The following videocassette is a presentation of Youth Enterprises.
Coming up next on Amazing Discoveries Home Videocassette Program, we're going to show
you how to become a human calculator.
You'll learn addition, subtraction, multiplication, squaring, and more.
We'll even teach you a trick to amaze everyone.
You'll finally learn how fun and easy math can really be.
So sit back, relax, and get ready to learn with the human calculator himself, Scott Landsberg.
Congratulations on taking your first step to becoming a human calculator.
Today in our program, I'll show you guys how to really make math fun, all right?
And I'll show you a lot of different ways to get to the right answer.
Remember, that's the key today, all right, to get the right answer.
Now to get started, let's get our brains warmed up a little bit.
So to start out, could you do some addition for me?
Go ahead and stand up.
I've got to add up a bunch of numbers in my head here.
It gets me going, okay?
So pick a whole bunch of three-digit numbers, and I'll try to add them up.
And you guys add them up on your calculator, all right?
So you give me a number, and I'll say plus, and you go back, and we'll just keep doing
it, okay?
And you guys just keep up on the calculator.
Go ahead.
Plus, plus, plus, and one more, 2,590, is that all right?
Okay, very good, thanks.
Let's try some multiplication right here.
Could you stand up?
Okay, let's start out with two-digit numbers.
Just give me two two-digit numbers, and I'll multiply them in my head, and you guys do
it on your calculator.
Go ahead.
Plus, times.
That'd be 2,400.
Is that all right?
Let's try another one.
Go ahead.
Could you pick a three-digit number times a two-digit number?
Times 68, 34,000.
Hang on, this is a real hard one.
You got me on this one.
I think it's 28, 34,000, 39, 690.
How about 38,556?
Is that all right?
That was really hard.
Okay, let's try some division.
Let's see.
Give me a division problem.
Pick like a three-digit number, and then divide it by a one-digit number, all right?
Well the other way around.
400 divided by 2 is pretty easy, it's 200.
Let's try another one.
Go ahead, right here.
Oh me?
Okay, 658 divided by 9.
That'd be 73.111111.
Okay, now let's try something a little bit harder.
How many of you know what a cube is?
All right, now let's try that.
Everybody with your calculator, go ahead and clear it.
Now pick a two-digit number and punch it in, all right?
Don't tell me what it is, and then hit your multiplication key, and then hit the same
two-digit number again, and hit your multiplication key, and hit the same two-digit number again,
and hit equals.
Okay, now what you just did was you cubed a number, you multiplied it times itself three
times, all right?
Now what you got to do is tell me the answer you have on your screen, and I'll try to tell
you the number you started with.
It's called extracting a cube root, and this is something I'll teach you a little bit later
on.
Who's got an answer?
Anybody?
Okay, what did you get?
Ninety-one thousand one hundred and twenty-five.
Forty-five.
All right?
Let's try another one.
Go ahead, what'd you get?
Twenty-one nine five two.
That'd be twenty-eight.
Okay, let's try another one.
Who else has one?
All right, go ahead.
One thousand three hundred and thirty-one.
Eleven.
That one's an easy one.
One more.
Let's try one more.
Did you get one?
One hundred and three thousand eight hundred and twenty-three.
Forty-seven.
Okay, now, that's called a cube root, but that's real easy.
I'll teach you how to do that.
Now, everybody with your calculator, this is a little bit different.
Everybody clear it.
Go to zero, and now I'm going to teach you, well, I'm going to show you how to do a constant.
Pick a three-digit number.
Three hundred and, keep going, some weird number.
Any number will do.
Yeah.
Three hundred and, try three hundred and something.
Three hundred and ninety-nine.
Three hundred and ninety-nine?
Okay, everybody go.
Three hundred and ninety-nine plus three hundred and ninety-nine equals.
Okay, everybody get seven hundred and ninety-eight.
Okay, now, keep hitting the equals key.
The next one would be eleven ninety-seven, fifteen ninety-six, nineteen ninety-five,
twenty-three ninety-four, twenty-seven ninety-three, thirty-one ninety-two, thirty-five ninety-one,
thirty-nine ninety, da-da-da-da-da-da.
It's real easy to do, okay?
Don't worry.
Now, what I want to do is go ahead and let's get things started.
How many of you think you can do mental math in your head?
A lot, like two and three-digit multiplication and stuff like that.
All right?
Some people don't.
So what I'm going to attempt to do is show you how to do that.
So the first thing we're going to learn how to do is addition because that's the easiest
thing, all right?
Let's start out with a column of numbers, a hundred and twenty-three, two hundred and
twenty-six, a hundred and twenty-one, and two hundred and fourteen.
Now, to add these numbers up in your head, there's a real easy way.
Don't we normally start over here on the right side in the ones, and then we carry
and add and carry and add, and all of a sudden, surprise, you get this big answer?
When I do it in my head, I do it left to right.
I start in the hundreds, and I go to the ones, okay?
And here's how it works.
This one right here, doesn't it stand for one hundred?
Okay, and what's this two stand for?
So now, we're going to keep a running total in our heads, all right?
What's one hundred plus two hundred?
Plus another hundred?
Plus two hundred?
Now, you take six hundred, and we go to the top of the next column, which is the tens.
So this two stands for two tens or twenty, correct?
So what's six hundred plus twenty?
Six hundred and twenty.
