WEBVTT 00:00:00.423 --> 00:00:04.370 - [Voiceover] Carly tried to solve an equation step by step. 00:00:04.370 --> 00:00:06.042 And they tell us, they see, we see 00:00:06.042 --> 00:00:07.667 how she tried to solve the equation. 00:00:07.667 --> 00:00:10.082 They say find Carly's mistake. 00:00:10.082 --> 00:00:11.289 So let's see what Carly did. 00:00:11.289 --> 00:00:15.817 She started with 7a = 28. 00:00:15.817 --> 00:00:19.578 Then on the left hand side she divides it by a 00:00:19.578 --> 00:00:23.201 and on the right hand side she divides by 7. 00:00:23.201 --> 00:00:24.663 Well this seems strange. 00:00:24.663 --> 00:00:25.824 When you're manipulating an equation 00:00:25.824 --> 00:00:27.589 whatever you do to one side, you have to do 00:00:27.589 --> 00:00:28.727 to the other side. 00:00:28.727 --> 00:00:31.722 Over here she decides to divide the left side by a, 00:00:31.722 --> 00:00:35.042 on the right side she should divide by a as well. 00:00:35.042 --> 00:00:37.527 Or if she wants to divide the right side by 7, 00:00:37.527 --> 00:00:40.104 she should divide the left side by 7 as well, 00:00:40.104 --> 00:00:42.542 but she's dividing both sides by two different things. 00:00:42.542 --> 00:00:46.211 So step 1 is where she makes the mistake. 00:00:46.211 --> 00:00:47.302 The right thing for her to do, 00:00:47.302 --> 00:00:49.392 or I guess maybe the most reasonable thing, 00:00:49.392 --> 00:00:52.758 if she wants to solve for a, divide both sides by 7. 00:00:52.758 --> 00:00:54.848 Then she would have been left with just an a 00:00:54.848 --> 00:00:56.682 on the left hand side, because it would have been 00:00:56.682 --> 00:00:58.679 7a/7 and a 4 over there. 00:00:58.679 --> 00:01:00.978 She would have said, oh, a must be equal to 4. 00:01:00.978 --> 00:01:02.232 So let's keep going. 00:01:02.232 --> 00:01:05.181 Let's do a few more of these. 00:01:05.181 --> 00:01:07.781 Trent tried to solve an equation step by step. 00:01:07.781 --> 00:01:09.592 All right. Find Trent's mistake. 00:01:09.592 --> 00:01:11.101 So a lot of mistakes happening 00:01:11.101 --> 00:01:12.913 in algebra problems right now. 00:01:12.913 --> 00:01:16.511 So g/3 = 4/3. 00:01:16.511 --> 00:01:17.997 Now let's see. The first step. 00:01:17.997 --> 00:01:22.223 g/3 x 3, so he's multiplying the left hand side times 3 00:01:22.223 --> 00:01:27.006 and on the right hand side, he's multiplying by 1/3. 00:01:27.006 --> 00:01:29.398 So once again, he's doing two different things 00:01:29.398 --> 00:01:30.930 to the left and the right hand side 00:01:30.930 --> 00:01:32.324 even though you're supposed to do the same thing. 00:01:32.324 --> 00:01:34.669 If you do two different things, the equality 00:01:34.669 --> 00:01:37.548 will not hold anymore. 00:01:37.548 --> 00:01:38.918 Notice, if these two things are... 00:01:38.918 --> 00:01:42.586 If g/3 = 4, if you multiply this times 3 00:01:42.586 --> 00:01:45.628 and you only multiply this times 1/3, 00:01:45.628 --> 00:01:47.184 well then this thing is going to become larger, 00:01:47.184 --> 00:01:49.134 because is you multiply by 3 that's going to be larger 00:01:49.134 --> 00:01:51.920 if you take the same thing and multiply it by 1/3. 