1 00:00:00,000 --> 00:00:00,660 2 00:00:00,660 --> 00:00:03,520 We're asked to subtract, simplify the answer and write 3 00:00:03,520 --> 00:00:04,710 as a mixed number. 4 00:00:04,710 --> 00:00:07,169 So we have two mixed numbers here, and like when you're 5 00:00:07,169 --> 00:00:09,300 adding mixed numbers, you can do it two ways. 6 00:00:09,300 --> 00:00:12,370 You can either turn both of these into improper fractions 7 00:00:12,369 --> 00:00:16,480 and then subtract, or you can subtract the whole number part 8 00:00:16,480 --> 00:00:18,469 and then the fraction part, so let's do it that way. 9 00:00:18,469 --> 00:00:22,099 So just to remind ourselves, 5 and 5/8 is the exact same 10 00:00:22,100 --> 00:00:27,280 thing-- let me write it here in yellow-- as 5 plus 5/8. 11 00:00:27,280 --> 00:00:29,240 These are the exact same thing. 12 00:00:29,239 --> 00:00:32,640 And subtracting-- let me write this subtraction sign in 13 00:00:32,640 --> 00:00:36,230 blue-- and then we're subtracting 2 and 1/5, but 2 14 00:00:36,229 --> 00:00:41,390 and 1/5 is the exact same thing as 2 plus 1/5. 15 00:00:41,390 --> 00:00:43,710 That's what 2 and 1/5 really is. 16 00:00:43,710 --> 00:00:46,539 Now if we're subtracting, that means we have to subtract 2 17 00:00:46,539 --> 00:00:48,359 and we're subtracting the 1/5. 18 00:00:48,359 --> 00:00:49,409 Distributive property. 19 00:00:49,409 --> 00:00:51,329 We're subtracting both of them. 20 00:00:51,329 --> 00:00:57,689 So we get 5 plus 5/8, and then we distribute the negative 21 00:00:57,689 --> 00:01:04,009 sign, minus 2 minus 1/5. 22 00:01:04,010 --> 00:01:05,440 And now we can rearrange it. 23 00:01:05,439 --> 00:01:08,090 We can say this is the same thing as-- let me do it in 24 00:01:08,090 --> 00:01:15,270 orange-- as 5 minus 2, that's the whole number parts, and 25 00:01:15,269 --> 00:01:20,329 then you have plus 5/8 minus 1/5. 26 00:01:20,329 --> 00:01:22,829 27 00:01:22,829 --> 00:01:25,010 Now, 5 minus 2, that's pretty straightforward. 28 00:01:25,010 --> 00:01:26,120 That's just 3. 29 00:01:26,120 --> 00:01:28,820 But what's 5/8 minus 1/5? 30 00:01:28,819 --> 00:01:30,719 Let's do that over here. 31 00:01:30,719 --> 00:01:34,929 So we have 5/8 minus 1/5. 32 00:01:34,930 --> 00:01:37,700 Now, just like when you're adding fractions, when you're 33 00:01:37,700 --> 00:01:39,950 subtracting fractions, you have to have a common 34 00:01:39,950 --> 00:01:41,370 denominator. 35 00:01:41,370 --> 00:01:45,000 8 and 5 are not the same denominator so we have to find 36 00:01:45,000 --> 00:01:47,939 the least common multiple of these two numbers. 37 00:01:47,939 --> 00:01:51,849 If we do a prime factorization of 8, you get 2 times 4. 38 00:01:51,849 --> 00:01:53,750 4 is 2 times 2. 39 00:01:53,750 --> 00:01:55,620 So 8 is 2 times 2 times 2. 40 00:01:55,620 --> 00:01:58,390 That's if you break it down into its constituent primes. 41 00:01:58,390 --> 00:02:01,180 5 is just 5, because it is a prime number. 42 00:02:01,180 --> 00:02:06,180 So the least common multiple of 8 and 5 has to have a 5 and 43 00:02:06,180 --> 00:02:07,350 three 2's in it. 44 00:02:07,349 --> 00:02:10,379 Or another way of saying it, it has to be 5 times 2 times 2 45 00:02:10,379 --> 00:02:13,900 times 2, which is the same thing as 5 times 8. 46 00:02:13,900 --> 00:02:16,680 So the least common multiple is going to be-- because these 47 00:02:16,680 --> 00:02:19,900 guys share no common factors other than 1 really. 48 00:02:19,900 --> 00:02:22,849 The least common multiple is just going to be 8 times 5. 49 00:02:22,849 --> 00:02:26,789 So the least common multiple is going to be 40. 50 00:02:26,789 --> 00:02:28,969 It's going to be 40. 51 00:02:28,969 --> 00:02:34,509 Now, to go from 8 to 40, you have to multiply by 5. 52 00:02:34,509 --> 00:02:35,969 Then we have to do the same thing to the numerator. 53 00:02:35,969 --> 00:02:38,689 If we multiplied 8 times 5, we have to multiply 5 54 00:02:38,689 --> 00:02:41,789 times 5 to get 25. 55 00:02:41,789 --> 00:02:45,419 So in either case, we're multiplying times 5, the 56 00:02:45,419 --> 00:02:47,289 numerator and the denominator. 57 00:02:47,289 --> 00:02:50,840 Now, to go from 5 to 40, we have to multiply by 8, so we 58 00:02:50,840 --> 00:02:55,780 also have to do that for the numerator, so 1 times 8 is 8. 59 00:02:55,780 --> 00:03:00,710 So now we have 25/40 minus 40/40, which would be equal 60 00:03:00,710 --> 00:03:03,420 to-- we're going to have 40 as the denominator. 61 00:03:03,419 --> 00:03:08,859 25 minus 8 is 17. 62 00:03:08,860 --> 00:03:13,350 So 5/8 minus 1/5, which is the same thing as 25/40 minus 63 00:03:13,349 --> 00:03:16,259 8/40, is equal to 17/40. 64 00:03:16,259 --> 00:03:18,789 And 17 is a prime number so it's not going to share any 65 00:03:18,789 --> 00:03:24,400 common factors with 40, or at least 40 isn't divisible by 17 66 00:03:24,400 --> 00:03:27,140 either, so this is as simplified as we can get. 67 00:03:27,139 --> 00:03:31,589 So this part, the fraction part, is 3 and the fraction 68 00:03:31,590 --> 00:03:35,150 part is 17/40. 69 00:03:35,150 --> 00:03:35,960 And we're done. 70 00:03:35,960 --> 00:03:37,040 And this worked. 71 00:03:37,039 --> 00:03:39,250 We were able to separate this out and do it pretty 72 00:03:39,250 --> 00:03:42,379 straightforward, because in this situation, the fraction 73 00:03:42,379 --> 00:03:44,530 part that we're subtracting from the other fraction part 74 00:03:44,530 --> 00:03:45,349 was smaller. 75 00:03:45,349 --> 00:03:47,430 If it was larger, it would've gotten a little bit messy. 76 00:03:47,430 --> 00:03:49,460 Maybe we would have ended up with a negative number and we 77 00:03:49,460 --> 00:03:51,650 would've done all this other stuff, so that's why sometimes 78 00:03:51,650 --> 00:03:53,879 it's easier to go straight to an improper 79 00:03:53,879 --> 00:03:54,769 fraction for both of them. 80 00:03:54,770 --> 00:03:58,240 But in this case, it worked out doing it this way. 81 00:03:58,240 --> 00:03:58,534