Plus twenty more?
Six forty.
Six sixty.
Six sixty plus ten.
So we have six hundred and seventy.
Now, let's go to the ones.
What's six hundred and seventy plus three?
Six seventy-three.
Plus six?
Six seventy-nine.
Six eighty.
And that's the answer, six hundred and eighty-four.
Does everybody see how that works?
You still get the same answer, but you don't throw anything down until you get the whole answer.
You're just keeping it in your head.
It does two things for you.
First of all, you had to identify what each number stood for.
This is a four.
This is twenty.
It's called place value.
The second thing is estimation.
As soon as you did this left side, you knew it was going to be six or seven hundred right away.
So it's real good for your estimation skills.
Now, who thinks they could probably do this?
Okay, come on up.
Let's try one and see how you do.
Okay, if I gave you two hundred and forty-five, a hundred and twenty-four, one eleven, and two hundred and sixteen.
Can you try that?
Yeah.
Go ahead and just talk it out loud to us.
See how you do.
Okay.
Two hundred.
Three hundred.
Four hundred.
Six hundred.
Now let's go to the top of the tens.
Six hundred and forty.
Good.
Six hundred and sixty.
Keep going.
Six hundred and seventy.
Six hundred and eighty-five.
Right.
Six hundred and eighty-nine.
Six hundred and ninety.
Six hundred and ninety-six.
Does everybody agree with that?
Yeah.
Six hundred and ninety-six.
That's right.
Good going.
Thank you.
Okay, so does everybody see how easy this is?
Yeah.
Okay, but you've got to practice.
So to practice, take your time and write down a bunch of two-digit numbers maybe and practice
with that first.
Then do three-digit, and you can do four-digit if you want, but what it does is it helps you
get used to being able to use this technique, all right?
And we're going to use this the rest of the program in our multiplication.
Everything we learn how to do, you've got to be able to add, all right?
So you've got to remember how to do this.
All right, now, let's try subtraction, all right?
But here's my little theory on subtraction.
I really don't do that.
What I do is a thing called negative addition, all right?
Because our minds really don't think in the way of subtraction.
Our minds are always adding, and it's just negative addition.
So let me give you an example of how I do this, all right?
Let's do four hundred and fifty-six minus two hundred and thirty-two, all right?
Now, again, instead of starting on the right, I start on the left, all right?
So what would four hundred minus two hundred be?
Two hundred.
Two hundred, and now what's fifty minus thirty?
So keeping a running total, how much do we have so far?
Two twenty.
Two twenty, and what's six minus two?
So what's the answer to four fifty-six minus two thirty-two?
Two twenty-four.
Two twenty-four, all right?
Does everybody see how we did that?
Okay, just keep track of the number, just like an addition, all right?
And doesn't it work out a lot easier?
Because right away you knew the answer was around two hundred something, right?
Let's try another one.
What's five hundred and forty-six minus three hundred and twelve?
But now, let's get somebody up here that thinks they can do it.
Right here.
Come on up.
Would you do that?
All right.
Five hundred and forty-six minus three hundred and twelve.
Now what do we do?
You take the five hundred and subtract three hundred from it, that's two hundred.
Right, and what do you get?
You got two hundred so far.
And then you take the forty, subtract the ten, that's thirty.
How much do you have so far?
Two thirty.
Right.
And then you take the six, subtract it by two, and that's four.
So what's the answer?
It's two thirty-four.
Very good.
Two hundred and thirty-four.
All right.
Now let's see what happens when we have to actually borrow doing subtraction.
Let's use five hundred and forty-six minus two hundred and twenty-seven, all right?
Now we've got to keep track of the number in our heads.
So first of all, what's five hundred minus two hundred?
Three hundred.
And now what's forty minus twenty?
So much do we have so far?
Three twenty.
But now here's where you've got to flash.
Right here.
Isn't this number bigger than this number?
Okay.
So we've got to borrow, right?
So we had three twenty, but now knock it down to three ten.
So what's sixteen minus seven?
So what would be the answer?
Three nineteen.
Very good.
Okay.
It takes a little bit of practice.
It's a little bit harder at first.
But once you get used to it, it'll help you get the answer real quick, and right away
you'll know what the answer's going to be about, okay?
Good estimated answer.
So practice a lot with that one, okay?
Now let's see.
Who could do this?
Five hundred and forty-two minus two hundred and twenty-four.
Who thinks they could try that?
All right.
Come on up.
You ready?
Yeah.
All right.
What do we do first?
Five hundred minus two hundred equals three hundred.
Three hundred.
And now what?
Three hundred, which is three hundred four, and forty is four.
Four equals forty, and two equals twenty, so forty minus twenty equals twenty.
Twenty.
So how much do you have so far?
Three twenty.
So you got three twenty.
Now what do you see?
Two over four.
Right.
This is bigger, right?
So we're going to have to borrow from that three twenty.
How much do you have left?
You have three ten.
Three ten.
And now what's twelve minus four?
Three eighteen.
Wow.
Okay.
That was the answer, right?
Way to go.
Wasn't it good?
All right.
Now let's try multiplication.
Let's see.
Who looks like they're really good at it?
Well, okay.
What I'll do is I'll show you how to do it first.
Then you guys pick if you want to try this, all right?
First of all, twelve times fourteen, it's a real easy problem.
