0:00:00.555,0:00:05.448 Find the sum 3 1/8 + 3/4 + ( -2 1/6) 0:00:05.448,0:00:06.539 Let's just do the first part first, 0:00:06.539,0:00:07.877 This is pretty straightforward. 0:00:07.877,0:00:11.544 We have two positive numbers, let me draw a 0:00:11.544,0:00:19.305 number line , we are going to start with 3 1/8, 0:00:19.305,0:00:28.078 this is 0, then we have 1, 2, 3 and then you have 4. 0:00:28.078,0:00:30.478 3 1/8 is going to be right about there 0:00:30.478,0:00:32.910 so let me just draw its absolute value 0:00:32.910,0:00:40.733 3 1/8, is going to be 3 1/8ths to the right of 0 0:00:40.733,0:00:42.786 So it is going to be exactly that distance 0:00:42.786,0:00:46.942 from 0 to the right. 0:00:46.942,0:00:50.541 The length of this arrow, you could view it as 3 1/8th. 0:00:50.541,0:00:52.541 Now, whenever I like to deal with fractions 0:00:52.541,0:00:54.855 especially when I have different denominators 0:00:54.855,0:00:57.405 i like to deal them with improper fractions, 0:00:57.405,0:00:59.285 it makes the addition, and the subtraction, 0:00:59.285,0:01:02.002 and actually the multiplication and divison a lot easier. 0:01:02.002,0:01:04.284 So 3 1/8 is the same thing as 0:01:04.284,0:01:09.127 8 times 3 is 24 plus one is 25 over 8. 0:01:11.148,0:01:14.207 which is the same thing as 3 1/8. 0:01:14.207,0:01:15.074 Another way to think about it, 0:01:15.074,0:01:17.374 3 is 24 over 8, 0:01:17.374,0:01:18.879 and then add 1/8 to that, 0:01:18.879,0:01:20.385 so that you get 25/8. 0:01:20.385,0:01:21.976 So this is our starting point. 0:01:21.976,0:01:25.240 To that we are going to add 3/4, 0:01:27.312,0:01:33.990 we are going to move another 3/4 0:01:37.538,0:01:42.334 to the right, this length of this is 3/4 0:01:42.334,0:01:44.041 So plus 3/4. 0:01:44.041,0:01:45.356 Where does this put us, 0:01:45.356,0:01:47.620 so both of these are positive intergers, 0:01:47.620,0:01:48.666 so we can just add them, 0:01:48.666,0:01:50.425 we just have to find the like denominators 0:01:50.425,0:02:00.443 we have 25/8 + 3/4. That's the same thing as, 0:02:00.443,0:02:01.679 we have to find the common denominator here, 0:02:01.679,0:02:03.744 the common denominator, or the least common multiple 0:02:03.744,0:02:07.412 of 4 and 8 is 8, so it's going to be something over 8. 0:02:07.412,0:02:09.535 To get from 4 to 8, we multiplied by 2, 0:02:09.535,0:02:11.543 so we have to multiply 3 by 2 as well. 0:02:11.543,0:02:12.963 So we get 6, 0:02:12.963,0:02:16.180 so 3/4 is the same thing as 6/8. 0:02:16.180,0:02:19.232 So we have 25/8, and we're adding 6/8 to that, 0:02:19.232,0:02:21.135 that gives us 25 plus 6 is 0:02:21.135,0:02:23.956 31, over 8. 0:02:23.956,0:02:30.934 So this number right over here is 31/8 0:02:33.071,0:02:35.774 And it makes sense, because 32/8 will be 4, 0:02:35.774,0:02:38.022 so it should be a litte bit less than 4 0:02:38.022,0:02:43.565 So this number right over here is 31/8 0:02:43.565,0:02:45.500 or the length of this arrow, 0:02:45.500,0:02:46.428 the absolute value of that number 0:02:46.428,0:02:48.517 is 31/8. 0:02:51.410,0:02:55.232 If you want to write it as a mixed number, it would be 0:02:55.232,0:03:00.100 3 7/8. 0:03:05.160,0:03:10.829 Now to that we want to add a -2 1/6. 0:03:10.829,0:03:13.008 So we're going to add a negative number. 0:03:13.008,0:03:16.654 So think about what -2 1/6 is going to be like. 0:03:16.654,0:03:19.672 Let me do this in a new color, do it in pink. 0:03:19.672,0:03:22.980 -2 1/6. So we're gonna subtract, or, 0:03:22.980,0:03:25.408 I guess we should say we are going to add a -1, 0:03:25.408,0:03:29.273 add a -2, and then a -1/6. 