Southbay Math Tutor: Fun Alternative Ways to do Long Division

Ok we're gonna look at some kind of unconventional ways of doing long
division.
And this video is primarily for people having problems with long division.
So we're gonna start off.
And we're going to look at a problem in a more
conventional way of doing division. So we're gonna start off with this problem here:
100 divided by 3.
And the first thing we're going to do is look at this from a more conventional way
of doing things.
Of course from a conventional way of doing things you'd first see,
"How many times does 3 go into 1?"
And of course it doesn't. So you see, "How many times does 3 go into 10."
And 3 goes into 10 three times. So you put a 3 here.
3 x 3 = 9...right?
And then 10 - 9 = 1.
And then you drop the zero.
And you have a zero here. So now you go,
"3 goes into 10 how many times?"
Well it goes in three times.
So then you say, "3 x 3 = 9"
Subtract one and there you go. 33 with a remainder of 1.
And that's a more conventional way of how to do long division.
So we're gonna look at something a little more unconventional.
And we're gonna do the same problem
in a different way.
So 3 goes into 100 how many times?
And rather than go through this guessing game here
of "how many times does 3 go into 1, 10 etc." We're just gonna make a guess.
How many times does 3 go into 100?
Now we know who during the problem already that the answer is 33 R 1.
But let's say we didn't know what the answer was. And let's say we weren't quite as up to speed
on our multiplication tables. We're instead gonna take a guess:
3 goes into 100...i don't know...
20 times.
So we go, "3 x 20" and well put the 20 there.
And 3 x 20 = 60.
And then we go, "0 - 0 = 0"
Of course 0 minus 6 we can't do so we borrow 1 here.
And we have 100 - 60 = 40.
So now we're gonna guess,
"How many times does 3 go into 40?"
I don't know. Let's say I'm not really that great at multiplication tables. I could
say, "Okay well 3 times 10
is gonna be 30.
So i put the 10 there, and I go 3 times 10 and I have a 30.
And then i go 0 - 0 = 0.
4 - 3 = 1.
Now I look at this and say, "How many times does 3 go into 10?"
Well I know 3 x 3 = 9.
So I put a 3 here.
3 x 3 = 9
10 - 9 = 1.
Now since 3 doesn't go into 1 any more times we're done there.
And to get our answer we add: 20 + 10 + 3 = 33. Remainder 1.
And there is our answer.
Now this is a simpler problem right? If we look back at the original way we did it,
we could look at this and say, "This is gonna take us longer with this method.
This one's alot shorter.
Well this is relatively simple long division problem.
And you might find that it might be a little bit more useful when you have
a harder problem.
So let's take something a little bit more complex like
22,801 divided by 24.
And when you have something like this
in more conventional long division you have to look at this and go,
"Ok 24 doesn't go into 2. So then you look at 22. Then you have to look at 228, right?
Oh let's see (sarcastically), "How many times does 4 go into 228?"
Well i don't know 24 x 4...is that the right answer?
Then you do the mulitplication.... well that's a little low...
How about 24 x 5 or 24 x 6?
And then you are doing all this multiplication and wasting alot of time,
when you might find it more useful to say, "Ok let's guess...
how many times do we think that 24 goes into 22,801?
Well let's see...24 x 1,000 = 24,000. So we know that can't be it.
It's got to be less. So I'll guess ...800.
So I put an 800 here.
And then I multiply 800 x 24
This we'll figure out on the side.
Let's see 800 x 24....multiply that and we get 0...0...3200 and then
another zero here, and 0...0...16
and we arrive at 19,200.
So we're gonna put 19,200 right there.
And we're gonna subtract: 1 - 0 = 1 , 0 - 0 = 0, 8 - 2 = 6,
2 - 9 we can't do so we're gonna cross this out...1...bring your 1
over here...12 - 9 = 3.
So now we are going to look at how many times 24 goes into 3,601.
I don't know. Let's try 24 x 100. It's easy to multiply by 100.
Of course for 24 x 100 you just add on two zeros to 24 and you get 2,400.
Then you subtract: 1 - 0 = 1, 0 - 0 = 0, 6 - 4 = 2, and 3 - 2 = 1.
So now we are going to look at how many times 24 will fit into 1,201.
Well, let's see. 24 x 100 = 2400, so half of that would be 24 x 50, and...
that would be half of 2,400, so 24 x 50 = 1,200.
But you can also multiply it out on the side...24 x 50...
and we get 0...0...0...carry your 2 ...and you get 1,200...right?
So now you subtract 1,200 from 1,201 and of course you get 1.
1 - 0 = 1, 0 - 0 = 0, 2 - 2 = 0, 1 - 1 = 0
Now you just add these up.
800 + 100 = 900. 900 + 50 = 950. And your remainder is 1.
And there is your answer.
And we had to do some side work here. We had to find these
two problems. But we don't have to do nearly as much side work
as in conventional division.
And you could have guessed really low. You could have guess 24 x 700.
Or 24 x 100 first.
And then it would have been a longer process.
So it's up to you whether you find this useful.
I would say practice this method.
Practice conventional long division. See which one works best for you.
And good luck to you!