But now don't we normally go two times four is eight, and one times four is four, and
drop is zero and all that?
Well, there's a couple of shortcuts I want to show you.
The first one is the technique is called right to left cross multiplication.
Here's how it works.
You go two times four, and what do you get?
Eight.
You write that down.
Now, to get the second digit in the answer, all you have to do is you multiply crosswise
both ways and add it together.
What's two times one?
Two.
And what's four times one?
Four.
So what's two plus four?
Six.
That's the second digit in the answer.
Now to get the other digit in the answer, this number here, all you have to do is multiply
these two numbers together.
What's one times one?
One.
So the answer to twelve times fourteen is?
One hundred sixty-eight.
All right.
Does everybody see how that works?
Yeah.
All right.
Come on up.
Twenty-four times twelve.
Okay.
What do we do first?
Four times two.
What do you get?
Eight.
And now we've got to cross multiply and add.
That's what it's called.
So what's four times one?
Four.
And two times two?
Four.
So what's four plus four?
Eight.
Very good.
And now the left side, what's two times one?
Two.
So the answer is two hundred eighty-eight.
Does everybody see how that worked?
Yeah.
It's pretty easy?
Yeah.
All right.
Let's see how she does.
Okay.
Let's use a little bit harder problem, and we're going to carry also, okay?
So we'll learn how to carry in this example.
Twenty-four times thirteen.
What's the first step?
Go ahead.
Three times four.
What do you get?
Twelve.
So what you do is you write down the two.
Now what you do is you have to carry the remainder to the next step.
So we have a one to carry, right?
Mm-hmm.
Now what's the next step?
Then you cross multiply.
Cross multiply.
What do you get each way?
Four and six.
Mm-hmm.
Four and six.
What's four plus six?
Ten.
And now we add the one in.
Mm-hmm.
What do you get?
Eleven.
Right.
Ten and one.
That's okay.
Now, so we write down the one, and we have to carry one again, all right?
Yeah.
Now what do we do?
Then you multiply these two.
Right.
What's two times one?
Two.
And add the one we carried.
Three.
So the answer is three hundred and twelve.
Okay?
See how it works?
Let's try another one.
What's thirty-two times fourteen?
All right.
Go ahead.
What do you get first?
Four times two.
And you get?
Eight.
Okay.
Now what?
Then you cross multiply.
Cross multiply.
Go ahead.
Tell us what you do.
Four times three is twelve.
Mm-hmm.
And one times two is two.
Right.
So fourteen.
Right.
What do I do?
Carry the four and carry the one.
Carry one.
And now what?
Then you multiply this times that.
Right.
What do you get?
Three.
And add the one.
Is four.
So the answer is four hundred and forty-eight.
Very good.
Is that pretty easy to do?
It's pretty easy because all you do is write down the answer.
Okay?
Now that's only one way.
It's called right-to-left cross multiplication.
But I'm going to show you another way that's called left-to-right cross multiplication.
So let's go back to the same example we used.
We did fourteen times twelve first.
Now here's how left-to-right cross multiplication works.
We're going to start over here instead of over here.
This one right there, what does this stand for?
One ten or ten, right?
And what does this stand for?
Ten.
Ten is two and four.
So think of it as four separate numbers, okay?
Ten, ten, two, and four.
Left-to-right cross multiplication.
We're going to do that running total in our head thing again, all right?
First thing we do is multiply these two together.
What's ten times ten?
A hundred.
That's our base number.
Remember, this is your base number, okay?
Now we're going to multiply across.
What's ten times two?
Twenty.
Now add it to our base number of a hundred.
What do you get?
So our new base number is a hundred and twenty, right?
Now we cross multiply the other way.
What's ten times four?
Forty.
What's our base number?
One sixty.
One sixty now.
A hundred and twenty and forty is one sixty.
And now we're going to multiply the two numbers on the right.
What's four times two?
Eight.
And add it to our base number of one sixty?
One sixty.
So the answer is a hundred and sixty-eight, all right?
All you do is keep track of that one number in your head again,
and you just keep multiplying across.
So let's try a little bit bigger.
Twenty-four times thirteen.
That's the one we did, right?
All right.
This two right here, what does this stand for?
Twenty, ten, three, and four.
So first, what's twenty times ten?
Two hundred.
Now we cross multiply.
What's twenty times three?
Add it to our two hundred.
Two sixty.
Now what's ten times four?
Add that to our two sixty and you get?
Three hundred.
Three hundred, very good.
And now four times three is?
Twelve.
So add it to three hundred.
That's three hundred and twelve, all right?
That's called left to right cross multiplication.
It's a little bit more involved, but it's really pretty easy
if you get used to the numbers, okay?
Now what I want to show you now is something that's really neat
because people have usually never seen this.
It's called complementary multiplication, all right?
Let's say you have two real big numbers like ninety-six times ninety-four.
Now that's a lot of multiplication.
Usually you have to do all the regular stuff.
But there's a real easy shortcut.
It's a three-step called complementary multiplication.
Here's how it works.
How far is ninety-six from a hundred?
Four.
So we write a four down.
And now how far is ninety-four from a hundred?
Six.
So we put a six down.
Now here's how you get the answer to ninety-six times ninety-four.
You subtract diagonally first.
What's ninety-six minus six?
Ninety.
You write down the ninety right here, okay?