00:01:51.920 --> 00:01:54.219 Then the equality won't hold true anymore. 00:01:54.219 --> 00:01:55.635 In order for it to hold true, if you're going to multiply 00:01:55.635 --> 00:01:58.608 the left by 3 you have to multiply the right by 3. 00:01:58.608 --> 00:02:01.835 So he made a mistake on step 1. 00:02:01.835 --> 00:02:02.532 All right. 00:02:02.532 --> 00:02:04.993 Ling tried to solve an equation step by step. 00:02:04.993 --> 00:02:07.013 All right. Find Ling's mistake. 00:02:07.013 --> 00:02:10.496 Let's see 12 = p + 6.2. 00:02:10.496 --> 00:02:12.794 All right. So now it looks like, 00:02:12.794 --> 00:02:17.554 on the left hand side Ling adds 6.2 00:02:17.554 --> 00:02:19.644 and on the right hand side, so there was 00:02:19.644 --> 00:02:21.594 p + 6.2 is the old right hand side, 00:02:21.594 --> 00:02:26.192 but it looks they then try to subtract 6.2. 00:02:26.192 --> 00:02:28.606 So it's the same number, but over here 00:02:28.606 --> 00:02:32.391 they're adding it and over here they're subtracting it. 00:02:32.391 --> 00:02:34.852 So they're not doing the same thing to both sides. 00:02:34.852 --> 00:02:36.687 If you want to add 6.2 to the left hand side 00:02:36.687 --> 00:02:38.846 you need to add 6.2 to the right hand side. 00:02:38.846 --> 00:02:40.982 If you want to subtract 6.2 from the right hand side 00:02:40.982 --> 00:02:44.651 you have to subtract 6.2 from the left hand side. 00:02:44.651 --> 00:02:47.646 So a lot of mistakes going on in step 1. 00:02:47.646 --> 00:02:51.361 Let me see one where there's not a mistake in step 1. 00:02:51.361 --> 00:02:52.034 All right. 00:02:52.034 --> 00:02:54.472 Alanna tried to solve an equation step by step. 00:02:54.472 --> 00:02:59.472 4c = 12, divides the left hand side by 4 00:03:00.254 --> 00:03:02.529 and then multiplies the right hand side by 4. 00:03:02.529 --> 00:03:04.619 No if you're going to divide the left hand side by 4 00:03:04.619 --> 00:03:06.987 you have to divide the right hand side by 4 as well. 00:03:06.987 --> 00:03:08.427 You don't multiply it by 4. 00:03:08.427 --> 00:03:11.260 So a mistake in step 1. 00:03:11.260 --> 00:03:13.489 Let's do one more of these. 00:03:13.489 --> 00:03:18.411 All right. n + 12 = 18.3. 00:03:18.411 --> 00:03:20.431 So over here you had n + 12 00:03:20.431 --> 00:03:23.705 and then Rico subtracts 12. 00:03:23.705 --> 00:03:25.493 So if he subtracts 12 from the left hand side 00:03:25.493 --> 00:03:27.931 he needs to subtract 12 from the right hand side. 00:03:27.931 --> 00:03:28.929 It looks like he does that. 00:03:28.929 --> 00:03:30.996 He had 18.3 and he subtracts 12. 00:03:30.996 --> 00:03:33.736 So he subtracts 12 from both sides. 00:03:33.736 --> 00:03:37.846 So the left side is now n + 12 - 12, was just n, 00:03:37.846 --> 00:03:39.471 which is why he subtracted 12, 00:03:39.471 --> 00:03:41.770 so you're just left with an n on the left hand side, 00:03:41.770 --> 00:03:46.762 and on the right hand side, let's see, 18.3 -12. 00:03:46.762 --> 00:03:51.336 Well 18 - 12 is 6, so this should be 6.3. 00:03:51.336 --> 00:03:53.542 So he made a little bit of an arithmetic mistake 00:03:53.542 --> 00:03:58.542 in step, he made an arithmetic mistake 00:03:58.673 --> 00:04:03.673 and I think we are all done.