1 00:00:00,373 --> 00:00:06,172 Let's add four elevenths to nine over thirteen 2 00:00:06,172 --> 00:00:09,916 In order to add these two fractions we need to find a common denominator 3 00:00:09,916 --> 00:00:14,384 And that common denominator used to be the least common multiple of eleven and thirteen 4 00:00:14,384 --> 00:00:17,617 And these two numbers don't share any common factors 5 00:00:17,617 --> 00:00:22,410 So their least common multiple is really just going to be the product of eleven and thirteen 6 00:00:22,410 --> 00:00:27,188 So we could say thirteen times eleven 7 00:00:27,188 --> 00:00:29,273 Thirteen times one is thirteen 8 00:00:29,273 --> 00:00:32,415 Thirteen times another one is thirteen 9 00:00:32,415 --> 00:00:35,394 Or you could say thirteen times ten is a hundred and thirty 10 00:00:35,394 --> 00:00:39,480 And we get: three, four, one - one hundred and forty-three 11 00:00:39,480 --> 00:00:41,540 So that's going to be our common denominator 12 00:00:41,540 --> 00:00:43,292 So I'll write it over here: 13 00:00:43,292 --> 00:00:45,523 Something over one hundred and forty-three plus 14 00:00:45,523 --> 00:00:48,756 Something else over one hundred and forty-three 15 00:00:48,756 --> 00:00:52,125 And to go from four elevenths to something over one forty-three 16 00:00:52,125 --> 00:00:55,438 We multiply the eleven times thirteen 17 00:00:55,438 --> 00:00:58,257 --Or we multiply the denominator times thirteen-- 18 00:00:58,257 --> 00:01:01,223 So we're going to have to multiply the numerator times thirteen as well 19 00:01:01,223 --> 00:01:04,938 And four times thirteen--let's see: four times ten is forty 20 00:01:04,938 --> 00:01:07,594 Four times three is twelve, so it gives us fifty-two 21 00:01:07,594 --> 00:01:10,106 And you can work that out by hand if you like 22 00:01:10,106 --> 00:01:12,291 Four times thirteen is fifty-two 23 00:01:12,291 --> 00:01:17,714 And then to go from thirteen to one forty-three we multiply by eleven 24 00:01:17,714 --> 00:01:20,104 So if we multiply the denominator by eleven 25 00:01:20,104 --> 00:01:22,018 (if we don't want to change the value of the fraction) 26 00:01:22,018 --> 00:01:24,722 We have to multiply the numerator by eleven 27 00:01:24,722 --> 00:01:27,331 Nine times eleven is ninety-nine 28 00:01:27,331 --> 00:01:33,925 And now we're ready to add: this is equal to--our common denominator is one hundred and forty-three 29 00:01:33,925 --> 00:01:35,591 And fifty-two plus ninety-nine 30 00:01:35,591 --> 00:01:37,959 --Fifty-two plus a hundred would be one hundred and fifty two 31 00:01:37,959 --> 00:01:39,739 And this is going to be one less than that 32 00:01:39,739 --> 00:01:43,073 So it's going to be one hundred and fifty-one 33 00:01:43,073 --> 00:01:45,739 And I think that's about as simplified as we can get 34 00:01:45,739 --> 00:01:51,714 As far as I know, it doesn't look like there are any common factors between one fifty-one and one forty-three 35 00:01:51,714 --> 00:01:54,732 So we just get one fifty-one over one forty-three 36 00:01:54,732 --> 00:01:56,585 --We can write this as a mixed number 37 00:01:56,585 --> 00:02:01,774 Because one forty-three goes into one fifty-one one time 38 00:02:01,774 --> 00:02:04,107 One times one forty-three is one forty-three 39 00:02:04,107 --> 00:02:07,678 When you subtract--let's see, this can become an eleven 40 00:02:07,678 --> 00:02:08,667 This is a four 41 00:02:08,667 --> 00:02:10,473 Eleven minus three is eight 42 00:02:10,473 --> 00:02:11,905 You have a remainder of eight 43 00:02:11,905 --> 00:02:21,260 So one fifty-one over one forty-three is the same thing as one and eight one forty-thirds 44 00:02:21,260 --> 00:02:25,294 And now it becomes even more clear that these can't be simplified anymore 45 00:02:25,294 --> 00:02:32,537 And we are done--this is the same thing as one and eight one forty-thirds