Now these two numbers we wrote over here on the right-hand side,
what's four times six?
Twenty-four.
So the answer is nine thousand and twenty-four.
Is that pretty easy?
Yes.
Okay, that's called complementary multiplication.
Right here, could you come up?
Sure.
All right, let's try one and see how you do.
How about ninety-five times ninety-seven?
Okay, what do we do first?
You figure out how far they are from a hundred.
Right, and how far is ninety-five from a hundred?
Five.
And how far is ninety-seven?
Three.
How do you do?
You subtract three from ninety-five.
Right, and what's ninety-five minus three?
Ninety-two.
Okay, so what do we do?
Just write down the ninety-two, right?
Ninety-two.
Okay, now what do we do?
You multiply three times five.
Right, and what's three times five?
Fifteen.
So what's the answer to ninety-seven times ninety-five?
Nine thousand two hundred and fifteen.
Okay, very good.
Is that pretty easy?
Yes.
All right, but now what if the numbers were over a hundred?
What if the numbers were real big, like let's use a hundred and six
times a hundred and four?
All right, now what do you think we'd do?
How far over a hundred is it, you think?
Let's try that.
So this is six over, and how far is this?
Four.
Four over a hundred.
Now, here's how we get the answer.
Same basic concept, except this time we're working over a hundred,
so we're going to add diagonally.
All right, so what's one hundred and six plus four?
One ten.
One ten, and now what do we do?
There you go, multiply six times four.
What do you get?
So what's a hundred and six times a hundred and four?
Eleven thousand and twenty-four.
Okay, is that pretty easy?
Let's see how you do it.
Come on up.
No pressure, okay?
Let's do a hundred and seven times a hundred and five.
All right?
Okay, what do I do first?
Okay, you write seven right there.
Seven.
And five.
Five.
Now what do we do?
And then you add five to a hundred and seven.
Very good.
What's a hundred and seven plus five?
A hundred and thirteen.
A hundred and twelve.
A hundred and twelve, there you go.
Okay, and now what?
You do seven times five.
What's seven times five?
Thirty-five.
Thirty-five, so the answer is?
Eleven thousand two hundred and thirty-five.
That's it, it's that easy, okay?
That's called complementary multiplication, all right?
All right, next, now I want to try box multiplication.
Has anybody ever heard of that?
No.
All right, let's see how this works.
This is real easy, this is real neat.
All you do is that when you have to multiply numbers together,
you make a little box like this.
Now let's say we had to multiply twenty-four times twelve, all right?
Here's how it works.
You put a little slash through each box, you're splitting it in half, like this, all right?
Now, to get the answer to twenty-four times twelve,
you're going to multiply the corresponding numbers.
Like in this box here, four times one is going to go in there.
In this box here, four times two is going to go here.
And then we're just going to go all the way around the box and fill it in first.
So this first box, what's four times one?
Four.
Now here's why it's split.
This is for the ones, this is for the tens.
Bottom is for the ones, top is for the tens.
So if four times one is four, do you think it would go in the top or the bottom?
Bottom.
So you put a little four right here.
Now, what's four times two?
Eight.
Top or bottom?
Bottom.
And how about two times one?
Two.
Top or bottom?
Bottom.
Two times two is?
Four.
Top or bottom?
Bottom.
Now, here's how you get the answer to twenty-four times twelve.
Inside this box, all you're going to do is add these numbers up diagonally.
Between here and here, what's the only number?
Eight.
So you put an eight here.
Now between this line and this line, what numbers are there?
Four.
Four and four is?
Eight.
And now between this line and this line, what do you have?
Two.
Two hundred and eighty-eight.
Okay?
It's called box multiplication.
Let's try one with somebody else.
You.
Come on up.
You want to try this?
Okay.
No pressure, right?
Let's try just a little bit bigger problem.
Let's do thirty-four times twenty-three.
Okay?
That's pretty easy.
Now, first I've got to split all the boxes, right?
Yeah.
Okay, now you're going to tell me where each number goes, okay?
First thing we have is four times two, right?
What's four times two?
Eight.
Now do you think it's going to go to the top or the bottom?
Bottom.
Okay, we've got an eight here, right?
Now what do we do next?
Three times.
Four.
Four, that's okay.
Now what's four times three?
Twelve.
How do you think I might put that in there?
Twelve.
Here's how it works.
I'll give you a clue.
The ones go here and the ones go here, all right?
So all you do is just like write down the number.
Twelve, okay?
Top is tens, bottom is ones.
Now what's the next one?
It's three times two, right?
Okay, what's three times two?
Six.
Top or bottom?
Bottom.
Bottom, there you go.
And now what's next?
What goes in this box right here?
Three.
Three times?
Three.
Three, there you go.
What's three times three?
Nine.
Nine, okay.
So would it go in the top or the bottom?
Bottom.
Bottom, all right.
Now how do we get the answer?
We're going to add them up diagonally, right?
That's okay, here you go.
Between this line and this line, all we have is what?
What do you see in here?
Twelve.
Two, right?
Just these lines here, what do you see?
Two.
Two, right?
Okay, all you got is just two.
Now everybody try this one.
Between this line and this line, what's eight plus one?
Nine.
Plus nine more is?
Eighteen.
Here's what you have to do.
You write down the eight and you carry one to the next line set, okay?
Now between this line and this line, what's six plus one?
Seven.
