WEBVTT 00:00:01.121 --> 00:00:05.038 Regina rode her bike 2 and 1/4 miles from her house to school 00:00:05.038 --> 00:00:08.604 and then 1 and 5/8 miles to her friend's house. 00:00:08.604 --> 00:00:11.454 How many miles did Regina ride in total? 00:00:11.454 --> 00:00:17.388 So she first rode 2 and 1/4 miles, and then she 00:00:17.388 --> 00:00:20.454 rode 1 and 5/8 miles. 00:00:20.454 --> 00:00:23.071 then she rode 1 and 5/8 miles 00:00:23.071 --> 00:00:27.772 So the sum is the total number of miles she rode. 00:00:27.772 --> 00:00:30.972 So to take this sum, we've seen that we can add the whole 00:00:30.972 --> 00:00:33.039 number parts, because this is really the same thing as 2 00:00:33.039 --> 00:00:37.554 plus 1/4 plus 1 plus 5/8, so we can just switch the order, 00:00:37.554 --> 00:00:39.154 if you want to view it that way. 00:00:39.154 --> 00:00:42.572 So we can add the 2 plus the 1 first, and then we get-- let 00:00:42.572 --> 00:00:43.489 me do that here. 00:00:43.489 --> 00:00:46.854 So 2 plus the 1, you get 3, and then we need to add the 00:00:46.854 --> 00:00:48.705 1/4 plus 5/8. 00:00:48.705 --> 00:00:57.189 And to add these two fractions, we have to find the 00:00:57.189 --> 00:00:59.972 least common multiple of 4 and 8. 00:00:59.972 --> 00:01:01.655 That'll be our new denominator. 00:01:01.655 --> 00:01:10.888 8 is divisible by both 8 and 4, so that is the least common 00:01:10.888 --> 00:01:19.038 multiple of 4 and 8, so our common denominator will be 8. 00:01:19.038 --> 00:01:21.372 Obviously, 5/8 will still be 5/8. 00:01:21.372 --> 00:01:24.154 Now to go from a denominator of 4 to 8, you have to 00:01:24.154 --> 00:01:26.572 multiply the denominator by 2, so we also need to multiply 00:01:26.572 --> 00:01:30.488 the numerator by 2, so 1 times 2 is 2. 00:01:30.488 --> 00:01:32.871 And, of course, we still have this 3 out there. 00:01:32.871 --> 00:01:36.788 So 2 and 1/4 plus 1 and 5/8 is the same thing as this right 00:01:36.788 --> 00:01:41.738 here, and this is equal to-- we have our 3 plus, and then 00:01:41.738 --> 00:01:50.221 over 8 we add the 2 plus 5. 00:01:50.221 --> 00:01:51.590 We have 7/8. 00:01:51.590 --> 00:01:55.188 So this is going to be equal to 3 and 7/8 miles. 00:01:55.188 --> 00:01:58.355 She rode a total of 3 and 7/8 miles. 00:01:58.355 --> 00:02:00.506 Now, I want to make one thing very clear. 00:02:00.506 --> 00:02:02.755 So far when we've been adding these mixed numbers, the 00:02:02.755 --> 00:02:05.604 fraction part always ended up as a proper fraction. 00:02:05.604 --> 00:02:07.739 The numerator was smaller than the denominator. 00:02:07.739 --> 00:02:09.655 But I want to do a quick example to show you what you 00:02:09.655 --> 00:02:13.221 do when the numerator is not smaller than the denominator. 00:02:13.221 --> 00:02:24.604 So let's say we had 1 and 5/8 plus 2 and 4/8. 00:02:24.604 --> 00:02:27.289 So if you add just the whole number parts, 1 00:02:27.289 --> 00:02:28.772 plus 2, you get 3. 00:02:28.772 --> 00:02:35.871 Plus 5/8 plus 4/8, 5/8 plus 4/8 is 9/8, so 00:02:35.871 --> 00:02:38.422 you get 3 plus 9/8. 00:02:38.422 --> 00:02:40.555 Now it would be really strange to just say, OK, that's the 00:02:40.555 --> 00:02:43.271 same thing as 3 and 9/8, because you have a mixed 00:02:43.271 --> 00:02:45.855 number with a whole number and an improper fraction. 00:02:45.855 --> 00:02:47.522 If you're going through the trouble of making it a mixed 00:02:47.522 --> 00:02:50.604 number, the fraction better be a proper fraction. 00:02:50.604 --> 00:02:53.239 So what you need to do is rewrite 9/8, and you know that 00:02:53.239 --> 00:02:59.521 9/8 is the same thing as 1 and 1/8, right? 00:02:59.521 --> 00:03:04.621 8 goes into 9 one time with 1 left over, so it's 1 and 1/8. 00:03:04.621 --> 00:03:08.639 So this is the same thing as 3 plus 1 and 1/8. 00:03:08.639 --> 00:03:10.439 So now we can add the whole number parts. 00:03:10.439 --> 00:03:14.422 3 plus 1 is equal to 4, and then you have your 1/8 over 00:03:14.422 --> 00:03:16.554 there: 4 and 1/8. 00:03:16.554 --> 00:03:18.805 I just wanted to give you that special circumstance when your 00:03:18.805 --> 99:59:59.999 fraction part ends up improper.