1 00:00:00,000 --> 00:00:00,780 2 00:00:00,780 --> 00:00:05,700 Welcome to the video on basic subtraction. 3 00:00:05,700 --> 00:00:10,339 Let's do a little bit a review of basic addition first. 4 00:00:10,339 --> 00:00:15,570 If I said 4 plus 3, what did this mean? 5 00:00:15,570 --> 00:00:19,050 6 00:00:19,050 --> 00:00:20,699 What did that equal? 7 00:00:20,699 --> 00:00:22,939 Well, there were a couple of ways we could have viewed this. 8 00:00:22,940 --> 00:00:24,640 We could have said I had 4 of something. 9 00:00:24,640 --> 00:00:28,100 Let's say I had 4 circles or I don't know, I had 10 00:00:28,100 --> 00:00:30,160 4 lemons for breakfast. 11 00:00:30,160 --> 00:00:36,179 So 1, 2, 3, 4 lemons for breakfast. 12 00:00:36,179 --> 00:00:40,759 And let's say, I had another 3 lemons for lunch. 13 00:00:40,759 --> 00:00:46,000 1, 2, 3, and so you could view 4 plus 3 as how many 14 00:00:46,000 --> 00:00:47,750 total lemons did I have? 15 00:00:47,750 --> 00:00:49,640 I'm adding 3 to 4. 16 00:00:49,640 --> 00:00:50,899 So how many total did I have? 17 00:00:50,899 --> 00:00:55,359 Well, it's 1, 2, 3, 4, 5, 6, 7. 18 00:00:55,359 --> 00:00:59,189 So I had a total of 7 lemons. 19 00:00:59,189 --> 00:01:01,439 Another way we could have viewed that is we could have 20 00:01:01,439 --> 00:01:04,060 drawn our number line. 21 00:01:04,060 --> 00:01:07,240 And I'll draw it in yellow because-- now that's 22 00:01:07,239 --> 00:01:09,719 not wide enough. 23 00:01:09,719 --> 00:01:13,709 I'll draw it in yellow because we're talking about lemons. 24 00:01:13,709 --> 00:01:15,354 So let's say that's our number line. 25 00:01:15,355 --> 00:01:18,070 26 00:01:18,069 --> 00:01:21,349 And if I start at the number-- let me draw all of the numbers. 27 00:01:21,349 --> 00:01:32,019 0, 1, 2, 3, 4, 5, 6, 7. 28 00:01:32,019 --> 00:01:34,469 So you could think about this as saying, well, 29 00:01:34,469 --> 00:01:35,379 we're on the number line. 30 00:01:35,379 --> 00:01:37,949 We start at the number 4. 31 00:01:37,950 --> 00:01:39,130 That's this number 4. 32 00:01:39,129 --> 00:01:40,699 And we're adding 3 to it. 33 00:01:40,700 --> 00:01:44,170 So we'll increase, along the number line by 3. 34 00:01:44,170 --> 00:01:48,650 So we'll go 1, 2, 3 and you end up at 7. 35 00:01:48,650 --> 00:01:51,920 So you could say if I have 4 and I get 3 more, I get 7. 36 00:01:51,920 --> 00:01:57,129 Or if I increase 4 by 3 I also get 7. 37 00:01:57,129 --> 00:01:59,349 So what's subtraction now? 38 00:01:59,349 --> 00:02:00,449 Because that's what this video is about. 39 00:02:00,450 --> 00:02:03,030 I shouldn't waste all of our time talking about addition. 40 00:02:03,030 --> 00:02:05,920 So let's take the example of 4 minus 3. 41 00:02:05,920 --> 00:02:08,500 What is that equal to? 42 00:02:08,500 --> 00:02:11,539 Let me switch colors just to keep things interesting. 43 00:02:11,539 --> 00:02:18,859 So what is 4 minus 3 equal to? 44 00:02:18,860 --> 00:02:23,050 Subtraction or minus is the opposite of addition. 45 00:02:23,050 --> 00:02:26,990 So in addition you're doing something more, you're adding. 