So now can you tell me what the answer is to 34 times 23?
Seven hundred and eighty-two.
Seven hundred and eighty-two, all right?
That's how you do it.
This is just real easy.
This technique works really well with students that aren't that good at multiplying the other
way because they lose track of their numbers, okay?
This really keeps it organized for them, makes it real easy.
Let's try another one but a little bit bigger because this works with any size set of numbers.
You can multiply a three-digit number times a two-digit number, a four-digit number times
a four-digit number, whatever you want.
So let's try a little bit bigger box and we'll do a three-digit times a two-digit.
Okay, well let's have three hundred and forty-five times twenty-seven, all right?
First we're going to split all the boxes up.
Okay, we got it.
Now, all we're going to do is fit each box in with the corresponding numbers, right?
So let's go right down the line.
What's five times two?
Ten.
How do I get that in there?
One on top, zero on the bottom.
What's five times seven?
Three on top.
How do I do it?
Three on top.
Three on top, five on bottom.
Four times two is?
Eight.
Which way?
Bottom.
Four times seven is?
Twenty-eight.
How do I do it?
Three on top and eight on the bottom.
Pretty easy.
And three times two is?
Six on the bottom.
Bottom.
Three times seven is?
Twenty-one.
Twenty-one is like that.
Now, so to get the answer to three forty-five times twenty-seven, what's between here and
here?
Five.
Now what's between this line and this line?
Eleven.
Eight and three and zero is eleven.
I write down one, carry one to the next column.
Between this line and this line, what do you have?
Thirteen.
What's one and eight?
Nine.
Plus two?
Eleven.
Plus one?
Plus one.
Thirteen.
What do I do?
Three.
Write down the three, carry one.
What's one, two and six?
Nine.
So what's the answer to three forty-five times twenty-seven?
Nine.
Nine thousand three hundred and fifteen.
Isn't that easy to do?
Yes.
Okay.
Alright.
Okay, now, everybody's favorite, division, right?
Everybody's favorite.
Okay.
But now, division, what I do is really reverse because I do multiplication, alright?
So let me give you an example.
If you ask me what sixty-four divided by three is, I don't do sixty-four divided by three.
I really do.
Three times what will get me up to sixty-four?
Alright?
So it's a little bit reverse.
Now let me show you what I'm doing.
Let's do that example, sixty-four divided by three.
Now what's three times ten?
Thirty.
And now, so what would three times twenty be?
Sixty.
So right away, I knew it was twenty-something.
Okay?
Now just by looking at that, we know three times twenty is sixty, right?
How much do we have left?
Four.
So how many more times will three go in there?
One.
So now the answer's gotta be twenty-one something, right?
So what's twenty-one times three?
Sixty-three.
There you go.
Sixty-three.
How much do we have left?
One.
So wouldn't the answer to this question be twenty-one with a remainder of one?
Yes.
Alright?
But see, it's not really division because doing the multiplication the way I do it,
it's a lot easier for me to get the answer to this problem by reverse division or multiplication.
Alright?
Let's try another one.
Let's do seven into a hundred and forty-two.
Okay?
So it's a pretty easy problem.
What do you know right away?
Seven times what is seventy?
Ten.
Ten times twenty?
One forty.
So now how much do you have left?
Two.
So the answer to this problem would be what?
Twenty.
Twenty with a remainder of two, okay?
Really what it comes down to is you gotta know your multiplication.
That's all I do is I do multiplication all the time.
It makes division an awful lot easier, okay?
Everybody think they can do it?
Yes.
Alright, let's see.
Who hasn't been up?
Right here.
Can you come up?
Let's, we wanna try a hard one.
Let's try a pretty easy one with you.
Let's see, how about six into a hundred and twenty-nine, okay?
Now go ahead and talk to me.
What do you think you're doing there?
Okay.
Six goes into twelve, two times.
Right.
So it would go into a hundred and twenty.
Two with a zero.
Twenty.
Twenty, sorry.
So now what's six times twenty?
A hundred and twenty.
Okay, so we know the answer's twenty something, right?
Yeah.
Okay, now how much do we have left?
Nine.
How many times do you think six will go into that?
Once.
So now we got twenty-one, right?
Yeah.
Okay, how much do we have left?
Remainder three.
So what's a hundred and twenty-nine divided by six?
Twenty-one remainder three.
Very good.
Way to go.
Twenty-one remainder three.
But what if the two numbers are the same?
It's called squaring a number, alright?
For example, six squared, which means six to the second power, or six times six.
What's that?
Six.
That all meant the same thing.
So seven squared means seven times seven, or forty-nine.
How about nine squared?
Nine times nine is?
Eighty-one.
What about ninety-six squared?
Ninety-six times ninety-six.
Okay, now here's how you do that.
Ninety-six squared, here's how you get the answer.
How far is ninety-six from a hundred?
Four.
So what you do is you write a little minus four underneath there.
What's ninety-six minus four?
Ninety-two.
You write down the ninety-two.
And now this number here, this four, all we do is square that.
What's four times four?
Sixteen.
And bring it down, and that's the answer, nine thousand two hundred sixteen.
Okay?
It's a lot quicker.
You don't have to do all the multiplication.
So let's try another one.
Let's try ninety-five squared.
No, I don't want to try this.
Let's hit somebody else.
How about you?
Come on up.
Okay?
