0:00:00.423,0:00:04.370 - [Voiceover] Carly tried to[br]solve an equation step by step. 0:00:04.370,0:00:06.042 And they tell us, they see, we see 0:00:06.042,0:00:07.667 how she tried to solve the equation. 0:00:07.667,0:00:10.082 They say find Carly's mistake. 0:00:10.082,0:00:11.289 So let's see what Carly did. 0:00:11.289,0:00:15.817 She started with 7a = 28. 0:00:15.817,0:00:19.578 Then on the left hand[br]side she divides it by a 0:00:19.578,0:00:23.201 and on the right hand[br]side she divides by 7. 0:00:23.201,0:00:24.663 Well this seems strange. 0:00:24.663,0:00:25.824 When you're manipulating an equation 0:00:25.824,0:00:27.589 whatever you do to one[br]side, you have to do 0:00:27.589,0:00:28.727 to the other side. 0:00:28.727,0:00:31.722 Over here she decides to[br]divide the left side by a, 0:00:31.722,0:00:35.042 on the right side she[br]should divide by a as well. 0:00:35.042,0:00:37.527 Or if she wants to divide[br]the right side by 7, 0:00:37.527,0:00:40.104 she should divide the[br]left side by 7 as well, 0:00:40.104,0:00:42.542 but she's dividing both sides[br]by two different things. 0:00:42.542,0:00:46.211 So step 1 is where she makes the mistake. 0:00:46.211,0:00:47.302 The right thing for her to do, 0:00:47.302,0:00:49.392 or I guess maybe the[br]most reasonable thing, 0:00:49.392,0:00:52.758 if she wants to solve for[br]a, divide both sides by 7. 0:00:52.758,0:00:54.848 Then she would have[br]been left with just an a 0:00:54.848,0:00:56.682 on the left hand side,[br]because it would have been 0:00:56.682,0:00:58.679 7a/7 and a 4 over there. 0:00:58.679,0:01:00.978 She would have said, oh,[br]a must be equal to 4. 0:01:00.978,0:01:02.232 So let's keep going. 0:01:02.232,0:01:05.181 Let's do a few more of these. 0:01:05.181,0:01:07.781 Trent tried to solve an[br]equation step by step. 0:01:07.781,0:01:09.592 All right. Find Trent's mistake. 0:01:09.592,0:01:11.101 So a lot of mistakes happening 0:01:11.101,0:01:12.913 in algebra problems right now. 0:01:12.913,0:01:16.511 So g/3 = 4/3. 0:01:16.511,0:01:17.997 Now let's see. The first step. 0:01:17.997,0:01:22.223 g/3 x 3, so he's multiplying[br]the left hand side times 3 0:01:22.223,0:01:27.006 and on the right hand side,[br]he's multiplying by 1/3. 0:01:27.006,0:01:29.398 So once again, he's doing[br]two different things 0:01:29.398,0:01:30.930 to the left and the right hand side 0:01:30.930,0:01:32.324 even though you're supposed[br]to do the same thing. 0:01:32.324,0:01:34.669 If you do two different[br]things, the equality 0:01:34.669,0:01:37.548 will not hold anymore. 0:01:37.548,0:01:38.918 Notice, if these two things are... 0:01:38.918,0:01:42.586 If g/3 = 4, if you multiply this times 3 0:01:42.586,0:01:45.628 and you only multiply this times 1/3, 0:01:45.628,0:01:47.184 well then this thing is[br]going to become larger, 0:01:47.184,0:01:49.134 because is you multiply by[br]3 that's going to be larger 0:01:49.134,0:01:51.920 if you take the same thing[br]and multiply it by 1/3. 0:01:51.920,0:01:54.219 Then the equality won't hold true anymore. 0:01:54.219,0:01:55.635 In order for it to hold true,[br]if you're going to multiply 0:01:55.635,0:01:58.608 the left by 3 you have to[br]multiply the right by 3. 0:01:58.608,0:02:01.835 So he made a mistake on step 1. 0:02:01.835,0:02:02.532 All right. 0:02:02.532,0:02:04.993 Ling tried to solve an[br]equation step by step. 0:02:04.993,0:02:07.013 All right. Find Ling's mistake. 0:02:07.013,0:02:10.496 Let's see 12 = p + 6.2. 0:02:10.496,0:02:12.794 All right. So now it looks like, 0:02:12.794,0:02:17.554 on the left hand side Ling adds 6.2 0:02:17.554,0:02:19.644 and on the right hand side, so there was 0:02:19.644,0:02:21.594 p + 6.2 is the old right hand side, 0:02:21.594,0:02:26.192 but it looks they then[br]try to subtract 6.2. 0:02:26.192,0:02:28.606 So it's the same number, but over here 0:02:28.606,0:02:32.391 they're adding it and over[br]here they're subtracting it. 0:02:32.391,0:02:34.852 So they're not doing the[br]same thing to both sides. 0:02:34.852,0:02:36.687 If you want to add 6.2[br]to the left hand side 0:02:36.687,0:02:38.846 you need to add 6.2 to[br]the right hand side. 0:02:38.846,0:02:40.982 If you want to subtract 6.2[br]from the right hand side 0:02:40.982,0:02:44.651 you have to subtract 6.2[br]from the left hand side. 0:02:44.651,0:02:47.646 So a lot of mistakes going on in step 1. 0:02:47.646,0:02:51.361 Let me see one where there's[br]not a mistake in step 1. 0:02:51.361,0:02:52.034 All right. 0:02:52.034,0:02:54.472 Alanna tried to solve an[br]equation step by step. 0:02:54.472,0:02:59.472 4c = 12, divides the left hand side by 4 0:03:00.254,0:03:02.529 and then multiplies the[br]right hand side by 4. 0:03:02.529,0:03:04.619 No if you're going to divide[br]the left hand side by 4 0:03:04.619,0:03:06.987 you have to divide the right[br]hand side by 4 as well. 0:03:06.987,0:03:08.427 You don't multiply it by 4. 0:03:08.427,0:03:11.260 So a mistake in step 1. 0:03:11.260,0:03:13.489 Let's do one more of these. 0:03:13.489,0:03:18.411 All right. n + 12 = 18.3. 0:03:18.411,0:03:20.431 So over here you had n + 12 0:03:20.431,0:03:23.705 and then Rico subtracts 12. 0:03:23.705,0:03:25.493 So if he subtracts 12[br]from the left hand side 0:03:25.493,0:03:27.931 he needs to subtract 12[br]from the right hand side. 0:03:27.931,0:03:28.929 It looks like he does that. 0:03:28.929,0:03:30.996 He had 18.3 and he subtracts 12. 0:03:30.996,0:03:33.736 So he subtracts 12 from both sides. 0:03:33.736,0:03:37.846 So the left side is now[br]n + 12 - 12, was just n, 0:03:37.846,0:03:39.471 which is why he subtracted 12, 0:03:39.471,0:03:41.770 so you're just left with[br]an n on the left hand side, 0:03:41.770,0:03:46.762 and on the right hand[br]side, let's see, 18.3 -12. 0:03:46.762,0:03:51.336 Well 18 - 12 is 6, so this should be 6.3. 0:03:51.336,0:03:53.542 So he made a little bit[br]of an arithmetic mistake 0:03:53.542,0:03:58.542 in step, he made an arithmetic mistake 0:03:58.673,0:04:03.673 and I think we are all done.