0:00:00.810,0:00:03.110 Welcome to the presentation[br]on dividing fractions. 0:00:03.110,0:00:04.490 Let's get started. 0:00:04.490,0:00:06.640 So before I give you the[br]intuition-- actually, I might 0:00:06.640,0:00:09.340 do that in a different module--[br]I'm just going to show you the 0:00:09.340,0:00:11.740 mechanics of how you[br]divide a fraction. 0:00:11.740,0:00:13.740 And it turns out that[br]it's actually not much 0:00:13.740,0:00:16.030 more difficult than[br]multiplying fractions. 0:00:16.030,0:00:21.410 If I were to ask you, 1/2[br]divided by 1/2, whenever you 0:00:21.410,0:00:25.110 divide by a fraction, or[br]actually, when you divide by 0:00:25.110,0:00:29.960 any number, it's the same thing[br]as multiplying by its inverse. 0:00:29.960,0:00:36.670 So 1/2 divided by 1/2 is[br]equal to 1/2 times 2/1. 0:00:36.670,0:00:44.990 We just inverted--[br]inverse-- the second 1/2. 0:00:44.990,0:00:47.630 And we know from the[br]multiplication module, 1/2 0:00:47.630,0:00:51.110 times 2/1, well, that's[br]just equal to 2/2, 0:00:51.110,0:00:53.560 or it's equal to 1. 0:00:53.560,0:00:56.020 And that makes sense because,[br]actually, any number divided 0:00:56.020,0:00:58.750 by itself is equal to 1. 0:00:58.750,0:01:03.220 1/2 divided by 1/2 is 1, just[br]like 5 divided by 5 is 1, just 0:01:03.220,0:01:05.240 like 100 divided by 100 is 1. 0:01:05.240,0:01:06.850 And this isn't a new principal. 0:01:06.850,0:01:08.970 Actually, you were[br]always doing it. 0:01:16.290,0:01:20.560 But isn't this also the[br]same thing as 2 times the 0:01:20.560,0:01:24.210 inverse of 2, which is 1? 0:01:24.210,0:01:24.950 I'll show it to you. 0:01:24.950,0:01:26.990 Actually, let me give you a[br]couple more examples to show 0:01:26.990,0:01:31.340 that dividing fractions really[br]isn't a new concept, this whole 0:01:31.340,0:01:34.840 notion of multiplying[br]by the inverse. 0:01:34.840,0:01:40.540 If I were to tell you[br]what is 12 divided by 4? 0:01:40.540,0:01:42.650 Well, we know the answer to[br]this, but I'm going to show 0:01:42.650,0:01:50.640 you that this is the same[br]thing as 12 times 1/4. 0:01:50.640,0:01:56.230 12/1 times 1/4 4 is[br]12/4, which is 3. 0:01:56.230,0:01:59.480 And 12/4 is really just another[br]way of writing 12 divided by 4, 0:01:59.480,0:02:02.535 so it's kind of a long way of[br]getting to the same point. 0:02:02.535,0:02:04.990 But I just wanted to show you[br]that what we're doing in this 0:02:04.990,0:02:07.970 module is nothing new than[br]what we've always been doing 0:02:07.970,0:02:09.320 when we divide by a number. 0:02:09.320,0:02:11.360 Division is the same thing. 0:02:11.360,0:02:14.310 Dividing by a number is the[br]same thing as multiplying by 0:02:14.310,0:02:15.960 the inverse of that number. 0:02:15.960,0:02:19.880 And just as a review, an[br]inverse, if I have a number 0:02:19.880,0:02:28.070 A, the inverse-- inv, short[br]for inverse-- is 1 over A. 0:02:28.070,0:02:36.290 So the inverse of 2/3 is 3/2,[br]or the inverse of 5, because 5 0:02:36.290,0:02:39.670 is the same thing as 5/1,[br]so the inverse is 1/5. 0:02:43.320,0:02:46.475 So let's do some fraction[br]division problems. 