Let's see how you do.
What do I do if I want to figure out ninety-five times ninety-five?
You see how far away it is from a hundred.
Okay, how far is it from a hundred?
Five.
And what do I do?
Put the five right here.
Minus five.
Right now what do you get?
Ninety-three.
Ninety-five minus five is?
Ninety-three.
Or no, ninety.
Close, close.
There you go, ninety.
That's all right.
Okay, and now what do we do?
You put a little two up there.
Right, the square.
And what's five times five?
Twenty-five.
So what's the answer to ninety-five times ninety-five?
Ninety thousand twenty-five.
That's good.
All right.
We'll work on the subtraction part, okay?
All right.
Now, that's if it's under a hundred, but let's try it over a hundred and see if it works.
We already got too much here.
Okay, let's do, let's try a hundred and six times a hundred and six.
Okay, that'd be a hundred and six squared.
Okay, here's how we do this.
How far over a hundred is that?
Six.
So what we're going to do is add six.
Instead of subtract, we're going to add now.
So what's a hundred and six plus six?
A hundred and twelve.
We write that down.
And now what's six times six?
So what's the answer to a hundred and six times a hundred and six?
Eleven thousand two thirty-six.
Is that pretty easy?
Okay, let's have, right back there.
Can you come up?
Yeah, we're going to see how you do, okay?
Let's try, let's try a real big one, too.
Let's try a hundred and nine squared.
What's a hundred and nine times a hundred and nine?
A hundred and nine times a hundred and nine.
Come on over here so you can see it and work it out.
Okay, now what do you do first?
Add nine.
Add nine?
Okay, very good.
And what do you get?
What's a hundred and nine plus nine?
A hundred and eighteen.
Right.
A hundred and eighteen.
Okay, now what do we do?
Uh, square the nine.
Square nine.
What's nine times nine?
Eighty-one.
So what's the answer to a hundred and nine times a hundred and nine?
Eleven thousand eight hundred and eighty-one.
Very good.
See, she's quick.
Okay, now that's, that's squaring if the number's the same.
But now, if the numbers are the same, but if it also ends in a five,
there's even an easier way to do it.
Let's say you have to multiply a number like thirty-five.
Thirty-five times thirty-five, okay?
Here's even a quicker way.
Whenever this last digit in the answer is five,
the answer will always end in twenty-five.
All right, that's a given.
Now here's how you get the first part of this answer.
What's the first number in thirty-five?
Three.
And what's one more than three?
Four.
So what's three times four?
Twelve.
So the answer to thirty-five squared is twelve twenty-five.
All right, let's try another one.
Sixty-five squared.
All right.
What's it always gonna end in?
Twenty-five.
So those are the last two.
Now what do we look at?
Six.
Six and one more than that is?
Seven.
So what's six times seven?
Forty-two.
So the answer is forty-two twenty-five.
Four thousand, two hundred and twenty-five.
Is that easy?
Yes.
All right, let's see.
Who thinks they could do this in their head?
Nobody yet?
All right.
Well, let's try one and see how you do.
Let's see, who's real?
Okay, you can try this.
Let's see if you can do seventy-five squared.
Seventy-five times seventy-five.
What do you know?
You take, it'll end up in twenty-five.
It'll end in twenty-five.
And now what do we do?
One number higher than seven.
Is?
Eight.
And now what's seven times eight?
Fifty-four.
Close.
Fifty-six.
You got it.
Fifty-six.
There you go.
Fifty-six.
So the answer is fifty-six twenty-five.
Five thousand, six hundred and twenty-five.
Now, remember earlier we did ninety-five squared, but we did it like how far it was
from a hundred and stuff?
So, if we did ninety-five squared, what do we know it ends in?
Twenty-five.
What's the first digit?
Nine.
Now what's one more than nine?
Ten.
So what's nine times ten?
Ninety.
So what's the answer to ninety-five times ninety-five?
Ninety-twenty-five.
Ninety-twenty-five, nine thousand twenty-five.
That's how that works.
Okay.
And it works for real big numbers, too.
Like, if you had to multiply six hundred and twenty-five times six hundred and twenty-five,
you just do the same thing.
Add one to sixty-two and it works real easy, alright?
Let's see, squaring, multiplying, adding.
Let's try something a little bit harder.
Remember we did the cube root?
OK, how many think they could do?
Extract the cube root out of a six-digit number.
Not yet, huh?
OK, I'm going to show you a little trick on how you can do
this.
What is 1 to the third power?
Does anybody know?
This means 1 times 1 times 1.
It's 1, right?
OK, how about 2 times 2 times 2?
8.
And what's 3 times 3 times 3?
27.
How about 4 times 4 times 4?
64.
And 5 times 5 times 5 is?
125.
And what's 6 times 6 times 6?
OK, 216.
I guess I'll start doing these, huh?
What's 7 times 7 times 7?
343.
And what's 8 times 8 times 8?
512.
Sounds like calculators are rolling.
And what's 9 times 9 times 9?
729.
See, calculators aren't always right.
OK, now here's how you figure out the cube root of numbers.
Let me take, for example, I just picked a two-digit number,
and I multiply it in my head three times,
and I get the answer of 195,112.
Now here's how you would figure out
what number I started with, all right?
You split the number at the comma,
and you draw a little line.
And I'll put a little line here, so it's
like a little workspace, OK?
