WEBVTT 00:00:00.600 --> 00:00:05.570 So we're asked to add 3/15 plus 7/15, and then simplify 00:00:05.570 --> 00:00:06.590 the answer. 00:00:06.590 --> 00:00:09.810 So just the process when you add fractions is if they 00:00:09.810 --> 00:00:12.000 already-- well, first of all, if they're not mixed numbers, 00:00:12.000 --> 00:00:14.650 and neither of these are, and if they have the same 00:00:14.650 --> 00:00:15.280 denominator. 00:00:15.280 --> 00:00:17.190 In this example, the denominators 00:00:17.190 --> 00:00:18.370 are already the same. 00:00:18.370 --> 00:00:20.460 The denominator is 15. 00:00:20.460 --> 00:00:24.590 So if you add these two fractions, your sum is going 00:00:24.590 --> 00:00:28.860 to have the same denominator, 15, and your numerator is just 00:00:28.860 --> 00:00:30.910 going to be the sum of the numerator, so it's going to be 00:00:30.910 --> 00:00:37.490 3 plus 7, or it's going to be equal to 10/15. 00:00:37.490 --> 00:00:39.340 Now if we wanted to simplify this, we'd look for the 00:00:39.340 --> 00:00:43.080 greatest common factor in both the 10 and the 15, and as far 00:00:43.080 --> 00:00:45.680 as I can tell, 5 is the largest number that goes into 00:00:45.680 --> 00:00:46.480 both of them. 00:00:46.480 --> 00:00:53.640 So divide the 10 by 5 and you divide the 15 by 5, and you get-- 00:00:53.640 --> 00:00:59.020 10 divided by 5 is 2 and 15 divided by 5 is 3. 00:00:59.020 --> 00:01:00.900 You get 2/3. 00:01:00.900 --> 00:01:04.099 Now, to understand why this works, let's draw it out. 00:01:04.099 --> 00:01:08.865 Let's split something up to 15 sections. 00:01:08.865 --> 00:01:11.462 So let me split it up into 15 sections. 00:01:11.477 --> 00:01:13.670 Let me see how well I can do this. 00:01:13.670 --> 00:01:16.300 Well, actually, even a better way, an easier way might be to 00:01:16.300 --> 00:01:17.740 draw circles. 00:01:17.740 --> 00:01:20.070 So let me do the 15 sections. 00:01:20.070 --> 00:01:21.783 So let me draw. 00:01:22.260 --> 00:01:25.692 So that is one section right over there 00:01:25.800 --> 00:01:30.137 That is one section and then if I copy and paste it, 00:01:33.170 --> 00:01:39.710 that is a second section, and then a third section, fourth 00:01:39.710 --> 00:01:44.760 section, and then we have a fifth section. 00:01:44.760 --> 00:01:46.960 Let me copy and paste this whole thing. 00:01:46.960 --> 00:01:49.920 So that's five sections right there. 00:01:49.920 --> 00:01:53.300 Let me copy and then paste that. 00:01:53.300 --> 00:01:56.200 So that is 10 sections, and then let me 00:01:56.200 --> 00:01:57.080 do it one more time. 00:01:57.080 --> 00:01:58.570 So that is 15 sections. 00:01:58.570 --> 00:02:01.010 So you can imagine this whole thing is like a candy bar or 00:02:01.010 --> 00:02:04.950 something, and we have now split it up into 15 sections. 00:02:04.950 --> 00:02:07.870 Now, what is 3/15? 00:02:07.870 --> 00:02:10.419 Well, it's going to be 3 of the 15 sections. 00:02:10.419 --> 00:02:17.570 So 3/15 is going to be one, two, three: 3/15. 00:02:17.570 --> 00:02:20.880 Now, to that, were adding 7 of the 1/15 00:02:20.880 --> 00:02:23.490 sections, or 7 of the sections. 00:02:23.490 --> 00:02:26.260 So we're adding 7 of those to it. 00:02:26.260 --> 00:02:35.240 So that's one, two, three, four, five, six, seven. 00:02:35.240 --> 00:02:37.940 And you see now, if you take the orange and the blue, 00:02:37.940 --> 00:02:41.310 you get one, two, three, four, five, six, seven, eight, nine, 00:02:41.310 --> 00:02:45.800 ten of the sections, or 10 of the 15 sections. 00:02:45.800 --> 00:02:49.230 And then to see why this is the same thing as 2/3, you can 00:02:49.230 --> 00:02:53.220 just split this candy bar into third, so each third would 00:02:53.220 --> 00:02:54.760 have five sections in it. 00:02:54.760 --> 00:02:55.460 So, let's do that. 00:02:55.460 --> 00:02:59.300 One, two, three ,four, five, so that is 1/3 right there. 00:02:59.300 --> 00:03:01.590 One, two, three, four, five, that is 00:03:01.590 --> 00:03:03.360 another third right there. 00:03:03.360 --> 00:03:06.810 And notice, when you do it like this, we have filled out 00:03:06.810 --> 00:03:11.190 exactly two-- one, two-- of the thirds. 00:03:11.190 --> 00:03:13.780 This is the third third, but that's not filled in. 00:03:13.780 --> 00:03:16.210 This is the third third, but that's not filled in. So 10/15 is the same thing as 2/3.