Two digit addition and subtraction
Addition 2 Adding 2-digit numbers
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- In the last video
- we got some practice
- adding what we could consider smaller numbers.
- For example, if we added 3 + 2
- we could imagine that if
- maybe I had three lemons -- 1, 2, 3 --
- and if I were to add to those three lemons
- maybe two lime-- Is it lime or limes?
- Let's just -- Well, two green lemons --
- or two more tart pieces of fruit
- How many-- how much tart, sour fruit do I have now?
- Well, we learned in the last video
- we have 1, 2, 3, 4, 5 pieces of fruit.
- So 3 + 2 = 5.
- And we also saw that
- that's the exact same thing as if
- we add 2 + 3.
- And I think that makes sense.
- Because this is the same thing as
- starting with -- Maybe you have 2 lemons
- and you add 3 limes to it.
- You're still going to end up with 5 pieces of fruit.
- 1, 2, 3, 4, 5.
- Just like that.
- So it doesn't matter what order you add in.
- You're still going to get five.
- And this way of thinking about addition
- I view as the counting way of thinking about addition
- The other thing we saw in the last video
- is the number line version
- And they're essentially the same thing
- So we could draw a line.
- And all a number line is
- it lists all of the numbers in order.
- It lists all of the numbers.
- And you can actually go as high as you need to go
- You could go up to a million, gazillion, trillion.
- We won't do that.
- I wouldn't have space or time in this video to do it.
- And you actually can go as low as possible.
- We'll start at 0, assuming --
- In future videos, I'll tell you
- about numbers smaller than 0.
- Maybe you can think about what that might mean tonight.
- But let's start at 0, and 0 means nothing.
- If I have 0 lemons, it means I have no lemons.
- So: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 --
- Let's go pretty high.
- 12 --
- That way I can reuse the number line.
- 13, 14.
- I could keep on going
- But maybe 14 will be enough for this video
- But let's use a number line
- for these addition problems up here.
- So in the last video -- just as a bit of a review --
- you can view 3 + 2 as starting at 3 --
- and then adding 2 to it.
- Or going two greater than 3.
- And just going greater --
- or adding on the number line --
- is just moving to the right -- or moving up by two.
- So let's move up by two.
- I'll do that in this orange color.
- So let's go up by 2.
- So we started at three and we go up by one.
- And then we go up by 2, or we're jumping,
- and we end up at 5.
- Which is exactly what we got before.
- If we have three lemons
- we add one lemon, we have four lemons.
- We add another lemon, we have 5 lemons --
- or limes -- or tart pieces of fruit.
- Whatever you might want to say.
- And when you look at this version of it --
- when you switched the order --
- We started at 2
- and we're adding 3 objects to it.
- In this case, they were lemons or limes.
- So we're going to add three to it.
- 1, 2, 3.
- And just like we expected,
- we got the same thing.
- We got 5 again.
- Now what I want to do in this video --
- and hopefully this was just a bit of a review --
- -- is I want to tackle harder problems.
- I want to tackle slightly larger numbers.
- And then in the next video --
- And in this video I want to just
- give you practice dealing
- with the slightly larger numbers.
- And then, in the next video
- we're going to dig a little deeper
- and think about what numbers even mean
- But let's just get some practice understanding
- "How do you actually do the addition problems with larger numbers?"
- Let me write it in a nice, soothing, purple color.
- Let's say I wanted to add 9 + 3.
- Well, there are a couple of ways we could do it.
- We could draw circles again.
- We could say, let's see, I have --
- Maybe I'll draw stars. 1, 2, 3, 4 --
- My stars are degrading,
- -- 5, 6, 7, 8, 9.
- That's 9 stars. And then I add 3 stars to it.
- So I add 1, 2, 3 stars.
- And then if you were to count
- the total number of stars, you would say --
- (Let me do that in a different color.)
- -- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
- I now have 12 stars.
- So, you would say that 9 + 3 = 12.
- It's equal to 12.
- If you looked at the number line --
- If you looked at the number line, you're, starting at 9.
- Maybe you have 9 stars
- and you add 1 star, 2 stars, 3 stars to that.
- And you end up with 12 stars.
- Which is the exact answer we got before.
- So you can do the same process when you start
- adding larger numbers, even though that now --
- And I want you to notice, the difference now is
- our answer has two digits in it.
- (And we'll talk more about digits in a future video.)
- But all a digit is is a numeral. Right?
- It has a 1 and a 2.
- That's what 12 is.
- I won't go into -- I won't dig too deep into that right now.
- I think you're pretty familiar with the number 12.
- But what I want to do is --
- Now what happens when you start adding more?
- When you start adding
- two-digit numbers like this?
- For example, if I were to add 27 plus -- let's say --
- I don't know -- plus15. (27 + 15.)
- Now, if you had a lot of time on your hands
- and you didn't care about how people judged you
- you could draw out 27 circles,
- and then draw out another 15 circles and then
- count the total number of circles you had.
- And that would give you an answer.
- Or you could draw a number line
- You could draw a number line that
- went all the way to whatever 27 + 15 is.
- So it's going to be this really, really large number,
- but that wouldtake you forever.
- So what I'm going to do
- is show you a way to
- do this type of problem
- where you really just have to know your addition
- almost have it memorized, or at least
- if you don't have it memorized
- be able to do something like this for
- relatively small numbers.
- And by doing it for the relatively small numbers,
- you can do the harder problems like this.
- So what you do, this is the fun part.