All we need to do is look at two things.
You need to look at the last number on the right side
and the whole number on the left side.
And this is how you figure it out.
The reason we look at this digit here, the ending digit,
look at the answers of 1 through 9 cubed.
Notice that this ends in a 1.
This ends in 2.
This ends in 3, 4, 5, 6, 7, 8, and 9.
None of these end in the same digit.
So if this ends in a 2, what number
had to be multiplied to end in a 2?
8 cubed ends in a 2.
So the back part of this answer is going to be 8, all right?
Now here's how you get the first part of the answer.
You look at the whole number.
In this case, it's 195, right?
What two numbers in the answer column does 195 fit?
Does 195 fit between 1 and 8?
How about between 64 and 125?
OK, where does it fit?
Between 5 and 6 cubed.
Always use the smaller of the two.
Which one's smaller?
5, so the answer is 5, 8, 58.
All right, so that's how we did that.
Let's try another one.
What's the cube root of 12,167?
What do we do first?
Split it at the comma.
What do we look at first?
The 7.
Now what number did we cube to get a 7 at the end?
3 cubed ends in a 7.
So 3 goes here.
And now what do we look at?
12.
OK, where does 12 fit?
Between 2 and 3, so use the smaller.
So what's the answer?
23.
Does everybody see how that works?
Let's try one more.
What is the cube root of 175,616?
You guys just look at it and try to figure it out.
How are we doing?
What does it end in?
OK, it's 6, and what goes here?
Right, now this ends in a 6.
6 cubed ends in a 6, so we knew that.
And now 175 goes right here between these two,
so the answer was 5, 6, or 56.
This only works for perfect cubes,
but what it does is it'll help you estimate
if it's not a perfect cube.
Let's say the answer was 30,254.
Well, you know that this is 27,000, right?
And this is 64,000, so it'd be between 30 and 40.
It'll help you with your estimation skills, too.
But if it's an exact cube, you can
get the answer just like that.
Just look at the last digit and the whole number on the left.
OK?
Pretty easy?
All right, you guys are ready for more.
All right, let's try something really hard.
Now, let's see.
When were you born?
May 4, 1977.
That was on a Wednesday.
Let's see, when was he born?
September 11, 1973.
That was on a Sunday.
OK, and when were you born?
June 16, 1975.
Monday.
I need one more.
How about you?
When were you born?
July 24, 1978.
July 24, 1978 was on a Monday.
But now, July 24, 1978.
So July 24, 1994, you'll turn 16.
And that's going to be on a Sunday.
And then you're going to turn 21 on July 24, 1999.
And that's going to be on a Saturday.
That's good.
And then you'll turn 65 on July 24, 2043.
And that's going to be on a Sunday.
OK?
So you've got to remember those.
But now, that's just a little formula that I did in my head.
But now, I'm going to teach you how to do that, OK?
Let's see.
How do I explain?
There's a real easy way to get this.
Here's the formula that you have to do.
First off, you start with the year,
plus the year divided by 4, plus the day,
plus SV, which stands for significant value.
And we're going to divide all that by 7,
because there's seven days in a week, all right?
Now, just to let you know, here are the significant values.
January is a 0.
February is a 3.
March is a 3.
April is 6.
May is 1.
June is 4.
July is 6.
August is 2.
September is 5.
October is 0.
November is 3.
And December is a 5.
OK?
Now, let me give you an example.
Don't worry.
It's really easy.
You just have to see it the first time.
Let's use your birthday.
When were you born?
December 22.
What year?
75.
OK.
Now, the first thing we do, what do we have here?
The year, right?
OK, what year was she born in?
So we put a 75 here.
Now, this says year divided by 4.
The reason we're doing this is to figure out
how many leap years there are in 75 years.
So can anybody divide 75 by 4?
18.75.
You drop off the decimal, all right?
So you just put 18.
Next is the day.
What day was she born on?
The 22nd.
So 22 goes here.
Plus significant values for the month, right?
Well, what month was she born in?
December, which is a 5.
So now all we're going to do is add all these numbers up
and divide it by 7.
So can anybody add these numbers up?
Let's use our left to right method and see how you do.
75, 18, 22, and 5.
What's 70 and 10?
80 plus 20?
100, 105, 113, 115, 120.
So now all we have to do is divide 120 by 7.
All right, now how many times will 7 go into 120?
17.
And that equals 119.
And here's all you need to know.
There's one left, right?
That's all you need to know is the remainder.
If the remainder here is 0, it's on a Sunday.
If the remainder is a 1, it's a Monday.
If the remainder is 2, it's a Tuesday.
If the remainder is 3, it's a Wednesday.
4 is a Thursday.
Who could guess what 5 is?
Oh, very good.
How about 6?
6 is Saturday.
And you know the remainder is 7 because you get a 0,
because it's divisible by 7, all right?
So how many people think you could do that?
OK, let's try another one.
And I'll give you the significant values, all right?
So you don't have to worry about looking at this chart again.
OK, let's use a real old, old, old birthday.
Who's really, really old here?
OK, when were you born?
28, June 28, 34.
Wow, that is a long time ago.
June 28, 34.
All right, what's the first thing we did?
The year, what year was he born in?
34, they didn't have calendars back then,
but we'll figure it out anyway.
Now, the next thing is 34 divided by 4, right?
We're going to divide it by 4.
