1 00:00:00,600 --> 00:00:05,570 So we're asked to add 3/15 plus 7/15, and then simplify 2 00:00:05,570 --> 00:00:06,590 the answer. 3 00:00:06,590 --> 00:00:09,810 So just the process when you add fractions is if they 4 00:00:09,810 --> 00:00:12,000 already-- well, first of all, if they're not mixed numbers, 5 00:00:12,000 --> 00:00:14,650 and neither of these are, and if they have the same 6 00:00:14,650 --> 00:00:15,280 denominator. 7 00:00:15,280 --> 00:00:17,190 In this example, the denominators 8 00:00:17,190 --> 00:00:18,370 are already the same. 9 00:00:18,370 --> 00:00:20,460 The denominator is 15. 10 00:00:20,460 --> 00:00:24,590 So if you add these two fractions, your sum is going 11 00:00:24,590 --> 00:00:28,860 to have the same denominator, 15, and your numerator is just 12 00:00:28,860 --> 00:00:30,910 going to be the sum of the numerator, so it's going to be 13 00:00:30,910 --> 00:00:37,490 3 plus 7, or it's going to be equal to 10/15. 14 00:00:37,490 --> 00:00:39,340 Now if we wanted to simplify this, we'd look for the 15 00:00:39,340 --> 00:00:43,080 greatest common factor in both the 10 and the 15, and as far 16 00:00:43,080 --> 00:00:45,680 as I can tell, 5 is the largest number that goes into 17 00:00:45,680 --> 00:00:46,480 both of them. 18 00:00:46,480 --> 00:00:53,640 So divide the 10 by 5 and you divide the 15 by 5, and you get-- 19 00:00:53,640 --> 00:00:59,020 10 divided by 5 is 2 and 15 divided by 5 is 3. 20 00:00:59,020 --> 00:01:00,900 You get 2/3. 21 00:01:00,900 --> 00:01:04,099 Now, to understand why this works, let's draw it out. 22 00:01:04,099 --> 00:01:08,865 Let's split something up to 15 sections. 23 00:01:08,865 --> 00:01:11,462 So let me split it up into 15 sections. 24 00:01:11,477 --> 00:01:13,670 Let me see how well I can do this. 25 00:01:13,670 --> 00:01:16,300 Well, actually, even a better way, an easier way might be to 26 00:01:16,300 --> 00:01:17,740 draw circles. 27 00:01:17,740 --> 00:01:20,070 So let me do the 15 sections. 28 00:01:20,070 --> 00:01:21,783 So let me draw. 29 00:01:22,260 --> 00:01:25,692 So that is one section right over there 30 00:01:25,800 --> 00:01:30,137 That is one section and then if I copy and paste it, 31 00:01:33,170 --> 00:01:39,710 that is a second section, and then a third section, fourth 32 00:01:39,710 --> 00:01:44,760 section, and then we have a fifth section. 33 00:01:44,760 --> 00:01:46,960 Let me copy and paste this whole thing. 34 00:01:46,960 --> 00:01:49,920 So that's five sections right there. 35 00:01:49,920 --> 00:01:53,300 Let me copy and then paste that. 36 00:01:53,300 --> 00:01:56,200 So that is 10 sections, and then let me 37 00:01:56,200 --> 00:01:57,080 do it one more time. 38 00:01:57,080 --> 00:01:58,570 So that is 15 sections. 39 00:01:58,570 --> 00:02:01,010 So you can imagine this whole thing is like a candy bar or 40 00:02:01,010 --> 00:02:04,950 something, and we have now split it up into 15 sections. 41 00:02:04,950 --> 00:02:07,870 Now, what is 3/15? 42 00:02:07,870 --> 00:02:10,419 Well, it's going to be 3 of the 15 sections. 43 00:02:10,419 --> 00:02:17,570 So 3/15 is going to be one, two, three: 3/15. 44 00:02:17,570 --> 00:02:20,880 Now, to that, were adding 7 of the 1/15 45 00:02:20,880 --> 00:02:23,490 sections, or 7 of the sections. 46 00:02:23,490 --> 00:02:26,260 So we're adding 7 of those to it. 47 00:02:26,260 --> 00:02:35,240 So that's one, two, three, four, five, six, seven. 48 00:02:35,240 --> 00:02:37,940 And you see now, if you take the orange and the blue, 49 00:02:37,940 --> 00:02:41,310 you get one, two, three, four, five, six, seven, eight, nine, 50 00:02:41,310 --> 00:02:45,800 ten of the sections, or 10 of the 15 sections. 51 00:02:45,800 --> 00:02:49,230 And then to see why this is the same thing as 2/3, you can 52 00:02:49,230 --> 00:02:53,220 just split this candy bar into third, so each third would 53 00:02:53,220 --> 00:02:54,760 have five sections in it. 54 00:02:54,760 --> 00:02:55,460 So, let's do that. 55 00:02:55,460 --> 00:02:59,300 One, two, three ,four, five, so that is 1/3 right there. 56 00:02:59,300 --> 00:03:01,590 One, two, three, four, five, that is 57 00:03:01,590 --> 00:03:03,360 another third right there. 58 00:03:03,360 --> 00:03:06,810 And notice, when you do it like this, we have filled out 59 00:03:06,810 --> 00:03:11,190 exactly two-- one, two-- of the thirds. 60 00:03:11,190 --> 00:03:13,780 This is the third third, but that's not filled in. 61 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.