples before we're doing a worksheet like no checkpoint one three check one two one three checkpoint yes so we're going to go a mix up addition and subt factor for this one.

[00:18:29]So 3 - 1/3 plus 2 9us 710.

[00:18:45]Okay.

[00:18:49]So what I think first so first thing I do is I check multiplication. So so one number do each of the numbers of so three 9 and 10. So we're going to do what? Yeah, we're gonna try 90 because 30 is not the nine family versus the 60s. So, so 90. So, we're going to test 90.

[00:19:29]We're going to test these three numbers three 9 10. Yeah, we're also checking one two.

[00:19:37]So like what times this number has to do with it 90. So I'm going to give you a minute class to do this to do the factoring correctly.

[00:19:55]Okay, I'll give you a minute. Okay.

[00:20:02]Okay.

[00:20:04]Ready?

[00:20:05]All right.

[00:20:08]Yeah.

[00:20:44]25 seconds.

[00:20:59]Correct. Thank you. 10 seconds.

[00:21:03]5 4 3 2 1.

[00:21:09]Okay.

[00:21:12]Except for the chat. You can chat if you want. So only two people are watching. Okay.

[00:21:19]Five. Five likes. Nice. Um, so we're gonna do blue. Where's my blue?

[00:21:30]Perfect.

[00:21:32]So, let's start with 10.

[00:21:36]What number times 10 could give us 290 without going over?

[00:21:46]Nine. So, let's count.

[00:21:49]10 20 30 40 50 60 70 80 90 nine times.

[00:21:56]Correct. Which means this is going to be suspicious because we already did nine.

[00:22:02]So it would be 10 here which would equal 90.

[00:22:13]So what about three?

[00:22:16]So 3 * 3 is 9. So 10 * 3 is 3.

[00:22:23]And then this would be 90. This would equal 90.

[00:22:29]I bet 90 would be so proud of us if we did. Yeah. 90.

[00:22:34]Yeah.

[00:22:36]90 is my favorite trans.

[00:22:39]Yeah. 90s grayish. [snorts] Okay. So we're going to do nine beats.

[00:22:45]So the denominator is 90. So So 90 90 90.

[00:23:03]So 30 * 90 is 270.

[00:23:11]1 * 30 30 2 * 10 20 7 * 9 63.

[00:23:34]Now I got all those numbers in. We're going to simplify the numerators to keep the denominators. So someone put as 360 and 240 + 20 or which is equal to 264us 360 - 50 which is equal to 200 over 360. If you do if you simplify the denominators that's wrong. So which is why we do not we do not simplify the denominators which means 90 - 90 + 90 or equal to infinity because any number by 0 is undefined or infinity which is what I taught my homework one class.

[00:24:32]Yes, the eighth grade class is going to go to square roots and cube roots. They were ting a chapter one capstone where they're doing well they are going to be doing equations and square roots and cube roots and whatever. So which is why we are going to find which is why we're going to be doing the one capstone the next time I do me.

[00:25:02]So, well, better stay tuned on July 19th at 9:40.

[00:25:12]But no, better stay tuned on Sunday, July 19th at at 10:00 a.m. PST for this cubes and squares.

[00:25:34]Okay, my next five probably going to be tonight. I don't know it yet. I really do not know yet. It's if if it's in the evening, then it's going to be between 6:00 and 9, but well 6:00 and 8 because I'm going to have to end my stream at 8:30 because I suck at 270US 30. So that would be 240ide by 90.

[00:26:11]So we're going to add 20 over 90 - 63 over 90, which is 260 / 90 - 63 over 90.

[00:26:26]What's 260 - 63?

[00:26:31]197ide by 90.

[00:26:38]If you want, you can leave it irrational, but for actual standards, you're going to divide 197 by 90, which will give us 2 and 17 90ths.

[00:26:59]These two can work just fine.

[00:27:09]Six people watching, five. Perfect. Oh, sure. Good. I'm okay.

[00:27:17]Okay, that's one example down. Two more to go before you take this cut point.

[00:27:29]We're going to do five decimals. So 2.15 2.16 plus 3.18 - 0.77 7US 2.9 four.

[00:28:05]Okay, so we're going to start off with these.

[00:28:13]So 2.16 + 3.18. So we're going to add 16 and 18 together first. So which will give us 34. So 34 and 2 + 3 is 5. So 2.16 + 3.18 is equal to 534 without going over. So now we're just going to do this - 0.77 + 6 - 2.94.

[00:28:48]Now we're going to do this which is 6.11 + 6 - 2.94.

[00:29:07]This will give us 121 - 2.94.

[00:29:13]And now that would equal to 10.05, 05 but 9.05 my bad 9.05 0 and one my calculator I found on okay we're going to double check to see if it's correct um yeah we're just going to check our results Wait, wait.

[00:30:02]Hold up.

[00:30:06]I added instead of subtracting. Sorry, I added instead of subtracting. So, this answer is going to be wrong this whole time. So 5.34 minus.77 is going to be 4 57.

[00:30:31]Yeah, 4.57. Now we get it. And at 10.57, which right about us down to 7 6 3.

[00:30:46]Yeah.

[00:30:47]Yeah.

[00:30:50]7.63 is our answer to number two.

[00:30:55]Always check your answers, kids, before you do something else. Okay.

[00:31:04]Okay, we have one final example to go over.

[00:31:10]It's almost 1:30. We have 1 hour left of class.

[00:31:15]So, uh, no more nos. Okay, perfect. Not perfect. Okay, we're going to use this very brownish.

[00:31:30]Okay, we are going to do um should we do a fraction or should we do a decimal one? So, raise your hand if you want decimals. 1 2 3 4 5 6 7 8.

[00:31:55]There should be 12 and eight out of 12.

[00:31:59]Let's break this. Okay. Basketball for this.

[00:32:32]Yeah, one more then shot time. So we are going to add this first which is 15.14us 3.34.

[00:32:49]We're going to do that now.

[00:32:55]which will give us 14.8 14 - 34 is -20.

[00:33:10]So now we're going to add 2.16 which will give us 16.96 plus 2.09 19.05.

[00:33:34]Now we're going to check our answers before we do the cat out.

[00:33:40]So one party correct correct correct correct.

[00:33:58]Perfect. [clears throat] You know I got sound gifts if you want.

[00:34:04]But anyways, it's pretty much too late now because it's time for shout outs.

[00:34:10]So once I erase all of this, you better stay tuned.

[00:37:34]I'm officially back. But behind me are Yeah. Behind me is my shout outs for today. So, this is going to be my one of two lives [snorts] today. So, Don't miss out on all the fun.

[00:37:58]Here are shout outs are beginning.

[00:38:03]Ready, set, go.

[00:38:11]So, we have four shout outs today that I wanted to give out.

[00:38:17]Ethan Scott X1 Y Gallo Tanova 4429 Uber guy.

[00:38:31]So if you want to learn more from this channel, please like and subscribe, please subscribe and I'll see you all next time. I will update the the top panel like where it says how much I am till 1,000.

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[00:39:08]Bye.