Hi everyone in this video
I'm going to show you how to multiply
decimals
So i'm going to first show you some
easier examples
on the left side such as 12 times 34
12 times 3.4 and 1.2 times 3.4
After that i'm going to introduce rules
for multiplying decimals
for the problems on the right side
in the middle of the video i will also
show you why we apply those
specific rules
So before we multiply decimals i want to
show you
how to multiply whole numbers first
because it will be very useful for later
on
So let's take 12 times 34 for example
we want to first write down the number
12
and then you want to write three
underneath one because they are both in
the tens place
and you write four underneath two
because they are both
in the ones place. So now that we write
them
vertically you can start multiplying so
first we want to multiply
12 by 4 so 2 times 4
is 8 and 1 times 4 is 4 so 12 times 4
is 48 and then we want to multiply
12 by 30. so what you're going to do is
you're going to first multiply
2 by 3 you get 6 and you write 6
underneath
4 because that's on the tens place
and that's basically saying we are
multiplying
2 by 30 and we get 60 right so we can
write a 0 here
and then we want to multiply 1 by
3 and we will get
3. so we write on the hundreds place
and that basically means we are
multiplying
ten by thirty and we get three hundred
so you know that sixty plus 300 does
gives
us 360. all right
so now we just need to add 48 and 360
together
so start from right to left eight plus
zero is eight
four plus six is ten so we write down
zero
and carry the one over to the hundreds
place
and three plus one gives us four
so the answer of this problem is 408
so the second example is 12 times 3.4
the only change is the second factor it
has changed from 34 to
3.4 so what you're going to do is again
you're going to
line up the two numbers and you're going
to
think of it as first
you're multiplying 12 by 34
same thing so i'm going to write down 12
and i'm going to write down 34 and i'll
put a decimal
point here for now all right so we just
follow the same process
and you should be able to get 408 again
but since this is 3.4 not 34
you want to change your final product to
40.8
and i'm going to prove to you why we're
doing it this way
so let's show our work horizontally now
so basically we have 12 times
34 divided by 10
and we want to group this because we
know 34 divided by 10 equals 3.4
and it's the same thing as 12
times the product of
34 and 0.1
because 34 divided by 10
is equivalent to 34 times
0.1 you will get 3.4
on both sides
all right so now that we have 12 times
34
times 0.1 I can apply the associate
property of
multiplication and I will write
the product of 12 and 34
times 0.1 instead and
from the previous example we already
know that
the product of 12 and 34 is 408 so
408 times 0.1
gives us 40.8
so that's why we change our product to
40.8
and let's look at the next example to
make connection
so for the next example again i'm going
to think of this
as i'm multiplying the whole numbers 12
and 34
first
and i'm going to write decimal points
here for now
and following the same procedure
I know that my product for the two whole
numbers would be
408 but this time
we have 1.2 instead of 12 and we have
3.4
instead of 34. so that means
I'm going to change my product to 4.08
and i'm going to show you why by showing
the horizontal steps so
here we originally have 12
times 34 but then based on the problem
above we know that
12 changed to 1.2 so that means we have
12 divided by 10 and that's the quotient
and then we multiply by the quotient of
34 and 10
because 34 divided by 10 is 3.4
so we can rewrite this using only
multiplication
so then we will have the product of 12
and 0.1 times the product of 34
and 0.1
and now I'm going to get rid of my
parentheses because it doesn't matter if
you have them or not
you will get the same result
okay and then I'm going to apply
commutative property of
multiplication so I'm going to move
12 and 34 together first
and then I multiply by 0.1
twice
so from the first example we know 12
times 34
is 408 and 0.1
times 0.1 is 0.01
and that's why our answer is 4.08
so now you should get an idea right here
when you're multiplying a decimal
by a decimal you want to first multiply
as with whole numbers and then to place
the decimal points
you find the sum of the number of
decimal places in each factor
and the product has the same number of
decimal places
so for example in the second example we
have one decimal place and that's why in
our final result we have one decimal
place
in the third example we have two decimal
places together
and that's why in our final product we
have
two decimal places
so I've put the first three rules on top
of this video
Let's continue to explore more types of
problems
The next problem is to multiply 1.2
by 0.34 so here we're going to again
follow the first rule multiply as with
whole numbers
so think of it as we're multiplying the
two whole numbers
12 and 34. after you write it down like
this
then you place the decimal points
so based on what we already did for the
previous problems
we know that 12 times 34 gives
us 408
and then we're going to look at the
second rule it says find the sum of
number
of decimal places in each factor the
first
number has one decimal place and the
second number has two decimal places
so together they have three decimal
places
that means we will need to start from
here
and then go three places 1
2 3 and we're going to place our decimal
point here
and since the decimal point is right in
front 4
we're going to write a 0 in front of the
decimal point
so the final answer of this problem is
0.408
and to quickly show you why the answer
works this way
again I write down the horizontal steps
so 1.2
is equivalent to 12 times 0.1 0.34
is equivalent to 34 times 0.01
after I take out the parentheses i can
apply
commutative property of multiplication
by writing
12 times 34 times
0.1 times 0.01
and 12 times 34 is 408
0.1 times 0.01 is 0.001
and that's why the final answer is 0.408
next example 0.12 times 0.0034
so first I write down 12 times 34
vertically
and then I will place my decimal point
and the zeros
and make sure you line up the numbers
so you can count accurately later
okay so 12 times 34 again
gives us 408
and we are going to count the sum of the
number of decimal places now so first
one has
two decimal places second one has four
decimal places
and together we have six decimal places
so we're going to start from here and go
one
two three four five
six and we know we need to put a decimal
point here
and we want to fill in the empty spaces
with zero
so one two three
and we also want to put a 0 in front of
the decimal point
so our final answer of this problem is
0.000408
so for the last problem we need to
multiply 1.002
by 3.004 we are
going to
follow the first rule by thinking we're
multiplying one
thousand two by 3004
and then we're going to place the
decimal point
all right so now let's multiply the
numbers
2 times 4 is eight
one times four is four so we're going to
place the four right here
because 1002 times 4
gives
us 4008 so we put zero
here and zero here
and then we're going to multiply two by
three gives us
six and then we have two
zero three times zero is zero three
times zero is zero and three times one
is three because we are basically
multiplying 1002
by 3000
and that should give us three zero
zero six zero zero zero
and we read this number as three million
six thousand
okay so we're going to add the digits
together
so eight plus zero is eight and then we
have 0
plus 0 equals 0 and 0 here
4 PLUS 6 is 10 so we write down the 0
and then carry the 1 over
and then the next one is just 0 and we
bring down the 3.
and now we're going to follow the next
rule by finding the sum of the number of
decimal places
so for the first decimal number we have
three decimal places
for the second number we have three
decimal places together we have six
decimal places
so we're going to start from here and go
one
two three four five
six and that means our final answer
is 3.010008
