1 00:00:00,555 --> 00:00:05,448 Find the sum 3 1/8 + 3/4 + ( -2 1/6) 2 00:00:05,448 --> 00:00:06,539 Let's just do the first part first, 3 00:00:06,539 --> 00:00:07,877 This is pretty straightforward. 4 00:00:07,877 --> 00:00:11,544 We have two positive numbers, let me draw a 5 00:00:11,544 --> 00:00:19,305 number line , we are going to start with 3 1/8, 6 00:00:19,305 --> 00:00:28,078 this is 0, then we have 1, 2, 3 and then you have 4. 7 00:00:28,078 --> 00:00:30,478 3 1/8 is going to be right about there 8 00:00:30,478 --> 00:00:32,910 so let me just draw its absolute value 9 00:00:32,910 --> 00:00:40,733 3 1/8, is going to be 3 1/8ths to the right of 0 10 00:00:40,733 --> 00:00:42,786 So it is going to be exactly that distance 11 00:00:42,786 --> 00:00:46,942 from 0 to the right. 12 00:00:46,942 --> 00:00:50,541 The length of this arrow, you could view it as 3 1/8th. 13 00:00:50,541 --> 00:00:52,541 Now, whenever I like to deal with fractions 14 00:00:52,541 --> 00:00:54,855 especially when I have different denominators 15 00:00:54,855 --> 00:00:57,405 i like to deal them with improper fractions, 16 00:00:57,405 --> 00:00:59,285 it makes the addition, and the subtraction, 17 00:00:59,285 --> 00:01:02,002 and actually the multiplication and divison a lot easier. 18 00:01:02,002 --> 00:01:04,284 So 3 1/8 is the same thing as 19 00:01:04,284 --> 00:01:09,127 8 times 3 is 24 plus one is 25 over 8. 20 00:01:11,148 --> 00:01:14,207 which is the same thing as 3 1/8. 21 00:01:14,207 --> 00:01:15,074 Another way to think about it, 22 00:01:15,074 --> 00:01:17,374 3 is 24 over 8, 23 00:01:17,374 --> 00:01:18,879 and then add 1/8 to that, 24 00:01:18,879 --> 00:01:20,385 so that you get 25/8. 25 00:01:20,385 --> 00:01:21,976 So this is our starting point. 26 00:01:21,976 --> 00:01:25,240 To that we are going to add 3/4, 27 00:01:27,312 --> 00:01:33,990 we are going to move another 3/4 28 00:01:37,538 --> 00:01:42,334 to the right, this length of this is 3/4 29 00:01:42,334 --> 00:01:44,041 So plus 3/4. 30 00:01:44,041 --> 00:01:45,356 Where does this put us, 31 00:01:45,356 --> 00:01:47,620 so both of these are positive intergers, 32 00:01:47,620 --> 00:01:48,666 so we can just add them, 33 00:01:48,666 --> 00:01:50,425 we just have to find the like denominators 34 00:01:50,425 --> 00:02:00,443 we have 25/8 + 3/4. That's the same thing as, 35 00:02:00,443 --> 00:02:01,679 we have to find the common denominator here, 36 00:02:01,679 --> 00:02:03,744 the common denominator, or the least common multiple 37 00:02:03,744 --> 00:02:07,412 of 4 and 8 is 8, so it's going to be something over 8. 38 00:02:07,412 --> 00:02:09,535 To get from 4 to 8, we multiplied by 2, 39 00:02:09,535 --> 00:02:11,543 so we have to multiply 3 by 2 as well. 40 00:02:11,543 --> 00:02:12,963 So we get 6, 41 00:02:12,963 --> 00:02:16,180 so 3/4 is the same thing as 6/8. 42 00:02:16,180 --> 00:02:19,232 So we have 25/8, and we're adding 6/8 to that, 43 00:02:19,232 --> 00:02:21,135 that gives us 25 plus 6 is 44 00:02:21,135 --> 00:02:23,956 31, over 8. 45 00:02:23,956 --> 00:02:30,934 So this number right over here is 31/8 46 00:02:33,071 --> 00:02:35,774 And it makes sense, because 32/8 will be 4, 47 00:02:35,774 --> 00:02:38,022 so it should be a litte bit less than 4 48 00:02:38,022 --> 00:02:43,565 So this number right over here is 31/8 49 00:02:43,565 --> 00:02:45,500 or the length of this arrow, 50 00:02:45,500 --> 00:02:46,428 the absolute value of that number 51 00:02:46,428 --> 00:02:48,517 is 31/8. 52 00:02:51,410 --> 00:02:55,232 If you want to write it as a mixed number, it would be 53 00:02:55,232 --> 00:03:00,100 3 7/8. 54 00:03:05,160 --> 00:03:10,829 Now to that we want to add a -2 1/6. 55 00:03:10,829 --> 00:03:13,008 So we're going to add a negative number. 56 00:03:13,008 --> 00:03:16,654 So think about what -2 1/6 is going to be like. 57 00:03:16,654 --> 00:03:19,672 Let me do this in a new color, do it in pink. 58 00:03:19,672 --> 00:03:22,980 -2 1/6. So we're gonna subtract, or, 59 00:03:22,980 --> 00:03:25,408 I guess we should say we are going to add a -1, 60 00:03:25,408 --> 00:03:29,273 add a -2, and then a -1/6. 