0:02:46.475,0:02:49.270 [br]What is 2/3 divided by 5/6? 0:02:56.340,0:03:05.970 Well, we know that this is the[br]same thing as 2/3 times 6/5, 0:03:05.970,0:03:09.230 and that's equal to 12/15. 0:03:09.230,0:03:14.570 We can divide the numerator and[br]denominator by 3, that's 4/5. 0:03:14.570,0:03:22.900 What is 7/8 divided by 1/4? 0:03:22.900,0:03:30.520 Well, that's the same[br]thing as 7/8 times 4/1. 0:03:30.520,0:03:32.820 Remember, I just[br]flipped this 1/4. 0:03:32.820,0:03:36.840 Divide by 1/4 is the same[br]thing as multiplying by 4/1. 0:03:36.840,0:03:38.230 That's all you've got to do. 0:03:38.230,0:03:39.990 And then we could use a little[br]shortcut we learned in the 0:03:39.990,0:03:41.480 multiplication module. 0:03:41.480,0:03:42.950 8 divided by 4 is 2. 0:03:42.950,0:03:44.800 4 divided by 4 is 1. 0:03:44.800,0:03:47.450 So that equals 7/2. 0:03:47.450,0:03:49.900 Or if you wanted to write that[br]as a mixed number, this is, of 0:03:49.900,0:03:51.200 course, an improper fraction. 0:03:51.200,0:03:53.440 Improper fractions have[br]a numerator larger 0:03:53.440,0:03:54.830 than the denominator. 0:03:54.830,0:03:58.670 If you wanted to write that as[br]a mixed number, 2 goes into 7 0:03:58.670,0:04:03.680 three times with a remainder[br]of 1, so that's 3 and a half. 0:04:03.680,0:04:04.440 You can write it either way. 0:04:04.440,0:04:05.990 I tend to keep it this[br]way because it's 0:04:05.990,0:04:07.800 easier to deal with. 0:04:07.800,0:04:10.130 Let's do a ton of more[br]problems, or at least as many 0:04:10.130,0:04:13.830 more as we can do in the[br]next four or five minutes. 0:04:13.830,0:04:23.850 What's negative 2/3[br]divided by 5/2? 0:04:23.850,0:04:29.110 Once again, that's the same[br]thing as minus 2/3-- whoops-- 0:04:29.110,0:04:34.850 as minus 2/3 times what? 0:04:34.850,0:04:40.110 It's times the inverse of[br]5/2, which is 2/5, and 0:04:40.110,0:04:45.630 that equals minus 4/15. 0:04:45.630,0:04:52.300 What is 3/2 divided by 1/6? 0:04:52.300,0:04:59.850 Well, that's just the same[br]thing as 3/2 times 6/1, 0:05:09.610,0:05:11.280 I think you might[br]be getting it now. 0:05:11.280,0:05:12.950 Let's see, let's[br]do a couple more. 0:05:12.950,0:05:16.290 And, of course, you can always[br]pause, and look at this whole 0:05:16.290,0:05:19.420 presentation again, so you can[br]get confused all over again. 0:05:19.420,0:05:27.240 Let's see, let's do minus[br]5/7 divided by 10/3. 0:05:27.240,0:05:33.880 Well, this is the same thing[br]as minus 5/7 times 3/10. 0:05:33.880,0:05:35.420 I just multiplied[br]by the inverse. 0:05:35.420,0:05:38.120 That's all I keep doing[br]over and over again. 0:05:38.120,0:05:40.180 Minus 5 times 3. 0:05:40.180,0:05:42.610 Minus 15. 0:05:42.610,0:05:47.350 7 times 10 is 70. 0:05:47.350,0:05:49.900 If we divide the numerator[br]and the denominator by 0:05:49.900,0:05:56.050 5, we get minus 3/14. 0:05:56.050,0:05:57.500 We could have also[br]just done it here. 0:05:57.500,0:05:59.890 We could have done 5, 2,[br]and we would have gotten 0:05:59.890,0:06:02.510 minus 3/14 as well. 0:06:02.510,0:06:05.420 Let's do one or two[br]more problems. 