How can you multiply
multiple digits numbers without writing anything down?
That's what we're going to talk about today.
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Like I sais in the intro. I'm going to teach you some of my techniques on
how you can multiply these multiple digit numbers without
writing anything down. My Goal here is for you guys,
hopefully,  be equipped of something to use
especially if you are taking an aptitude test that has time limit
and you are not allowed to use the calculator.
You can also use this technique when it comes to estimations
Because when it comes to multiple choice questions sometimes you don't even
need to know the exact answer, you just need to eliminate
the things that are not possible to be the right answer. And I'm going to
walk you through on how you can do this.
So in order for me to explain better? I'm going to switch over my PC. I'll see in a bit.
Okay, so this is our lesson on multiplying the numbers.
This is a speed math technique
that I use. I called them break them up. It is not for
someone in the relationship. But we are going to break up the
numbers that we are multiplying
I actually discuss this technique
that is somehow fleetingly on the
exclusive explainer videos for the practice test booklets.
I talked about a few of those, I used this technique
actually at the other question there.
So if you have the booklets or the videos
Probably you saw it that I used this there. And
I already used it at my other earlier videos as well.
But I never discussed it.
So I figured that it could be helpful for you guys
and that is why we are going to talk about it today.
Now, why are we using it on multiplying numbers?
Now, again, We have an option if we are going to use
the traditional technique or the traditional method, it can be.
But if you notice, if you start multiplying numbers
especially if its multiple digits like
this, it is a two digit numbers. You have
a 1and you have a 2 to form the 12.
Sometimes it takes
time for you to solve it. Because
what the teacher said is that we need to go from right first.
So 4 times 2? That would be 8
then
we will do it one by one. So 0 times 2?
Is going to give you zero.
Because any number multiplied by zero is zero.
And then you will have the
3 times 2? Which is going to give you 6.
Okay? That's the first level.
Then you will have the second level.
Your second level would be 4 times 1?
0 times 1? and 3 times 1? Not that
it is just times 1. Which is easier.
What would you do there is just copy it. So 4 0 3
And then the last step is you are going to add this.
So 8, the last number.
And then 0 plus 4 is 4.
And then 6 plus 0 is 6. And then
the 3 because it has nothing to add with, we will just bring it down. So 3
is the answer. So 3648 is the final answer.
Now. It is fine, honestly it is easier because we are used to it.
But the thing is
if you are taking an exam that has a timer or time limit?
You have restrictions like,
the scratch paper is short,
or there is no calculator?
hopefully this option that I'll be giving to you
will be able to help you because this is what I'm really using
especially on estimation. Okay? Now, again. We're going to take
the same
problem. So we already know the answer is 3648
We will confirm later if we'll still get
the correct answer.
This is the speed technique. Now instead of going like this?
All of them. And another level again.
What I am doing is, I'm breaking them down
into numbers that I will be able to
understand it better. So for example,
the 12.
The number 12 can be 10 and 2.
So instead of multiplying 304 by 12?
I'll go straight multiplying 304 the same number
to 10 and then I'll mutiply it also in 2.
And then Ill just add it.
And the more you do it, the faster you get,
the easier it will be for you to do things mentally.
Let me show you how to do it. Okay?
So the 304 times 10? I'll go straight to
3040. Because in
times 10 you will just put zero at the end. Okay?
Now, why it can help in the exam? Because you know right away
that the answer has to be higher than 3040
So if you have an option, A, B, C, and D
or A, B, C, D, and E.
You'll into it and the answer must be higher than that.
It should be higher than 3040.
Now, by chance? In the option there is
one higher than 3040. Automatically that is the answer.
That is the reason why I am saying why it helps
in the speed in the exam.  Because now, you don't need to solve the whole problem.
You can
Start from there. Now, for example that there are two higher
than 3040
That is the only time that you will to the next
which is the times 2. Now, why it is easy?
Because any number times 2 we can do mental math.
304 times 2 that is just going
to give you 608.