How many times will 4 go into 34?
8 times.
Then we add, what day was he born?
28, and then we add what?
Significant value for June is a 4, very good.
All right, how'd you remember that?
All right, now, we divide it all by what?
7, because there's 7 days in a week.
So what's 34 plus 8 plus 28 plus 4?
You guys should be able to do this stuff now.
74, is that right?
So we have 42, very good, 74.
You guys are quick, all right.
So we have 74 divided by 7, what do we know right away?
It'll go in how many times?
10 times, and that's 7 times 10 is 70,
so how many do we have left?
4, so what day of the week was June 28th, 1934?
4 is a Thursday, right.
0 is Sunday, 1 is Monday, so you're born on a Thursday.
But now, let's figure out what he was this year
and see how we do differently.
June 28th, 1934, so June 28th, 1991.
All right, so 91 plus, what's 91 divided by 4?
Anybody can get it, it's 22.75.
Very good, 22.
You're quick, all right.
So we had 22 plus, the day is the 28,
plus the significant value of June was what?
4, and we're going to divide it by 7.
So what's 91, 22, 28, and 4?
145.
Very good, 145.
So we got 145 divided by 7.
How many times will it go in there?
20, and that's 140, how many days do we have left?
So what day was that?
So this year, your birthday's on a Friday, all right.
Very good, you guys did great.
OK, so far today, we've had a lot of fun with math,
but what I want to do is show you now
a trick that you can use on your friends and family, OK.
So I need you, because you were really good at subtraction.
Come on up.
Now, it's just a trick, all right.
And I'll do it first, then I'll explain how I did it.
What I need you to do is pick a three-digit number, OK,
and you're going to write it up here,
and then I want you to reverse that number and write it here.
So for example, you have 321, 123, all right.
Now, after you do that, you're going to subtract them,
and you're going to get a three-digit answer, hopefully.
Now, after you do that, I want you to circle
the answer for everybody, and everybody
look at the answer, all right.
And now, the whole time she does that,
I'm going to have my back turned,
so I can't see any of the numbers that you used.
And now, after you get the answer,
you're just going to tell me any one of the digits.
Like, say, OK, Scott, the first number is whatever,
or whatever like that, OK.
And I'll tell you the whole answer, all right.
And it's just a trick.
I'll show you how you do it afterwards.
So here you go.
You take the pen and do it, OK.
And you guys need to check her work.
Make sure she gets the right answer, OK.
Let's see.
I can't tell what she's writing up there, but I'm OK.
No, I can't tell.
Are you doing it right?
Subtracting right?
Everybody checking her answer?
OK.
All right, now you got an answer?
Yep.
All right, so now tell me, like, first or last digit?
Scott, the last number is 7.
OK, so the answer is 297.
Yes.
All right.
OK.
No, you did good.
All right.
But now, here's how the trick works.
Any time you take a three-digit number and reverse it,
and you get the three-digit answer, there's a key.
The answer will always have a 9 in the middle.
Always has his 9.
And the other two numbers add up to 9.
So in this case, 2 and 7 is 9, right?
So if I said to you guys, 3 is the first number,
what would the answer be?
396, right?
So try one more.
OK, the first number.
No, the last number is 2.
What's the answer?
792, real good.
All right, now, one thing real quick.
Remember at the beginning, I asked you guys
if anybody could do mental math in your head,
and not too many people responded.
OK.
Now, all we did here was we just, did everybody do this?
We just added up a bunch of three-digit numbers in our head.
We multiplied 2 and three-digit numbers in our head.
And we squared two-digit numbers in our head
and three-digit numbers in our head.
And then we were extracting cube roots out of six-digit numbers.
And then we did birthdays out of the calendar and stuff.
And everybody here basically caught on.
But what you need to do is practice.
All right, you've got to really practice.
If you start adding up columns and numbers,
you'll see how useful it is in everyday life.
Like, you go to the grocery store.
You have your checkbooks.
Not you guys yet.
I hope you don't have your checkbook.
But if you have checkbooks in the future,
you have to be able to add and subtract real quickly, all right?
It'll come into use in everyday life.
And also, with the multiplication and all the rest of this stuff,
it'll help you with anything you do in math.
But more importantly, what I really want to point out to everybody here
is, before I asked you and you said
you couldn't do the mental math, and now you can, right?
With just a little bit of practice and a little bit of imagination
and creativity involved.
Now, what else did you always tell yourself that you could never do,
but you probably could if you tried just a little bit harder
and looked at it a little bit differently than how you have in the past?
So that's the key issue.
Our program's called Motivation Through Mathematics,
because math is a great tool to build your self-esteem
and your self-confidence.
When you see that you can add up columns and numbers
when you thought you never could, it should make you stop and think,
boy, I wonder what else I could do if I tried just a little bit harder,
all right?
And that's the key message.
So math is important.
We need to use it in our everyday life,
because it'll make a significant difference in the way you live.
But also remember, never limit yourself, OK?
And math is just one key thing.
You've got a lot of other things you have to do in your life.
Make sure you give 100%, OK?
You guys did really good.
Thanks a lot for coming.
Good luck with your program.
And you've got your video, so take it.
And when you want to practice, just pop it back in.
You can go through the examples as slow as you like,
and make sure you understand each thing before you go on and on.
Good luck becoming a human calculator.
Thank you.