0:03:29.273,0:03:32.467 So -2 1/6, we can literally draw it like this. 0:03:36.860,0:03:39.339 -2 1/6, we can draw it with an arrow 0:03:39.339,0:03:41.130 that looks something like that, 0:03:41.130,0:03:44.341 so this is -2 1/6. 0:03:44.341,0:03:45.577 There are a couple of ways to think about it, 0:03:45.577,0:03:46.378 we could just say, 0:03:46.378,0:03:50.671 when you add this arrow, this thing is moving to the left. 0:03:50.671,0:03:51.412 We could put it over here 0:03:51.412,0:03:53.155 and you would get straight to -2 1/6. 0:03:53.155,0:03:55.010 But we're adding this -2 1/6, 0:03:55.010,0:03:59.319 it is same thing as subtracting a 2 1/6; 0:03:59.319,0:04:01.213 we're moving 2 1/6 to the left. 0:04:01.213,0:04:05.242 And we're going to end up with a number 0:04:05.242,0:04:06.656 whose absolute value is going to 0:04:06.656,0:04:08.700 look something like that. 0:04:08.700,0:04:09.485 It is actually going to be to the right, 0:04:09.485,0:04:11.206 so it's not only going to be its absolute value, 0:04:11.206,0:04:14.226 the absolute value is going to be the number, 0:04:14.226,0:04:16.478 since it's going to be a positive number. 0:04:16.478,0:04:17.755 So let's just think about what it is. 0:04:17.755,0:04:18.670 This value right here, 0:04:18.670,0:04:20.475 which is going to be the answer to our problem, 0:04:20.475,0:04:25.209 is going to be the difference of 31/8 and 2 1/6. 0:04:25.209,0:04:26.821 And it's a positive difference, 0:04:26.821,0:04:28.612 because we're dealing with a positive number. 0:04:28.612,0:04:30.281 So we just take 31/8, and 0:04:30.281,0:04:33.185 from that, we will subtract 2 1/6. 0:04:34.854,0:04:37.548 So this orange value is going to be 31/8 0:04:39.929,0:04:43.055 minus 2 1/6. 0:04:43.055,0:04:45.743 So 2 1/6 is the same thing as 0:04:45.743,0:04:50.160 6 times 2 is 12 plus 1 is 13. 0:04:51.577,0:04:55.930 -13/6, and this is equal to -- 0:04:55.930,0:04:55.883 once again we're going to get 0:04:55.883,0:04:58.065 the common denominator over here - 0:04:58.065,0:05:01.791 and it looks like 24 will be the common denominator. 0:05:05.367,0:05:10.479 This is the 31/8, and this is the 2 1/6. 0:05:12.896,0:05:16.684 So 31/8, over 24, you have to multiply by 3 0:05:16.684,0:05:18.012 to get the 24 over here, 0:05:18.012,0:05:20.333 so we multiply by 3 on the 31, 0:05:20.333,0:05:22.865 that gives us 93. 0:05:22.865,0:05:25.070 And then to go from 6 to 24, 0:05:25.070,0:05:27.335 you have to multiply by 4, 0:05:27.335,0:05:28.981 I'll do that in another color, 0:05:28.981,0:05:35.135 so you have to multiply by 4 up here as well. 0:05:35.596,0:05:37.997 So 4 times 13, let's see. 0:05:37.997,0:05:42.336 4 times 10 is 40, 4 times 3 is 12, 0:05:42.336,0:05:44.413 so that's 52. 0:05:44.413,0:05:46.934 So this is going to be equal to 0:05:46.934,0:05:51.610 93 minus 52 over 24, and that is, 0:05:55.221,0:05:58.921 3 minus 2 is 1, 9 minus 5 is 4. 0:05:58.940,0:06:04.821 So it is 41/24, positive. 0:06:04.821,0:06:05.711 You can see that here, 0:06:05.711,0:06:07.411 just by looking at the number line. 0:06:07.411,0:06:12.068 This right here is 41/24, and it should be 0:06:12.068,0:06:13.508 a little bit less than 2, 0:06:13.508,0:06:17.004 because 2 would be 48/24. 0:06:17.004,0:06:18.951 So this would be 48/24, and it makes sense 0:06:18.951,0:06:20.978 because we're are a little bit less than that.