Okay? Now, if you can't do it mentally just times it by 2
one by one. 4 times 2 is 8
0 times 2 is 0.
Then 3 times 2 is 6. 608.
And then I'm just going to add this. Okay?
Now again, even in just in the mind, we can see that
the answer is still 3648.
It's still the same as
as the question a while ago.  In fact
what is written here is as same as before it is just in a different position.
Because if you notice? In the traditional method
using saw it is in the upper part and
the 304 is in the lower part. It is still the same.
So the final answer is the same. Now again
what is the break them up method?
The break them up method revolves around
where we multiply the other. Okay?
You will just split it, but the total should be,
because like 10 plus 2 is 12. The total
of what you are multiplying should be equal to 12.
Then you will just multiply it one by one. Now if you think?
But coach it seems
more complicated than the traditional method? That's okay. Again.
If you are used to it and you're having a hard time to unlearn
before you learn something new. You can stick
to what you are used to. But if not yet?
and you want  an alternative you can practice it a few times
and you'll see if it is working or it has a
a click for you and your style. Okay? Now the other thing
actually that you can break down would be
the 304. You can do it like that as well. 12
times 304?
So I will just multiply it by 300
and then multiply it by 4
Now why it is easy? Because 12 times 3 is just
3 6, 36
Then there is two 0. 3600
Then the 12 times 4 is going to give me 48
And if you notice? If I'll add it.
3648, it is still the same
with here. Okay? Now
why it is like that? Because multiplication has a property.
What we called it is computative property. I talked
about the properties of addition and multiplication in another video.
Just hit the i button here at the top if you haven't watched it yet.
So basically what it means is that, 304 times 12
is equals to 12 times 304. So
what I wanted you guys to understand is
or to get it is the freedom to be creative
about the math problems. If you are having a hard time in traditional method?
Manipulate it, move the other numbers
because the outcome will just be the same.  Okay?
Now, let's talk about another example.
This one. Let's take things up a notch.
Because the 304 times 2 6 or 26
It is not as easy as the one earlier.
Because it is not times
12. The first digit is not 1
so it will not be times 10 anymore. But what can you do about it?
You can still use the
same technique. We will just break them down.
Again, we will just build the 26. It can be times 20 or times 5
times 1
Now again. Why did I break it down like this?
Because we have a technique at times 5. If you haven't
watched the Speed math technique? I shot it
during the Youtube Next up event 2017
I had a guess there, if you know Ralph,
Mae,
the other youtube
people from my Next UP batch. They are also there.
So if you want to watch that? Watch it at the top,
I'll show you that later. But again,
The concept is that you will just build or make the 26 whole.
it should be, 25, 1. so it should be 26 with the total if you add it.
So the 26 is already built.
I'll just fill the information. Now, why it is
still easy with times 20? Because the
times 20 is basically times 2
then you will just add the zero at the last part because that is the times 10
Okay? Again, why? Because for you to build the 20
That is basically 2 times 10
So I will just multiply is at 2
Then I will just put zero in the end, I will put one 0 at the end. That is the answer.
Okay?
So the times 20. 304 timse 2
608
That is the times 2 of this.
Now, because
what we are looking for is times 20? We will just put
one zero. So 6080
Then you are finished there. Now again, if there is an option
your answer should be higher than 6080.
Now, for example if there are a lot of those answers in the option?
What you'll do is the times 5. The times
5? Basically my technique there is
you will divide it by 2
then you will multiply it by 10.
Okay? I talked about that in the video
It is like the opposite of divided by 5
that I taught a few weeks back.
In there? That is a different technique because
it is times 2. Times 2 then dived by 10
This one is dived by 2 times 10.
So what I'll do is 304
divided by 2
Okay. That would give 1 and you have a carry here. So 10.
10 divided by 2 is 5. This is divided by 2 is 2.
And then I will just add zero at the end.
So that is times 5. 1520.
Okay? So now, just by looking at it?