46 00:02:26,990 --> 00:02:29,850 I don't want to use the word adding to define addition, but 47 00:02:29,849 --> 00:02:31,039 that's what you're doing. 48 00:02:31,039 --> 00:02:33,889 I had 4 lemons and then I had 3 more. 49 00:02:33,889 --> 00:02:36,279 In subtraction you're taking away. 50 00:02:36,280 --> 00:02:42,915 So this example, if I started with 4 lemons, let's say I 51 00:02:42,915 --> 00:02:45,210 had 4 lemons on a plate. 52 00:02:45,210 --> 00:02:50,070 If I'm subtracting 3, if I'm saying minus 3, instead of 53 00:02:50,069 --> 00:02:53,719 adding these 3 and getting 7, I'm going to take 3 away. 54 00:02:53,719 --> 00:02:55,909 So maybe I'm eating them or maybe I'm giving them 55 00:02:55,909 --> 00:02:59,759 to you in exchange for watching these videos. 56 00:02:59,759 --> 00:03:04,259 So to take away 3 from this 4, let's say this one goes away, 57 00:03:04,259 --> 00:03:06,909 this one goes away, and this one goes away. 58 00:03:06,909 --> 00:03:09,900 How many lemons would we have left? 59 00:03:09,900 --> 00:03:11,819 Well, this is the only one that I haven't crossed out. 60 00:03:11,819 --> 00:03:13,984 So we would have 1 lemon left. 61 00:03:13,985 --> 00:03:16,570 62 00:03:16,569 --> 00:03:18,120 And this would be the lemon that's left. 63 00:03:18,120 --> 00:03:19,439 Didn't have to be that one, I could have crossed 64 00:03:19,439 --> 00:03:21,210 out any of the 3. 65 00:03:21,210 --> 00:03:24,520 Another way to view that, let's draw the same lemon 66 00:03:24,520 --> 00:03:28,045 colored number line. 67 00:03:28,044 --> 00:03:30,809 Let's say that this is the number line right here. 68 00:03:30,810 --> 00:03:34,400 69 00:03:34,400 --> 00:03:36,180 And I'll draw all the same numbers. 70 00:03:36,180 --> 00:03:47,240 So that's 0, 1, 2, 3, 4, 5, 6, 7. 71 00:03:47,240 --> 00:03:49,530 Of course, the number line keeps going. 72 00:03:49,530 --> 00:03:51,145 There's no largest number. 73 00:03:51,145 --> 00:03:55,189 And you can imagine, any number that you can think of, I can 74 00:03:55,189 --> 00:03:56,579 think of one higher than that. 75 00:03:56,580 --> 00:03:57,670 So there is no largest number. 76 00:03:57,669 --> 00:03:59,039 So that's why we draw that arrow there. 77 00:03:59,039 --> 00:04:00,729 I could never draw the entire number line. 78 00:04:00,729 --> 00:04:03,019 But anyway, back to subtraction. 79 00:04:03,020 --> 00:04:06,710 So we're starting at 4 lemons, right? 80 00:04:06,710 --> 00:04:12,129 When we added 3-- plus 3-- we went to the right 4 spaces 81 00:04:12,129 --> 00:04:12,840 on the number line. 82 00:04:12,840 --> 00:04:15,090 And that's because the right is increasing value. 83 00:04:15,090 --> 00:04:16,269 So we went from 4 to 5. 84 00:04:16,269 --> 00:04:17,449 That was one more. 85 00:04:17,449 --> 00:04:20,990 5 to 6 was two more, and 7 was 3 more. 86 00:04:20,990 --> 00:04:23,509 Now we're taking away from 4. 87 00:04:23,509 --> 00:04:24,860 So what do we do? 88 00:04:24,860 --> 00:04:26,689 What would you think we do? 89 00:04:26,689 --> 00:04:29,579 Well, since we're taking away we're going to decrease the 90 00:04:29,579 --> 00:04:31,789 total number of lemons we have. 91 00:04:31,790 --> 00:04:33,680 So we take away one, we get to 3. 