Welcome to a lesson
on multiplying whole numbers.
Here we have three times two.
And the first thing we should notice
is there are many ways to write multiplication.
All of these mean three times two,
and we can see the product is equal to six.
Three times two means we have three groups of two,
or three copies of two.
And you can also think of multiplication as scaling.
Well, if we have three groups of two,
there's one group of two,
there's a second group of two,
and there's a third group of two.
And to show the groups,
we could even circle these,
so there's one group of two,
there's a second group of two,
and there's a third group of two.
So we could see when we have three groups of two,
we have a total of six.
Now you might also notice that if we view this
as two groups of three,
the total is still six.
And this is due to the fact
that when we change the order of multiplication,
the answer or the product is still the same.
Three times two is equal to two times three.
This is a property we'll take a look at in just a moment.
Now for some vocabulary.
The numbers being multiplied together are the factors,
so three and two are the factors,
and the product is the result
or the answer when we multiply.
So our product is equal to six.
Before we take a look at some more involved examples,
let's go and take a look at a couple properties.
Multiplication is commutative,
and what that means is that
we can change the order of the multiplication
and the product will be the same.
And from the previous example,
we know that three times two is equal to six,
and so is two times three.
And then lastly, if we have zero times a number
or a number times zero,
the product is always zero.
Now if we're just learning how to multiply,
this multiplication table may be very helpful,
and you might want to make one of your own.
The way this works is we have the factors in red
and the products in blue.
For example, to find the product of seven and six,
here's a seven and here's a six,
we just determine where this row and this column intersect.
Like this, so seven times six is equal to 42.
And this does occur twice in this table
due to the commutative property of multiplication,
meaning if I select the six from this row
and the seven from this column,
of course, the product is still 42.
So you may find this table very helpful.
Let's go and take a look at some examples.
If we want to find the product of 43 and six,
we're first going to write this in vertical form.
And now we're going to multiply the six by the three.
Well, six times three would be 18,
so we'll write down the eight in the ones column
and carry a one over to the tens column.
Now we're going to multiply the six times the four.
Well, six times four is 24,
but then we have to add this one,
so we'll have 25.
So 43 times six is equal to 258.
Let's try 21 times 32.
You can view this as two problems.
We're going to multiply the two times the 21,
and then the three times the 21.
So we're going to have two times one,
that's two, and then two times two,
that'll give us four.
Now we are going to multiply by the three,
but since this is in the tens column,
we're really multiplying by 30.
So what we have to do is add a zero to the ones column,
so this first product will be in the tens column.
Three times one would be three.
Notice this is really 30 times one,
and that's why we have to have this zero here.
And then we have three times two,
that would be six.
And now we add the columns.
We have two, seven, and six,
so this product is 672.
Let's go ahead and try another one.
Notice here we have 27 times 3,425.
It's usually easier to multiply
if the second factor has less digits.
And since multiplication is commutative,
we can change the order of this multiplication.
So we're going to write this as 3,425
times 27.
Notice now we just have to multiply by the seven
and then the two,
so now we'll start by multiplying by the seven.
Well, seven times five,
that would be 35,
so you write the five down and we carry a three.
Now we have seven times two,
that's 14, plus the three,
that would be 17, carry the one,
seven times four would be 28,
plus the one, that would be 29,
so we write the nine down and carry the two,
and now we have seven times three,
that's 21, plus two, that's 23.
And now we multiply by the two,
but since this two is in the tens column,
we have to start by adding a zero in the ones column.
And we have two times five, that's 10,
so we write down the zero and carry the one.
Two times two would be four,
plus the one, that would be five.
Then we have two times four,
that would be eight,
and then we have two times three,
that would be six.
And now we add the columns.
So it'd be five, seven,
14, so we carry a one,
this would be one plus three plus eight,
that's 12, carry the one,
that would be one plus two plus six,
that would be nine.
Our product is 92,475.
Let's take a look at a word problem.
You notice that your favorite restaurant
is offering lunch for $4 per person, tax included,
instead of the regular $6 per person.
As a result, you decide to buy lunch for your five friends.
If you have $30, how much money
will you have left after lunch?
Of course, you are going to eat, too.
So if you're going to pay for your five friends and yourself,
you'll have to purchase six lunches at $4.
So the cost of the lunch would be six times four,
which is equal to $24.
So if you have $30,
and lunch is going to cost you $24,
you need to find the difference.
So the amount of money you will have left will be $30,
the amount of money you have,
minus the cost of the lunch, which is $24,
which will equal $6.
You will have $6 left after you buy lunch
for you and your friends.
That'll do it for this video.
Thank you for watching.