61 00:03:29,273 --> 00:03:32,467 So -2 1/6, we can literally draw it like this. 62 00:03:36,860 --> 00:03:39,339 -2 1/6, we can draw it with an arrow 63 00:03:39,339 --> 00:03:41,130 that looks something like that, 64 00:03:41,130 --> 00:03:44,341 so this is -2 1/6. 65 00:03:44,341 --> 00:03:45,577 There are a couple of ways to think about it, 66 00:03:45,577 --> 00:03:46,378 we could just say, 67 00:03:46,378 --> 00:03:50,671 when you add this arrow, this thing is moving to the left. 68 00:03:50,671 --> 00:03:51,412 We could put it over here 69 00:03:51,412 --> 00:03:53,155 and you would get straight to -2 1/6. 70 00:03:53,155 --> 00:03:55,010 But we're adding this -2 1/6, 71 00:03:55,010 --> 00:03:59,319 it is same thing as subtracting a 2 1/6; 72 00:03:59,319 --> 00:04:01,213 we're moving 2 1/6 to the left. 73 00:04:01,213 --> 00:04:05,242 And we're going to end up with a number 74 00:04:05,242 --> 00:04:06,656 whose absolute value is going to 75 00:04:06,656 --> 00:04:08,700 look something like that. 76 00:04:08,700 --> 00:04:09,485 It is actually going to be to the right, 77 00:04:09,485 --> 00:04:11,206 so it's not only going to be its absolute value, 78 00:04:11,206 --> 00:04:14,226 the absolute value is going to be the number, 79 00:04:14,226 --> 00:04:16,478 since it's going to be a positive number. 80 00:04:16,478 --> 00:04:17,755 So let's just think about what it is. 81 00:04:17,755 --> 00:04:18,670 This value right here, 82 00:04:18,670 --> 00:04:20,475 which is going to be the answer to our problem, 83 00:04:20,475 --> 00:04:25,209 is going to be the difference of 31/8 and 2 1/6. 84 00:04:25,209 --> 00:04:26,821 And it's a positive difference, 85 00:04:26,821 --> 00:04:28,612 because we're dealing with a positive number. 86 00:04:28,612 --> 00:04:30,281 So we just take 31/8, and 87 00:04:30,281 --> 00:04:33,185 from that, we will subtract 2 1/6. 88 00:04:34,854 --> 00:04:37,548 So this orange value is going to be 31/8 89 00:04:39,929 --> 00:04:43,055 minus 2 1/6. 90 00:04:43,055 --> 00:04:45,743 So 2 1/6 is the same thing as 91 00:04:45,743 --> 00:04:50,160 6 times 2 is 12 plus 1 is 13. 92 00:04:51,577 --> 00:04:55,930 -13/6, and this is equal to -- 93 00:04:55,930 --> 00:04:55,883 once again we're going to get 94 00:04:55,883 --> 00:04:58,065 the common denominator over here - 95 00:04:58,065 --> 00:05:01,791 and it looks like 24 will be the common denominator. 96 00:05:05,367 --> 00:05:10,479 This is the 31/8, and this is the 2 1/6. 97 00:05:12,896 --> 00:05:16,684 So 31/8, over 24, you have to multiply by 3 98 00:05:16,684 --> 00:05:18,012 to get the 24 over here, 99 00:05:18,012 --> 00:05:20,333 so we multiply by 3 on the 31, 100 00:05:20,333 --> 00:05:22,865 that gives us 93. 101 00:05:22,865 --> 00:05:25,070 And then to go from 6 to 24, 102 00:05:25,070 --> 00:05:27,335 you have to multiply by 4, 103 00:05:27,335 --> 00:05:28,981 I'll do that in another color, 104 00:05:28,981 --> 00:05:35,135 so you have to multiply by 4 up here as well. 105 00:05:35,596 --> 00:05:37,997 So 4 times 13, let's see. 106 00:05:37,997 --> 00:05:42,336 4 times 10 is 40, 4 times 3 is 12, 107 00:05:42,336 --> 00:05:44,413 so that's 52. 108 00:05:44,413 --> 00:05:46,934 So this is going to be equal to 109 00:05:46,934 --> 00:05:51,610 93 minus 52 over 24, and that is, 110 00:05:55,221 --> 00:05:58,921 3 minus 2 is 1, 9 minus 5 is 4. 111 00:05:58,940 --> 00:06:04,821 So it is 41/24, positive. 112 00:06:04,821 --> 00:06:05,711 You can see that here, 113 00:06:05,711 --> 00:06:07,411 just by looking at the number line. 114 00:06:07,411 --> 00:06:12,068 This right here is 41/24, and it should be 115 00:06:12,068 --> 00:06:13,508 a little bit less than 2, 116 00:06:13,508 --> 00:06:17,004 because 2 would be 48/24. 117 00:06:17,004 --> 00:06:18,951 So this would be 48/24, and it makes sense 118 00:06:18,951 --> 00:06:20,978 because we're are a little bit less than that.