You know that the answer has to be at least be more than
7000. So again, you can eliminate in the options.
Now, if there is still something close to the answer? You will add one more.
So 1 is just 304
Then I will just add it.
So this is 4. This is going to give me 10. So this is zero.
This is going to give me 1 that I carried there.
So this is 9.
This is 7.
So 7 9 0 4 or 7904
Okay? Now again.
The more you do it the faster you get. That is just to avoid
the confusion of that, and
when you do the carry
at the traditional method. Because
not all people are comfortable at that,
at the longer solution. For me, honestly, the reason that
I do this. Why I do this is because
I am careless, I forget the carry sometimes
or I miss placed it. So
this is my of solving it without actually solving it
using the traditional method. Now, I do have
other techniques like this.
If you are interested let me know in the comment below.
I have a lot of speed math techniques that I made.
That I am not sure if others are doing or there is name there.
But hopefully, it will be a help for you.
Now of course, it is not enough if I'm just explaining
I wanted you to try it out for yourself.
In my earlier video, I notice that
some of you guys actually were surprised
at yourself. You yourself
are surprised that you can solve it
just in a few seconds. But
I hope that it will happen to you as well. It is a joy
because you will really see it. Like this one
Rafael Babida. He says, Wow nakuha ko in less than one minute.
even if im not good in math. Thanks by the way.
So again, what I wanted here is, for you guys to
experience that, you, yourself
can do the mental math as well. That it is also easy.
Okay? So this time I will be going to give a minute
to try it out.
Again, try to use the method that I taught you guys.
Okay? So your timer starts now.
All right. Let's see how you did? Okay.
So 232 times 32. Okay.
Now again, what we will do is just build the 32
we need to complete it
So we will break it. So let's break them up.
What we are going to do is we will split it
into times 30 and times 2. Now, why?
Because times 30 is easy. That is just
times 3 and just put one zero at the end.
So using the number right here. You can deduce
that if it is 232 times
30? That would actually give you,
times 3 first. 6 9 6
and then add a zero. 6960
Again if there is an option the exam, you know the answer has to be
higher than that.
Now, 232 times 2
Okay? That is the second part.
So what we are going to do is 232 times 2? Again.
we will do is 2times 2 is 4.
3 times 2 is 6. And then
2 times 2 is 4. So 464
We will just add it up. So 4
then
6 plus 6 is 12.
this is going to give me 14 and this will be 7
So this answer is 7424
Again, I hope that the technique was a help for you.
I hope that you used it
instead of the traditional method. And
I just want to emphasize, that it's not just
for two digit number. Because if we will use a
bigger number
for example, we are going to multiply 232 by, let's just say,
121
You can use the same technique of breaking it up.
To break this up into parts
times 100. times 20. And
then times 1. Again,
our goal is to build it up and the total should be
100 plus 20 plus 1. A 121. Okay?
They are the same.
So we can break it down like that. So the 232
times 100? That is just 232
then two 0. 232 times 20?
That is just 4
6 4 and then one 0
because times 2 then you will just add zero at the end.
And then the times 1, you will just copy it. 2 3 2
So you have 2 7
0 1 then 7
8 2. So I'm just adding them all.
So the answer is 28072
Okay? And again, the more you do it
the better you'll get, the faster you'll get.
And sometimes you won't even need to have
pen and paper handy. Because you can do it mentally. Okay?
Now.
At the beginning, it is better
that you have a paper so you can write it down this part.
And if you notice? at least you are at that part and you will just write the answer
right away. Not the 232
times 121. then you'll do it one by one
Somehow it is more tedious.
The thing is you will go straight to the answer.
That is the reason why  I am doing this break,
Break them up technique. Okay? I hope that it can
help you in your exam.
All right. I hope you learn something new today. If you did? Click thumbs up. Make sure that
you share this with your friends especially if they will take an exam.
So that we can help more. And as always if you want to
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Aja! Aja! Kaya niyo 'yan! I'll see you on my next video.
And bye for now.
