1 00:00:00,000 --> 00:00:00,300 2 00:00:00,300 --> 00:00:01,570 Divide. 3 00:00:01,570 --> 00:00:07,440 Simplify the answer and write as a mixed number. 4 00:00:07,440 --> 00:00:11,720 So we have 4 divided by 2/3, and we've seen when you divide 5 00:00:11,720 --> 00:00:14,900 by the fraction, it's the same thing as multiplying by its 6 00:00:14,900 --> 00:00:15,940 reciprocal. 7 00:00:15,939 --> 00:00:21,259 So this is going to be the same thing as 4 times the 8 00:00:21,260 --> 00:00:25,840 reciprocal of 2/3, which is 3/2, just swapping the bottom 9 00:00:25,839 --> 00:00:29,050 and the top number, the denominator and the numerator. 10 00:00:29,050 --> 00:00:32,219 Now, 4, we've seen this before, where we're saying, 11 00:00:32,219 --> 00:00:34,329 OK, well, we know how to multiply fractions. 12 00:00:34,329 --> 00:00:36,659 You multiply the numerators times each other and the 13 00:00:36,659 --> 00:00:38,169 denominators times each other, but 4 14 00:00:38,170 --> 00:00:39,410 doesn't look like a fraction. 15 00:00:39,409 --> 00:00:41,879 Well, you always have to remember: a whole number can 16 00:00:41,880 --> 00:00:44,650 be written as that same whole number over one. 17 00:00:44,649 --> 00:00:47,609 4 is the same thing as 4/1. 18 00:00:47,609 --> 00:00:51,740 And now this becomes kind of a plain vanilla multiplying 19 00:00:51,740 --> 00:00:53,140 fractions problem. 20 00:00:53,140 --> 00:00:54,710 And so we can just multiply it out. 21 00:00:54,710 --> 00:00:57,899 We could just say this is 4 times 3, which would be 12 22 00:00:57,899 --> 00:01:01,039 over 1 times 2, which would be 2. 23 00:01:01,039 --> 00:01:03,390 Or we could divide right now. 24 00:01:03,390 --> 00:01:05,189 Well, let's do it both ways, actually. 25 00:01:05,189 --> 00:01:07,319 So we could say this is 4 times 3 in the numerator, 26 00:01:07,319 --> 00:01:11,799 which is 12, over 1 times 2 in the denominator, which is 2. 27 00:01:11,799 --> 00:01:14,149 Now, what is 12 divided by 2? 28 00:01:14,150 --> 00:01:17,780 12/2 is the same thing as 12 divided by 2. 29 00:01:17,780 --> 00:01:21,310 Well, this is equal to 6. 30 00:01:21,310 --> 00:01:24,740 Or another way we could think about it is divide the 31 00:01:24,739 --> 00:01:26,229 numerator by 2. 32 00:01:26,230 --> 00:01:27,420 Well, that would give you 6. 33 00:01:27,420 --> 00:01:29,310 And divide the denominator by 2. 34 00:01:29,310 --> 00:01:30,340 That'll give you 1. 35 00:01:30,340 --> 00:01:33,900 6/1, which is the same thing as 6. 36 00:01:33,900 --> 00:01:35,719 Now, the other thing we could've done at this stage 37 00:01:35,719 --> 00:01:37,870 right here is say, well, look, we have things in the 38 00:01:37,870 --> 00:01:40,570 numerator divisible by 2, we have things in the denominator 39 00:01:40,569 --> 00:01:43,479 divisible by 2, so let's divide both by 2. 40 00:01:43,480 --> 00:01:45,960 So 4 divided by 2 is 2. 41 00:01:45,959 --> 00:01:47,769 2 divided by 2 is 1. 42 00:01:47,769 --> 00:01:53,929 So it becomes 2 times 3, which is 6, over 1 times 1 over 1, 43 00:01:53,930 --> 00:01:56,220 or this is equal to 6. 44 00:01:56,219 --> 00:01:58,519 Now, this could be a fun one to visualize so let's think 45 00:01:58,519 --> 00:01:59,489 about what this is. 46 00:01:59,489 --> 00:02:01,780 4 divided by 2/3. 47 00:02:01,780 --> 00:02:05,269 Let's draw four boxes here. 48 00:02:05,269 --> 00:02:05,890 Let me do this. 49 00:02:05,890 --> 00:02:10,979 So let's say I have one, two-- let me separate 50 00:02:10,979 --> 00:02:11,460 them a little bit. 51 00:02:11,460 --> 00:02:17,090 One, two, three, and four. 52 00:02:17,090 --> 00:02:20,120 And you can view 4 divided by 2/3 as let's divide these four 53 00:02:20,120 --> 00:02:23,569 boxes into groups of 2/3 of a box and figure out how many 54 00:02:23,569 --> 00:02:24,909 groups do we have. 55 00:02:24,909 --> 00:02:26,389 So where are our groups? 56 00:02:26,389 --> 00:02:29,799 So let's see the first group is going to have 2/3 of a box 57 00:02:29,800 --> 00:02:32,320 in it, so the first group is going to look like this. 58 00:02:32,319 --> 00:02:35,139 It's going to have 2/3 of a box. 59 00:02:35,139 --> 00:02:37,669 Now, the next group is going to have 2/3 of a box, so it'll 60 00:02:37,669 --> 00:02:40,559 have 1/3 from here and then it'll have 1/3 61 00:02:40,560 --> 00:02:42,090 from the next box. 62 00:02:42,090 --> 00:02:44,159 The next group is going to have 2/3 of the box. 63 00:02:44,159 --> 00:02:46,770 There's 2/3 left right over here. 64 00:02:46,770 --> 00:02:50,520 Then the group after that will have another 2/3 of a box. 65 00:02:50,520 --> 00:02:52,870 That is that right over there. 66 00:02:52,870 --> 00:02:55,450 Then the next will have 1/3 from here and 1/3 from here, 67 00:02:55,449 --> 00:02:58,509 so it'll have 1/3 from here and 1/3 from here. 68 00:02:58,509 --> 00:02:59,629 That'll be 2/3. 69 00:02:59,629 --> 00:03:02,169 And then the last group will have 2/3, the leftover on this 70 00:03:02,169 --> 00:03:03,500 box right here. 71 00:03:03,500 --> 00:03:06,150 Now, how many groups of 2/3 do we have? 72 00:03:06,150 --> 00:03:13,189 We have one, two, three, four, five, six, so we have six. 73 00:03:13,189 --> 00:03:16,189 Four can be divided into six groups of 2/3. 74 00:03:16,189 --> 00:03:18,289 So it's just like regular division, sometimes a little 75 00:03:18,289 --> 00:03:20,969 harder to visualize because we're dealing with fractions. 76 00:03:20,969 --> 00:03:21,598