- You add, and I'll talk more about
- what this means in the future.
- You look at each of the digits.
- So we call this place, the rightmost place
- we call that the ones place.
- And why do we call that the ones place?
- Because 27 is 20 and 7 ones.
- It's twenty plus seven.
- It's twenty plus seven ones.
- You could view it as it's twenty plus seven pennies.
- And this place right here is called the tens place.
- Now why is it called the tens place?
- I mean there's a two right there.
- It's the place that's called the tens place.
- So putting a two here means two tens.
- The number twenty, that's two tens.
- If I have one dime and you gave me another dime
- I now have two dimes, and that's twenty cents
- So that's what the tens place is.
- I don't want to confuse you
- I just want to show you how to
- do these problems right now.
- We'll dig a little bit deeper in future videos.
- But I just want to give you that idea.
- But the way to do these problems is
- you look at the numbers in the ones place
- and add those up first.
- So you say, OK, I'm not going to worry about
- this whole thing right now.
- Let me just add the seven and the five.
- So I'm going to add the seven and the five.
- And if you don't know what that is
- hopefully you'll be able to do that
- in your head fairly shortly
- -- you could look
- at the number line.
- Let's look at the number line here.
- So if you add seven
- if you take seven, and you add five to it.
- -- 1, 2, 3, 4, 5 --
- We end up at twelve.
- Or if you started at five and added seven
- you'd also end up at twelve.
- So let's write that down.
- We know that 7 + 5 = 12.
- So what we do is we say 7 + 5 is equal to
- -- and now this is a new thing.
- It might be a little bit of a mystery
- magical thing for you right now.
- And in future videos I'll explain to you why this works.
- We write -- we want to write the 12.
- 7 + 5 is 12. But we just write the 2 here
- and we carry the 1.
- 12. one, two
- Well, we wrote the 2 there,
- but we put the 1 up here, right?
- And the reason --
- (I'll give you a simple reason for doing that right now.)
- (I'll give you a better reason in the future.)
- -- Is that you only had space to put one digit here
- and twelve is a two-digit number
- so we had to think of some
- other place to put that 1.
- If you really want to think about it even more
- 12 is the same thing
- as 10 + 2, right?
- That's the same thing as 12.
- So if we say 7 + 5, that's the same thing as 12
- which is the same thing as two ones. Right?
- Two 1s. 2 pennies, plus 1 dime.
- Plus 1 ten. Plus 1 dime.
- So we put that 1 dime in the 10s place.
- So we really just said 7 + 5 is one 10 plus two 1s.
- Or 1 dime plus 2 pennies.
- If that confuses you, just write, just say,
- well I just write the 1s digit of the 2 there
- and I carry the 1.
- And then you do the exact same thing in the 10s place.
- You add the 1 plus the 2 plus the 1.
- So 1 + 2 -- Let's do that on a number line.
- This is fun.
- So let's see.
- 1 + 2.
- Let's start -- let me do it in a vibrant color.
- (Let me do it in this magenta.)
- So we start at one.
- We're going to add two to it.
- 1 + 2.
- We take that 1 from our 12..
- 1 + 2. So you go up 1, 2.
- You end up at 3.
- Then you're going to add up another one.
- So you add another 1.
- You're going to end up at 4.
- So you ended up at 42.
- And this was pretty neat, right?
- Because we didn't have to
- draw a number line all the way to 42.
- And we'd didn't have to draw 42 objects.
- Just by knowing what 7 + 5 was
- and by knowing what 1 + 2 + 1 was
- we were able to figure out that
- 27 + 15 = 42.
- Let's do another example.
- Maybe I'll do a little bit of a simpler example.
- Let's say I had 78 + 3.
- We do the exact same thing as before.
- We just look at the 1s place only.
- So we look at 8 + 3.
- What's 8 + 3?
- Hopefully, we can do that
- in our heads at this point.
- But let's just think about it.
- 8 + 1 = 9.
- 8 + 2 = 10.
- 8 + 3 is going to be equal to 11.
- You could do that on the number line
- if it makes it easier to visualize for you.
- So 8 + 3 = 11.
- So what we do here, we just have 8 + 3 = 11.
- Put this one right here, put that there
- and carry the other one.
- Because eleven is
- one ten -- one dime -- plus one penny.
- That's eleven.
- And then we add the tens place.
- 1 dime plus 7 dimes is equal to 8 dimes.
- So 78 + 3 = 81.
- And now there's one thing I want to show you.
- You don't always have to carry numbers like that.
- Only if the answer to one of these
- has more than one digit in it.
- 11 is a two-digit number.
- So, for example, if I have 56 + 2.
- Here, I could just say 6 + 2 is 8. Right?
- Hopefully, we're getting good practice at this.
- So 6 + 2 = 8.
- And then, I don't have anything to add this 5 to.
- So, I just bring the five down here.
- So 56 + 2 = 58.
- Just like that.
- And this is one you actually
- could have drawn on the number line.
- It wouldn't have been too hard.
- So, if you were to draw the number line like that,
- 0 would be way off to the left some place.
- But let's say I had 50, no I think you'd have 49
- you could keep going to the left
- but you have 51, 52 --
- Actually let me start a little higher than that.
- Because I'm going to run out of space.
- Let me start at maybe 55, 56, 57, 58, 59 --
- And I could go in both directions -- keep going.
- But if we start at fifty-six right there and we add two
- We go up one, we go up two.
- We end up at 58.
- So just like, that we're able to do that problem.
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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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