0:00:00.600,0:00:05.570 So we're asked to add 3/15 plus 7/15, and then simplify 0:00:05.570,0:00:06.590 the answer. 0:00:06.590,0:00:09.810 So just the process when you add fractions is if they 0:00:09.810,0:00:12.000 already-- well, first of all, if they're not mixed numbers, 0:00:12.000,0:00:14.650 and neither of these are, and if they have the same 0:00:14.650,0:00:15.280 denominator. 0:00:15.280,0:00:17.190 In this example, the denominators 0:00:17.190,0:00:18.370 are already the same. 0:00:18.370,0:00:20.460 The denominator is 15. 0:00:20.460,0:00:24.590 So if you add these two fractions, your sum is going 0:00:24.590,0:00:28.860 to have the same denominator, 15, and your numerator is just 0:00:28.860,0:00:30.910 going to be the sum of the numerator, so it's going to be 0:00:30.910,0:00:37.490 3 plus 7, or it's going to be equal to 10/15. 0:00:37.490,0:00:39.340 Now if we wanted to simplify this, we'd look for the 0:00:39.340,0:00:43.080 greatest common factor in both the 10 and the 15, and as far[br] 0:00:43.080,0:00:45.680 as I can tell, 5 is the largest number that goes into 0:00:45.680,0:00:46.480 both of them. 0:00:46.480,0:00:53.640 So divide the 10 by 5 and you divide the 15 by 5, [br]and you get-- 0:00:53.640,0:00:59.020 10 divided by 5 is 2 and 15 divided by 5 is 3. 0:00:59.020,0:01:00.900 You get 2/3. 0:01:00.900,0:01:04.099 Now, to understand why this works, let's draw it out. 0:01:04.099,0:01:08.865 Let's split something up to 15 sections. 0:01:08.865,0:01:11.462 So let me split it up into 15 sections. 0:01:11.477,0:01:13.670 Let me see how well I can do this. 0:01:13.670,0:01:16.300 Well, actually, even a better way, an easier way might be to 0:01:16.300,0:01:17.740 draw circles. 0:01:17.740,0:01:20.070 So let me do the 15 sections. 0:01:20.070,0:01:21.783 So let me draw. 0:01:22.260,0:01:25.692 So that is one section right over there 0:01:25.800,0:01:30.137 That is one section and then if I copy and paste it, 0:01:33.170,0:01:39.710 that is a second section, and then a third section, fourth 0:01:39.710,0:01:44.760 section, and then we have a fifth section. 0:01:44.760,0:01:46.960 Let me copy and paste this whole thing. 0:01:46.960,0:01:49.920 So that's five sections right there. 0:01:49.920,0:01:53.300 Let me copy and then paste that. 0:01:53.300,0:01:56.200 So that is 10 sections, and then let me 0:01:56.200,0:01:57.080 do it one more time. 0:01:57.080,0:01:58.570 So that is 15 sections. 0:01:58.570,0:02:01.010 So you can imagine this whole thing is like a candy bar or 0:02:01.010,0:02:04.950 something, and we have now split it up into 15 sections. 0:02:04.950,0:02:07.870 Now, what is 3/15? 0:02:07.870,0:02:10.419 Well, it's going to be 3 of the 15 sections. 0:02:10.419,0:02:17.570 So 3/15 is going to be one, two, three: 3/15. 0:02:17.570,0:02:20.880 Now, to that, were adding 7 of the 1/15 0:02:20.880,0:02:23.490 sections, or 7 of the sections. 0:02:23.490,0:02:26.260 So we're adding 7 of those to it. 0:02:26.260,0:02:35.240 So that's one, two, three, four, five, six, seven. 0:02:35.240,0:02:37.940 And you see now, if you take the orange and the blue, 0:02:37.940,0:02:41.310 you get one, two, three, four, five, six, seven, eight, nine, 0:02:41.310,0:02:45.800 ten of the sections, or 10 of the 15 sections. 0:02:45.800,0:02:49.230 And then to see why this is the same thing as 2/3, you can[br] 0:02:49.230,0:02:53.220 just split this candy bar into third, so each third would 0:02:53.220,0:02:54.760 have five sections in it. 0:02:54.760,0:02:55.460 So, let's do that. 0:02:55.460,0:02:59.300 One, two, three ,four, five, so that is 1/3 right there. 0:02:59.300,0:03:01.590 One, two, three, four, five, that is 0:03:01.590,0:03:03.360 another third right there. 0:03:03.360,0:03:06.810 And notice, when you do it like this, we have filled out 0:03:06.810,0:03:11.190 exactly two-- one, two-- of the thirds. 0:03:11.190,0:03:13.780 This is the third third, but that's not filled in.[br] 0:03:13.780,0:03:16.210 This is the third third, but that's not filled in.[br]So 10/15 is the same thing as 2/3.[br]