92 00:04:33,680 --> 00:04:35,550 Take away two, get to 2. 93 00:04:35,550 --> 00:04:38,910 Take away three, we took away three, right? 94 00:04:38,910 --> 00:04:41,980 So we'll go back 1, 2, 3 along the number line 95 00:04:41,980 --> 00:04:44,210 and we'll end up at 1. 96 00:04:44,209 --> 00:04:47,339 And that's this 1 right here. 97 00:04:47,339 --> 00:04:52,339 So just to review, addition is you're doing more or something. 98 00:04:52,339 --> 00:04:55,119 Subtraction is you are taking away. 99 00:04:55,120 --> 00:04:58,180 If you think about it on the number line, addition is 100 00:04:58,180 --> 00:05:00,740 increasing along the number line by that amount. 101 00:05:00,740 --> 00:05:04,199 So in this case we increased along the number line by 3. 102 00:05:04,199 --> 00:05:06,339 And so we went from 4 to 7. 103 00:05:06,339 --> 00:05:10,169 In the subtraction case we decrease back on 104 00:05:10,170 --> 00:05:11,350 the number line. 105 00:05:11,350 --> 00:05:13,550 So we decrease by the amount that you're subtracting. 106 00:05:13,550 --> 00:05:17,480 So in this case we decreased by 3. 107 00:05:17,480 --> 00:05:21,180 We went back 1, 2, 3 and we had 1. 108 00:05:21,180 --> 00:05:22,740 And the other way to view it, if I have 4 of something. 109 00:05:22,740 --> 00:05:26,579 If I give 3 away or if I ate 3 of them or I don't know 110 00:05:26,579 --> 00:05:27,680 what I did to 3 of them. 111 00:05:27,680 --> 00:05:31,050 If I lost 3 of them I would have 1 left. 112 00:05:31,050 --> 00:05:33,259 Now let me show you some interesting things 113 00:05:33,259 --> 00:05:34,839 about subtraction. 114 00:05:34,839 --> 00:05:38,509 So we know that 4 minus 3 is equal to 1. 115 00:05:38,509 --> 00:05:40,899 Let me show you something else that's interesting. 116 00:05:40,899 --> 00:05:46,049 What is 4 minus 1? 117 00:05:46,050 --> 00:05:49,509 Well, we could use either example. 118 00:05:49,509 --> 00:05:51,439 Let's do the lemon example. 119 00:05:51,439 --> 00:05:54,129 Let's do apples now; I'm bored of the lemons. 120 00:05:54,129 --> 00:06:01,159 Let's say I 1, 2, 3, 4. 121 00:06:01,160 --> 00:06:03,620 I have a new pen, sometimes it doesn't draw right. 122 00:06:03,620 --> 00:06:05,389 Let's say I had 4 apples. 123 00:06:05,389 --> 00:06:07,139 This is the example we're dealing with. 124 00:06:07,139 --> 00:06:09,449 And I were to eat one of them. 125 00:06:09,449 --> 00:06:10,829 So one of them were to go away. 126 00:06:10,829 --> 00:06:12,639 How many apples would I have left? 127 00:06:12,639 --> 00:06:15,560 Well, 3-- 1, 2, 3. 128 00:06:15,560 --> 00:06:18,600 So 4 minus 1 is equal to 3. 129 00:06:18,600 --> 00:06:21,640 And if we did it on the number line, if we started at 4 and we 130 00:06:21,639 --> 00:06:23,779 subtracted 1-- we took 1 away. 131 00:06:23,779 --> 00:06:26,019 So we're going to become one smaller. 132 00:06:26,019 --> 00:06:28,379 We go back one, we get 3. 133 00:06:28,379 --> 00:06:29,569 Either way works. 134 00:06:29,569 --> 00:06:30,819 But isn't this interesting? 