>> Hi, this is Julie Harland,
and I'm your Math Gal.
Please visit my website
at yourmathgal.com
where you can search for any
of my videos organized
by topic.
All right we're going
to multiply decimals using
a lattice.
You need to already understand
how to use the lattice method
for multiplying
with whole numbers.
So make sure you know how
to do that first.
I have a video
on multiplying using
a lattice.
Now, we're going to do it
with decimals.
So here's an example.
Let's take 3.21 times 4.6.
So, we start off the same
as if it was just 321
times 46.
So, we can go ahead
and put 321 times 46.
So, notice I'm ignoring the
decimals here.
I'm going to go ahead
and just do my
regular lattice.
I'm not going to use cups
because it might be a little
confusing; I'm just going
to go ahead
and put the numbers
under the place
where they go along the sides.
So we have 1 times 4 that's 0,
4; and 1 times 6 is 0, 6;
2 times 4 is 0, 8;
3 times 4 is 12;
2 times 6 is 12;
and 3 times 6 is 18.
Then we're going
to take the numbers
in the lattice along the
diagonals because that's the
1s, 10s, 100s, 1000s,
10,000s if they're
whole numbers.
So this is 6.
Here I've got 4, 0,
and 2 that's a 6; 8,
1 and 8 that's 16 plus 1
that's 17.
So I'm going to put 1
over here for the carry
so it's 17.
I've got 2, 1 and 1 is 4
and a 1 over here.
Now there's two ways
of getting the answer
and figuring
out where the decimal
place is.
One way is to remember
when you multiply decimals you
just multiply the numbers
and what do I get here
for the number is 14766
if it was whole numbers.
So, keep in mind I got 1, 4,
7, 6, 6 and then remember you
have to see how many digits
are after the place values
and add them up.
I've got 2 digits plus another
digit over here.
So, I've got 3 total
so my answer I have
to have 3 digits
after so the decimal has got
to go right here.
Now so that's one way
of getting it.
The other way is put the
decimal right in the lattice.
So, this way; 3.21.
Put the decimal point here,
3.21, and 4.6.
Put the decimal right here.
What you do is you see
if this one is going down
and this one is going
across where do they meet?
Where do the decimal
points meet?
So, this decimal goes down,
this decimal goes across,
it goes right here,
and what you do is you follow
the diagonal down and that is
where the decimal goes.
So, that would be 14.766
or 14 766/1000.
Let's do it again
but let's put the 4.6
across the top and the 3.21
across the bottom
and we should get exactly the
same answer.
So we have the same problem
3.21 times 4.6 except
that we're going
to put the one
with the 2 digits
across the top.
I'm going to write this as 4.6
and across the side 3.21.
Let's decide
where the decimal place is
going to go ahead
of time this time.
So, I see the decimal point
here and the decimal point
here where do they meet?
Right here.
Follow it down and that's
where the decimal is going
to be so you can figure
out they decimal point ahead
of time.
Now let's go ahead and fill
out the lattice.
So we have 4 times 3 is 12;
6 times 3 is 18;
6 times 2 is 12;
6 times 1 is 6,
remember to put the 6
in the 1s place so it's 06;
4 times 2 is 8,
again put the 8 here
in this row there;
4 times 1 is 4, 04.
We drop it
into the answer here
so the 6 goes here.
Two plus 4 is 6; 8,
8 and 1 is 17.
So remember I'm going
to write 1, 7 for 17; 1,
2 and 1 is 4
and the 1 goes here.
If I read this going around,
I get 14.766.
Kind of cool.
Now if I had left off the
decimal point
and just multiplied the
numbers, I would have just
written the 14766
and then I would have seen
that there are 2 places here,
1 place here
so my final answer should end
up with 3 places
after they decimal point.
So, again,
you could just do the lattice
method without filling
in your decimal points
and write the whole number
and then decide
where the decimal point goes.
How about trying another one
on your own?
All right let's try this one,
1.532 times 3.6 and go ahead
and try that using the lattice
method on your own
by putting the video on pause
and trying it
on your own first.
All right so first we've got 4
digits by 2 digits.
So I'm going to do the 4
across the top,
but remember you can do it the
other way;
just put the box sideways.
So you have two numbers
across the top.
Usually it's easier
to put the bigger number
across the top.
There's less numbers to add
up in the diagonals;
you might notice that.
Okay. So, we've got 1.532,
3.6.
Let's see where the
decimals meet.
They meet right here;
this one comes down,
this one comes across
and they meet right here.
They follow it down and that's
where the decimal is going
to be.
Now we just go ahead and fill
in all the
multiplications here.
We're going
to have 8 different things
to multiply here.
So let's fill that in.
That's 3, that's 15,
that's 9, that's 6.
Notice I'm not putting all the
0s but you can fill
in the 0s there, 18, 30 and 6.
So you could leave it
like that or if you feel
like you could put all the
0s in.
There we go.
All right.
We just drop them
in so it's a 2, 6,
1 and 8 that's 15.
I'm going to write that as 1,
5; 9, 1, 1 that's 10,
11 so I'm going to write
that as 11;
5 and 3 is 8 plus 7 here
so that's a 15; and 1, 3,
and 1 is 5.
So it looks
like my answer is reading it
around 5.5152.
It seems reasonable
because my original problem,
you know, if you just estimate
the whole number it's
like a number little bit
bigger than 1
but it's 1 times 3;
it's going
to be a little bit bigger
than 1 times 3 and it's 5.
If you got 55,
you'd be way off, right?
If you had the decimal
in the wrong place.
Also notice there's 3 places
after the decimal point here
and 1 place.
So, 3 and 1 is 4
so in my answer there should
also be 4 places
after the decimal point.
All right let's do the problem
one more time.
We already got the answer,
5.5152, putting the 1.532
across the top.
Now how about doing it 3.6
across the top and 1.532
down along the side and see
if you get the same answer.
So let's figure
out where the decimal point is
going to end up first.
So the 2 decimal points
meet here.
You go down and across.
It meets here so that's
where the decimal point is
going to be.
Now, let's go ahead and fill
in everything else; 3 times 1,
3; 6 times 1, 6; 6 times 5,
30; 3 times 5, 15; 6 times 3,
18; 3 times 3, 9; 6 times 2,
12; and 3 times 2 is 6.
So, we've got 2, 8,
1 and 6 so that's 15
so I'm going to put 1, 5.
We have 1, 9 and 1 that's 11.
So I'm going to put 11
like that.
We have 6, 3,
5 and 1 so that's 9, 10, 15;
3, 1 and 1 is 5; and 0,
we don't need to write down;
and if we read starting top
left and going
around we have 5.512
same answer.
So now you know how you can
use a lattice
to do multiplication
with decimals and, of course,
you could just put the whole
numbers in here
and just decide at the end
where the decimal place goes
based on how many digits are
after each decimal point
in the original problem.
Please visit my website
at yourmathgal.com
where you can view all
of my videos
which are organized by topic.