1 00:00:00,000 --> 00:00:00,750 2 00:00:00,750 --> 00:00:04,290 Write 7/4 as a mixed number. 3 00:00:04,290 --> 00:00:06,209 So right now it's an improper fraction. 4 00:00:06,209 --> 00:00:07,580 7 is larger than 4. 5 00:00:07,580 --> 00:00:09,160 Let's write it is a mixed number. 6 00:00:09,160 --> 00:00:11,109 So first I'm just going to show you a fairly 7 00:00:11,109 --> 00:00:12,509 straightforward way of doing it and then we're going to 8 00:00:12,509 --> 00:00:15,830 think a little bit about what it actually means. 9 00:00:15,830 --> 00:00:20,210 So to figure out what 7/4 represents as a mixed number, 10 00:00:20,210 --> 00:00:22,560 let me write it in different colors. 11 00:00:22,559 --> 00:00:26,044 So this is going to be equal to-- the easiest way I do it 12 00:00:26,045 --> 00:00:29,540 is you say, well, you divide 4 it 7. 13 00:00:29,539 --> 00:00:36,280 14 00:00:36,280 --> 00:00:38,910 If we're dealing with fourths, 4 goes into 7 a 15 00:00:38,909 --> 00:00:40,239 total of one time. 16 00:00:40,240 --> 00:00:43,370 17 00:00:43,369 --> 00:00:44,619 Let me do this in another color. 18 00:00:44,619 --> 00:00:47,099 19 00:00:47,100 --> 00:00:50,219 1 times 4 is 4. 20 00:00:50,219 --> 00:00:52,600 And then what is our remainder? 21 00:00:52,600 --> 00:00:55,160 7 minus 4 is 3. 22 00:00:55,159 --> 00:00:57,679 So if we wanted to write this in plain-- well, let me just 23 00:00:57,679 --> 00:00:59,149 do the problem, and then we'll think about what 24 00:00:59,149 --> 00:01:00,460 it means in a second. 25 00:01:00,460 --> 00:01:05,019 So you see that 4 goes into 7 one time, so you have one 26 00:01:05,019 --> 00:01:10,200 whole here, and then how much do you have left over? 27 00:01:10,200 --> 00:01:15,810 Well, you have 3 left over, and that comes 28 00:01:15,810 --> 00:01:16,700 from right over there. 29 00:01:16,700 --> 00:01:19,630 That is the remainder when you divide 4 into 7. 30 00:01:19,629 --> 00:01:26,000 3 left over, but it's 3 of your 4, or 3/4 left over. 31 00:01:26,000 --> 00:01:28,879 So that's the way we just converted it from an improper 32 00:01:28,879 --> 00:01:30,199 fraction to a mixed number. 33 00:01:30,200 --> 00:01:31,650 Now, it might seem a little bit like 34 00:01:31,650 --> 00:01:33,190 voodoo what I just did. 35 00:01:33,189 --> 00:01:36,780 I divided 4 into 7, it goes one time, and then the 36 00:01:36,780 --> 00:01:40,530 remainder is 3, so I got 1 and 3/4. 37 00:01:40,530 --> 00:01:42,480 But why does that make sense? 38 00:01:42,480 --> 00:01:44,480 Why does that actually makes sense? 39 00:01:44,480 --> 00:01:46,230 So let's draw fourths. 40 00:01:46,230 --> 00:01:53,540 Let's draw literally 7 fourths and maybe it'll become clear. 41 00:01:53,540 --> 00:01:56,460 So let's do a little square as a fourth. 42 00:01:56,459 --> 00:02:03,750 So let's say I have a square like that, and that is 1/4. 43 00:02:03,750 --> 00:02:07,170 Now, let's think about what seven of those mean, so let me 44 00:02:07,170 --> 00:02:08,409 copy and paste that. 45 00:02:08,409 --> 00:02:11,500 Copy and then paste it. 46 00:02:11,500 --> 00:02:17,509 So here I have 2 one-fourths, or you could see I have 2/4. 47 00:02:17,509 --> 00:02:20,739 Now I have 3 one-fourths. 48 00:02:20,740 --> 00:02:22,950 Now, I have 4 one-fourths. 49 00:02:22,949 --> 00:02:24,429 Now this is a whole, right? 50 00:02:24,430 --> 00:02:25,800 I have 4 one-fourths. 51 00:02:25,800 --> 00:02:27,310 This is a whole. 52 00:02:27,310 --> 00:02:28,909 So let me start on another whole. 53 00:02:28,909 --> 00:02:31,500 So now I have 5. 54 00:02:31,500 --> 00:02:37,889 Now I have 6 one-fourths, and now I have 7 one-fourths. 55 00:02:37,889 --> 00:02:39,409 Now, what does this look like? 56 00:02:39,409 --> 00:02:43,490 So all I did is I rewrote 7/4, or 7 one-fourths. 57 00:02:43,490 --> 00:02:45,629 I just kind of drew it for you. 58 00:02:45,629 --> 00:02:47,349 Now, what does this represent? 59 00:02:47,349 --> 00:02:52,109 Well, I have 4 fourths here, so this is 4/4. 60 00:02:52,110 --> 00:02:55,750 This right here is 3/4. 61 00:02:55,750 --> 00:03:01,979 Notice, 7/4 is 4/4 with 3/4 left over. 62 00:03:01,979 --> 00:03:03,109 So let me write it this way. 63 00:03:03,110 --> 00:03:09,330 7/4 is 4/4 with 3/4 left over. 64 00:03:09,330 --> 00:03:10,580 Now what is 4/4? 65 00:03:10,580 --> 00:03:13,350 66 00:03:13,349 --> 00:03:16,319 4/4 is one whole. 67 00:03:16,319 --> 00:03:20,969 So you have one whole with 3/4 left over, so you end 68 00:03:20,969 --> 00:03:23,400 up with 1 and 3/4. 69 00:03:23,400 --> 00:03:27,469 So that is the 3/4 part and that is your one whole. 70 00:03:27,469 --> 00:03:29,590 Hopefully that makes sense and hopefully you understand why 71 00:03:29,590 --> 00:03:30,439 it connects. 72 00:03:30,439 --> 00:03:32,759 Because you say, well, how many wholes do you have? 73 00:03:32,759 --> 00:03:36,099 When you're dividing the 4 into the 7 and getting the 74 00:03:36,099 --> 00:03:38,549 one, you're essentially saying how many wholes? 75 00:03:38,550 --> 00:03:42,250 76 00:03:42,250 --> 00:03:47,069 So the number of wholes, or you can imagine, the number of 77 00:03:47,069 --> 00:03:48,189 whole pies. 78 00:03:48,189 --> 00:03:50,680 And then how many pieces do we have left over? 79 00:03:50,680 --> 00:03:53,770 Well, we have 3 pieces and each piece is 1/4, so we have 80 00:03:53,770 --> 00:03:55,430 3/4 left over. 81 00:03:55,430 --> 00:03:59,080 So we have one whole pie and three pieces, which are each a 82 00:03:59,080 --> 00:04:01,200 fourth left over.