135 00:06:30,819 --> 00:06:37,519 4 minus 3 is equal to 1 and 4 minus 1 is equal to 3. 136 00:06:37,519 --> 00:06:41,069 You might say, well, did I pick the numbers just so it worked? 137 00:06:41,069 --> 00:06:42,790 Well, it turns out that it's always true. 138 00:06:42,790 --> 00:06:45,360 139 00:06:45,360 --> 00:06:47,439 Well, I don't want to get too technical, but we're already 140 00:06:47,439 --> 00:06:50,860 touching on something that you'll learn later, maybe 141 00:06:50,860 --> 00:06:52,210 in algebra one day. 142 00:06:52,209 --> 00:06:54,839 But actually I don't want to go into all that right now. 143 00:06:54,839 --> 00:06:56,459 So where does this come from? 144 00:06:56,459 --> 00:07:02,169 Well, this is also based on the fact that 3 plus 1-- I 145 00:07:02,170 --> 00:07:03,660 didn't want to confuse you. 146 00:07:03,660 --> 00:07:05,700 So I apologize if I did. 147 00:07:05,699 --> 00:07:07,439 But I'll show you another interesting thing. 148 00:07:07,439 --> 00:07:10,610 What is 3 plus 1? 149 00:07:10,610 --> 00:07:12,710 3 plus 1 is equal to what? 150 00:07:12,709 --> 00:07:13,370 Well, that's easy. 151 00:07:13,370 --> 00:07:15,399 You know that from basic addition. 152 00:07:15,399 --> 00:07:20,719 You can start on the number line at 3 and add 1 do it. 153 00:07:20,720 --> 00:07:22,000 And where do you end up? 154 00:07:22,000 --> 00:07:23,310 You end up at 4. 155 00:07:23,310 --> 00:07:25,060 3 plus 1 is equal to 4. 156 00:07:25,060 --> 00:07:29,420 Or you could have started at 1 on the number line and added 3. 157 00:07:29,420 --> 00:07:33,160 1, 2, 3 and you would have also ended up at 4. 158 00:07:33,160 --> 00:07:36,689 So we also know that you could have switch this either way. 159 00:07:36,689 --> 00:07:38,879 Both of those are equal 4. 160 00:07:38,879 --> 00:07:40,139 What do you see here? 161 00:07:40,139 --> 00:07:42,629 Well, there's a bunch of things I've written here and they all 162 00:07:42,629 --> 00:07:43,930 kind of relate to each other. 163 00:07:43,930 --> 00:07:45,660 1 plus 3 is equal to 4. 164 00:07:45,660 --> 00:07:47,780 3 plus 1 is equal to 4. 165 00:07:47,779 --> 00:07:49,739 4 minus 1 is 3. 166 00:07:49,740 --> 00:07:53,920 Essentially, 4 minus 1 and getting 3 is the exact same-- 167 00:07:53,920 --> 00:07:59,199 you're saying the same thing as 3 plus 1 is equal to 4. 168 00:07:59,199 --> 00:08:03,170 This statement says if I add 1 to 3 I get 4. 169 00:08:03,170 --> 00:08:08,120 This is saying if I take away 1 from 4 I get 3. 170 00:08:08,120 --> 00:08:10,600 So if I start at 4, move back, I get 3. 171 00:08:10,600 --> 00:08:15,280 This is saying if I start at 3, and I move up 1, I get 4. 172 00:08:15,279 --> 00:08:17,599 Hopefully that gives you a little bit of intuition 173 00:08:17,600 --> 00:08:19,670 about what subtraction is. 174 00:08:19,670 --> 00:08:24,870 In the next video I'll just do as many basic subtraction 175 00:08:24,870 --> 00:08:27,800 problems I can do in 10 minutes. 176 00:08:27,800 --> 00:08:30,030 And then you'll be ready to do the exercises. 177 00:08:30,029 --> 00:08:31,531 See you soon.