0:06:05.420,0:06:06.630 I think you kind of[br]get it, though. 0:06:06.630,0:06:09.600 Let's say 1/2[br]divided by minus 3. 0:06:14.500,0:06:14.965 Ah-ha! 0:06:14.965,0:06:17.940 So what happens when you take a[br]fraction and you divide it by 0:06:17.940,0:06:19.730 a whole number or an integer? 0:06:19.730,0:06:22.970 Well, we know any whole number[br]can be written as a fraction. 0:06:22.970,0:06:29.010 This is the same thing as[br]1/2 divided by minus 3/1. 0:06:29.010,0:06:33.870 And dividing by a fraction is[br]the same thing as multiplying 0:06:33.870,0:06:37.430 by it's inverse. 0:06:37.430,0:06:42.150 So the inverse of negative 3/1[br]is negative 1/3, and this 0:06:42.150,0:06:45.200 equals negative 1/6. 0:06:45.200,0:06:46.040 Let's do it the other way. 0:06:46.040,0:06:51.880 What if I had negative[br]3 divided by 1/2? 0:06:51.880,0:06:52.500 Same thing. 0:06:52.500,0:07:00.370 Negative 3 is the same thing as[br]minus 3/1 divided by 1/2, which 0:07:00.370,0:07:07.940 is the same thing as minus 3/1[br]times 2/1, which is equal to 0:07:07.940,0:07:12.010 minus 6/1, which[br]equals minus 6. 0:07:12.010,0:07:15.810 [br]Now, let me give you a[br]little bit of intuition 0:07:17.350,0:07:19.730 of why this works. 0:07:19.730,0:07:24.240 Let's say I said 2[br]divided by 1/3. 0:07:24.240,0:07:27.650 Well, we know that this[br]is equal to 2/1 times 0:07:27.650,0:07:30.120 3/1, which equals 6. 0:07:30.120,0:07:32.700 So how does 2, 1/3,[br]and 6 relate? 0:07:32.700,0:07:33.690 Well, let's look[br]at it this way. 0:07:33.690,0:07:36.930 If I had two pieces of pizza. 0:07:36.930,0:07:38.660 I have two pieces of pizza. 0:07:38.660,0:07:41.520 Here's my two pieces[br]of pizza right. 0:07:41.520,0:07:42.530 Two right here. 0:07:42.530,0:07:45.050 So I have two pieces of pizza,[br]and I'm going to divide 0:07:45.050,0:07:48.080 them into thirds. 0:07:48.080,0:07:50.600 So I'm going to divide[br]each pizza into a third. 0:07:50.600,0:07:52.860 I'll draw the little[br]Mercedes sign. 0:07:52.860,0:07:57.050 So I'm dividing each pizza[br]into a third, right? 0:07:57.050,0:07:58.210 How many pieces do I have? 0:07:58.210,0:08:02.925 Let's see, 1, 2, 3, 4, 5, 6. 0:08:02.925,0:08:04.800 I have 6 pieces. 0:08:04.800,0:08:08.140 So you might want to sit and[br]ponder that for a little bit, 0:08:08.140,0:08:12.850 but I think it might make a[br]little bit of sense to you. 0:08:12.850,0:08:17.190 Let's do one more just[br]to tire your brain. 0:08:17.190,0:08:25.750 If I had negative 7/2 divided[br]by 4/9-- let's pick a negative 0:08:25.750,0:08:30.580 4/9-- well, that's the same[br]thing as minus 7/2 times 0:08:30.580,0:08:33.720 minus 9/4, right? 0:08:33.720,0:08:37.950 I just multiplied by the[br]inverse of negative 4/9. 0:08:37.950,0:08:41.220 9 times 7 is equal to--[br]negative 7 times negative 0:08:41.220,0:08:47.800 9 is positive 63,[br]and 2 times 4 is 8. 0:08:47.800,0:08:51.460 Hopefully, I think you have a[br]good idea of how to divide by 0:08:51.460,0:08:55.960 a fraction now, and you can[br]try out the dividing 0:08:55.960,0:08:57.310 fractions modules. 0:08:57.310,0:08:58.890 Have fun!