1 00:00:00,000 --> 00:00:00,610 2 00:00:00,610 --> 00:00:04,480 Simplify 48/64 to lowest terms. 3 00:00:04,480 --> 00:00:06,440 Let's see if we can visualize this. 4 00:00:06,440 --> 00:00:08,179 So we have 64. 5 00:00:08,179 --> 00:00:12,199 I guess 64 would be a whole, so let's draw a whole here. 6 00:00:12,199 --> 00:00:13,399 So let's say that's a whole. 7 00:00:13,400 --> 00:00:16,019 Maybe we're talking about a candy bar. 8 00:00:16,019 --> 00:00:17,910 Let me draw the whole. 9 00:00:17,910 --> 00:00:20,230 We're talking about a whole candy bar. 10 00:00:20,230 --> 00:00:21,789 That would be 64 fourths. 11 00:00:21,789 --> 00:00:24,230 It would be the whole candy bar right there. 12 00:00:24,230 --> 00:00:28,359 And 48 of the 64, you could imagine splitting this up into 13 00:00:28,359 --> 00:00:29,929 64 super-small pieces. 14 00:00:29,929 --> 00:00:33,179 You wouldn't be able to see what I drew here, but if we 15 00:00:33,179 --> 00:00:41,090 had 48 of them, it would get us about that much of them, so 16 00:00:41,090 --> 00:00:47,960 that would be the 48 out of the 64. 17 00:00:47,960 --> 00:00:50,370 So this whole blue area is 64. 18 00:00:50,369 --> 00:00:53,549 The 48 is this purple area right over here. 19 00:00:53,549 --> 00:00:54,359 So let me write it over here. 20 00:00:54,359 --> 00:01:00,700 48/64, and we want to write it in lowest terms, and we'll 21 00:01:00,700 --> 00:01:04,109 talk more about what lowest terms even means. 22 00:01:04,109 --> 00:01:08,819 Now, is there a way to group these 48 or these 64 into 23 00:01:08,819 --> 00:01:10,889 groups of numbers that will maybe simplify 24 00:01:10,890 --> 00:01:11,890 them a little bit? 25 00:01:11,890 --> 00:01:14,739 And to think about that, you'd have to think about what is 26 00:01:14,739 --> 00:01:20,099 the largest factor that is common to both 48 and 64? 27 00:01:20,099 --> 00:01:21,549 Or you can think of it as what is their 28 00:01:21,549 --> 00:01:24,230 greatest common divisor? 29 00:01:24,230 --> 00:01:26,640 Well, the largest number that I can think of that goes into 30 00:01:26,640 --> 00:01:30,650 48-- you could do it either by just thinking about it or you 31 00:01:30,650 --> 00:01:32,200 could actually write out all of its factors. 32 00:01:32,200 --> 00:01:34,310 But if you were to write all the factors for 48 and all the 33 00:01:34,310 --> 00:01:37,629 factors for 64, the one that pops out at me as the largest 34 00:01:37,629 --> 00:01:39,929 that goes into both is 16. 35 00:01:39,930 --> 00:01:43,860 So you could say that 48 is equal to-- well, what is it? 36 00:01:43,859 --> 00:01:53,769 It's 3 times 16, and 64 is 4 times 16. 37 00:01:53,769 --> 00:01:55,079 Now this is interesting. 38 00:01:55,079 --> 00:01:59,134 So this 48 that we drew in magenta right here, we could 39 00:01:59,135 --> 00:02:01,500 view this as three groups of 16. 40 00:02:01,500 --> 00:02:05,189 So that's one, two-- let me make them a 41 00:02:05,189 --> 00:02:06,209 little bit more even. 42 00:02:06,209 --> 00:02:12,729 So one, two, three groups of 16, so that's 16, that's 16, 43 00:02:12,729 --> 00:02:14,139 and that is 16. 44 00:02:14,139 --> 00:02:15,169 That would be 48. 45 00:02:15,169 --> 00:02:17,829 I could draw 16 bars here so that we have 16 pieces, but 46 00:02:17,830 --> 00:02:21,040 that's a group of 16, a group of 16 and a group of 16. 47 00:02:21,039 --> 00:02:22,789 That's what 48 is. 48 00:02:22,789 --> 00:02:25,959 Now, 64 is four groups of 16. 49 00:02:25,960 --> 00:02:30,050 So we could make, if you look at the 64, that is a 16, that 50 00:02:30,050 --> 00:02:34,750 is a 16, that is a 16, and then that is another 16. 51 00:02:34,750 --> 00:02:36,585 These should all be the same length. 52 00:02:36,585 --> 00:02:38,300 I drew it a little bit off. 53 00:02:38,300 --> 00:02:42,750 So what is 48/64 in lowest terms? 54 00:02:42,750 --> 00:02:45,590 We want to write this in as simple as possible fraction. 