1 00:00:00,500 --> 00:00:05,400 Let's try to evaluate seven and six-ninths minus three and two-fifths. So like 2 00:00:05,400 --> 00:00:09,349 always I like to separate out the whole number parts from the fractional parts. 3 00:00:09,349 --> 00:00:11,099 This is the same thing as 4 00:00:11,099 --> 00:00:12,419 seven 5 00:00:12,419 --> 00:00:17,039 plus six-ninths minus three 6 00:00:17,039 --> 00:00:18,040 minus 7 00:00:18,040 --> 00:00:19,289 two-fifth. 8 00:00:19,289 --> 00:00:22,180 And the reason why I'm saying minus three minus two-fifths 9 00:00:22,180 --> 00:00:26,740 as this is the same thing as minus three plus two-fifths. 10 00:00:26,740 --> 00:00:29,789 So you distribute the negative sign: subtracting at three and then you're 11 00:00:29,789 --> 00:00:32,020 subtracting the two-fifths. 12 00:00:32,020 --> 00:00:35,590 And so now we can worry about the whole number parts: seven 13 00:00:35,590 --> 00:00:37,369 minus three. 14 00:00:37,369 --> 00:00:41,320 Well, seven minus three is going to give us 15 00:00:41,320 --> 00:00:45,990 four. So that's going to give us four. And then we're going to have six-ninths 16 00:00:46,445 --> 00:00:46,900 minus 17 00:00:46,900 --> 00:00:48,280 two-fifths. 18 00:00:48,280 --> 00:00:51,340 So let me think about what six-ninths minus two-fifths are. 19 00:00:51,340 --> 00:00:56,000 Six-ninths minus two-fifths. Well we're gonna have to find a common denominator. So this is 20 00:00:56,000 --> 00:01:00,230 going to be the same thing and I think the least common multiple of nine and five is 21 00:01:00,230 --> 00:01:04,210 going to be forty-five. Literally them multiplied. They have no common 22 00:01:04,210 --> 00:01:05,200 factors. 23 00:01:05,200 --> 00:01:07,400 So it's going to be over forty five, 24 00:01:07,400 --> 00:01:11,200 till from nine to forty-five to multiply by five so I'm gonna have to multiply the numerator by 25 00:01:11,200 --> 00:01:11,990 five. 26 00:01:11,990 --> 00:01:14,460 So six times five is thirty. 27 00:01:14,460 --> 00:01:15,689 And I'm gonna subtract, 28 00:01:15,689 --> 00:01:18,689 to go from five to forty-five have to multiply by nine, 29 00:01:18,689 --> 00:01:21,490 so have to multiply the numerator right nine if I don't wanna change the values. 30 00:01:21,490 --> 00:01:23,480 So two times nine is 31 00:01:23,480 --> 00:01:24,540 eighteen. 32 00:01:24,540 --> 00:01:27,909 And thirty over thirty forty-fifth minus eighteen forty-fifths is going to be 33 00:01:27,909 --> 00:01:32,530 something over forty-five. Thirty minus eighteen is twelve. 34 00:01:32,530 --> 00:01:37,620 So this is - if I subtract these two fractions right over here - 35 00:01:37,620 --> 00:01:39,020 I get twelve, 36 00:01:39,020 --> 00:01:41,030 twelve forty-fifths. 37 00:01:41,030 --> 00:01:45,220 So it's four plus twelve forty-fifths, or if we want it to write it as a mixed number, 38 00:01:45,220 --> 00:01:48,260 this is equal to four and twelve 39 00:01:48,260 --> 00:01:49,240 fourty-fifths. 40 00:01:49,240 --> 00:01:53,400 But we're not done yet! We can simplify this further: twelve and forty-five have 41 00:01:53,400 --> 00:01:54,770 common factors. 42 00:01:54,770 --> 00:01:57,049 They're both divisible by, 43 00:01:57,049 --> 00:01:59,520 they're both divisible by three! 44 00:01:59,520 --> 00:02:01,680 So we can say that this is, 45 00:02:01,680 --> 00:02:05,460 actually they are both divisible by that while we continue to divide more after that. 46 00:02:05,460 --> 00:02:07,820 So let's see if we divide the numerator by three 47 00:02:07,820 --> 00:02:09,310 and the denominator 48 00:02:09,310 --> 00:02:10,829 by three. 49 00:02:10,829 --> 00:02:14,400 We end up with four and twelve divided by three 50 00:02:14,400 --> 00:02:15,909 is four. 51 00:02:15,909 --> 00:02:18,419 And forty-five divided by three, 52 00:02:18,419 --> 00:02:21,639 forty-five divided by three is fifteen. 53 00:02:21,639 --> 00:02:24,430 Four and four-fifteen, so actually we're done! 54 00:02:24,430 --> 00:02:27,129 These two can't be simplified anymore. 55 00:02:27,129 --> 00:02:29,029 Four and four-fifteenths.