Adding and subtracting negative numbers
Adding/Subtracting negative numbers Adding and subtracting negative numbers
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- Welcome to the presentation
- on adding and subtracting negative numbers.
- So let's get started.
- So what is a negative number, first of all?
- Well, let me draw a number line.
- Well it's not much of a line,
- but I think you'll get the picture.
- So we're used to the positive numbers, so if that's 0
- you have one, you have 2, you have 3, you have 4
- and you keep going.
- And if I were to say what's 2+2
- you'd start at 2, and then you'd add 2
- you'd get to 4.
- I mean most of us it's second nature.
- But if you actually drew it on a number line,
- you'd say 2+2=4
- And if I asked you what's 2-1
- or let's say what's 3-2
- If you start at 3 and you subtracted 2
- you would end up at 1
- That's 2+2=4, and 3-2=1
- And this is a joke for you.
- Now what if I were to say what is 1-3?
- Huh.
- Well, it's the same thing.
- You start at 1 and we're going to go 1--
- well, now we're going to go below 0
- what happens below 0?
- Well then you start going to the negative numbers.
- -1, -2, -3, and so on.
- So if I start at 1 right here, so 1-3
- so I go 1,2,3, I end up at -2
- So 1-3=-2
- This is something that you're probably already doing
- in your everyday life
- If I were to tell you that
- boy, it's very cold today, it's one degree,
- but tomorrow it's going to be three degrees colder,
- you might already know intuitively,
- well then we're going to be
- at a temperature of negative two degrees.
- So that's all a negative number means.
- And just remember when a negative number is big,
- so like -50, that's actually colder than -20, right?
- So a -50 is actually even a smaller number than -20
- because it's even further to the left of -20
- That's just something you'll get an intuitive feel for.
- Sometimes when you start you feel like
- oh, 50 is a bigger number than 20
- but it's a -50 as opposed to a 50
- So let's do some problems,
- and I'm going to keep using the number line
- because I think it's useful
- So let's do the problem 5-12
- I think you already might have an intuition
- of what this equals.
- But let me draw a line, 5-12
- So let me start with -10, -9, -8--
- I think I'm going to run out of space-- -7, -6, -5
- I should have this pre-drawn -- -4, -3, -2, -1
- 0,1,2,3,4, and I'll put 5 right here.
- I'm gonna push this arrow out a little bit. Okay.
- 5-12
- So if we start at 5-- let me use a different color--
- we start at 5 right here and we're going to go to the left 12
- because we're subtracting 12
- So then we go 1,2,3...
- Negative 7
- That's pretty interesting.
- Because it also happens to be
- that 12 - 5 = +7
- So, I want you to think a little bit about why that is.
- Why the difference between 12 and 5 is 7,
- and the difference between
- -- well, I guess it's either way.
- In this situation we're also saying
- that the difference between 5 and 12 is -7,
- but the numbers are that far apart,
- but now we're starting with the lower number.
- I think that last sentence just completely confused you,
- but we'll keep moving forward.
- We just said 5-12=-7
- Let's do another one.
- What's -3+5?
- Well, let's use the same number line.
- Let's go to -3 plus 5
- So we're going to go to the right 5
- One, two, three, four, five.
- It's a two.
- It equals two.
- So -3 + 5 = 2
- That's interesting because 5 - 3 is also equal to 2
- Well, it turns out that 5 - 3 is the same thing,
- it's just another way of writing 5 plus -3
- or -3 plus 5
- A general, easy way to always do negative numbers
- is it's just like regular addition and subtraction,
- but now when we subtract
- we can go to the left below zero
- Let's do another one.
- So what happens when you get
- let's say, 2 minus -3?
- Well, if you think about how it should work out,
- I think this will make sense.
- But it turns out that the negative number,
- the negative signs actually cancel out.
- So this is the same thing as 2 plus +3
- and that just equals 5
- Another way you could say is-- let's do another one--
- what is -7 minus -2?
- Well that's the same thing as -7 + 2
- And remember, so we're doing to start at -7
- and we're going to move 2 to the right.
- So if we move 1 to the right we go to -6
- and then we move 2 to the right we get -5
- That makes sense because -7 + 2
- that's the same thing as 2 - 7
- If it's two degrees and
- it gets seven degrees colder, it's -5
- Let's do a bunch of these.
- I think the more you do, the more practice you have,
- and the modules explain it pretty well.
- Probably better than I do.
- So let's just do a ton of problems.
- So if I said -7 - 3
- Well, now we're going to go 3 to the left of -7
- We're going to get 3 less than -7
- so that's -10, right?
- That makes sense, because if we had 7 + 3
- we're at 7 to the right of 0
- and we're going to go 3 more to the right of 0
- and we get positive 10
- So for 7 to the left of 0 and go 3 more to the left,
- we're going to get -10
- Let's do a bunch more.
- I know I'm probably confusing you,
- but practice is what's going to really help us.
- So let's say 3 minus -3
- well, these negatives cancel out,
- so that just equals 6
- What's 3-3?
- Well, 3-3, that's easy.
- That's just 0
- What's -3 nimus 3?
- Well now we're going to get 3 less than -3
- well that's -6
- What's -3 minus -3
- Interesting.
- Well, the minuses cancel out, so you get -3 plus 3
- Well, if we start 3 to the left of 0 and we move 3 to the right,
- we end up at 0 again.
- So that makes sense, right?
- Let me do that again.
- -3 minus -3
- Anything minus itself should equal 0, right?
- That's why that equals 0
- And that's why it makes sense that
- those two negatives cancel out
- and that's the same thing as this.
- Let's do a bunch more.
- Let's do 12 - 13
- That's pretty easy.
- Well, 12 - 12 = 0, so12 - 13 = -1
- because we're going to go 1 the left of 0
- Let's do 8 - 5
- Well, this one is just a normal problem, that's 3
- What's 5 - 8?
- Well, we're going to go all the way to 0
- and then 3 more to the left of 0, so it's -3
- I could draw a number line here.
- If this is 0, this is 5
- and now we're going to go to left 8,
- then we end up at -3
- You could do that for all of these.
- That actually might be a good exercise.
- I think this will give you good introduction
- and I recommend that you just do the modules,
- because the modules actually
- especially if you do the hints
- it has a pretty nice graphic
- that's a lot nicer than
- anything I could draw on this chalkboard.
- So, try that out
- and I'm going to try to record some more modules
- that hopefully won't confuse you as badly.
- You could also attend the seminar
- on adding and subtracting negative numbers.
- I hope you have fun!
- Bye.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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