55 00:02:45,590 --> 00:02:49,390 Well, if we make each of the pieces equal to 16 of our old 56 00:02:49,389 --> 00:02:55,449 pieces, if we make this into one piece, if we turn 16 into 57 00:02:55,449 --> 00:02:59,789 one, then we are talking about instead of 48/64, we're 58 00:02:59,789 --> 00:03:03,310 talking about three. 59 00:03:03,310 --> 00:03:07,920 So this is one piece, two pieces, three pieces of a 60 00:03:07,919 --> 00:03:09,319 total of four. 61 00:03:09,319 --> 00:03:13,840 So this is going to be equal to 3/4. 62 00:03:13,840 --> 00:03:16,819 And hopefully, you see kind of a mathematical way of 63 00:03:16,819 --> 00:03:17,889 immediately thinking about it. 64 00:03:17,889 --> 00:03:20,709 If you can factor this out and you can actually factor out 65 00:03:20,710 --> 00:03:26,510 its greatest common factor, so 48 is 3 times 16, 64 is 4 66 00:03:26,509 --> 00:03:29,929 times 16, and then these cancel each other out. 67 00:03:29,930 --> 00:03:42,430 view This is equivalent to 3/4 times 16/16. 68 00:03:42,430 --> 00:03:43,810 This is the same thing as that. 69 00:03:43,810 --> 00:03:49,289 And 16/16 is 1, and you're just left with 3/4. 70 00:03:49,289 --> 00:03:52,519 Now, if you didn't immediately recognize that 16 goes into 71 00:03:52,520 --> 00:03:57,300 both 48 and 64, you could do it step by step. 72 00:03:57,300 --> 00:04:02,439 So let's say we started off with 48/64. 73 00:04:02,439 --> 00:04:04,680 Now, the key thing to remember with any fraction, whatever 74 00:04:04,680 --> 00:04:07,780 you do to the numerator, you have to do to the denominator. 75 00:04:07,780 --> 00:04:17,588 So let's say we divide the numerator by 2, we also have 76 00:04:17,588 --> 00:04:21,469 to divide the denominator by 2, so we could get 2. 77 00:04:21,470 --> 00:04:23,010 We know that these are both divisible by 2. 78 00:04:23,009 --> 00:04:23,800 They're both even. 79 00:04:23,800 --> 00:04:28,160 So that would get us to 24/32. 80 00:04:28,160 --> 00:04:30,780 And we'll say, well, look, these two numbers, those are 81 00:04:30,779 --> 00:04:32,019 both divisible by 2. 82 00:04:32,019 --> 00:04:33,240 Well, see if we can think of a larger number. 83 00:04:33,240 --> 00:04:35,829 Well, actually, they're both divisible by 4, so maybe you 84 00:04:35,829 --> 00:04:38,180 don't realize that they're also both divisible by 8. 85 00:04:38,180 --> 00:04:39,769 So let's say you did it with 4. 86 00:04:39,769 --> 00:04:42,799 So now we divide the top by 4. 87 00:04:42,800 --> 00:04:44,579 So we're going to divide by 4. 88 00:04:44,579 --> 00:04:45,680 We get 6. 89 00:04:45,680 --> 00:04:47,879 You have to do the same to the bottom, to the denominator. 90 00:04:47,879 --> 00:04:50,519 Divide by 4, you get 8. 91 00:04:50,519 --> 00:04:53,879 So 48/64 is the same thing as 24/32, which is the 92 00:04:53,879 --> 00:04:55,560 same thing as 6/8. 93 00:04:55,560 --> 00:04:59,139 And these are both divisible by 2, so if you divide the 94 00:04:59,139 --> 00:05:01,169 numerator by 2, you get 3. 95 00:05:01,170 --> 00:05:04,860 You divide that the denominator by 2, you get 4. 96 00:05:04,860 --> 00:05:08,030 And so this is the simplest possible terms, because 3 and 97 00:05:08,029 --> 00:05:13,399 4 share no common factors greater than 1, so we're in 98 00:05:13,399 --> 00:05:14,919 lowest possible terms. 99 00:05:14,920 --> 00:05:15,800 So however you want to do it. 100 00:05:15,800 --> 00:05:18,520 The easiest way or the fastest way is to say, hey, 16 is the 101 00:05:18,519 --> 00:05:20,289 biggest number that goes into both of these. 102 00:05:20,290 --> 00:05:22,120 Divide both by 16. 103 00:05:22,120 --> 00:05:23,399 You get 3/4. 104 00:05:23,399 --> 00:05:25,659 And really when you're dividing the numerator and 105 00:05:25,660 --> 00:05:29,770 denominator by 16, you're turning groups of 16 into one 106 00:05:29,769 --> 00:05:33,459 piece or 16 super-small pieces of the pie into one bigger 107 00:05:33,459 --> 00:05:34,479 piece of the pie. 108 00:05:34,480 --> 00:05:37,310 So this goes from 64 pieces to 4 pieces. 109 00:05:37,310 --> 00:05:40,629 This goes from 48 pieces to 3 pieces. 110 00:05:40,629 --> 00:05:41,134