The Multiplication Symbol
In this video, we’re going to learn
how to use the multiplication symbol. Here’s a pair of socks. Two socks make a pair, don’t
they? Here’s another pair and another and
one more. We now have four pairs of
socks. We could say that we have four
groups of two socks.
Another way of writing down how
many socks we can see is as an addition. There are two plus two plus two
plus two socks. Now, two plus two plus two plus two
is quite a long way of writing out what we’ve got. Wouldn’t it be good if there was a
shorter way to write four groups of two? Well, there is. This is what we call the
multiplication symbol. It looks a little bit like a small
letter x, doesn’t it? We use it when we want to show a
few lots of or groups of the same number.
Our picture shows four lots of two,
four equal groups with two socks in each group, four groups of two. So, instead of writing two plus two
plus two plus two, we can use the multiplication symbol to write four multiplied by
two. Another way of saying this is four
times two. It’s simply another way of writing
four groups of two.
Now that we can use the
multiplication symbol, we can save a lot of time. These coins are all in equal
groups. How could we say how many there
are? We could say there are three plus
three plus three plus three plus three plus .... Let’s stop right there because this
is turning into a really long addition. And we know a much clearer way to
write down how much there are of something when there are equal groups.
There are one, two, three, four,
five, six, seven, eight lots of three coins. And we can use the multiplication
symbol here. We can say that the number of coins
is worth eight times three or eight multiplied by three. Eight is the number of groups, and
three is the number in each group. So, instead of saying a big long
list of three plus three plus three plus three and so on, we can just say eight
times three, and the person listening knows exactly what we mean.
Let’s try putting into practice
what we’ve learned. We’ll go through some questions
where we need to use and understand the multiplication symbol. Let’s see, especially, whether you
can use your knowledge of eight times three in this first question.
Pick the picture where the total
number of dots is eight multiplied by three.
We’ve got four pictures here, and
they each show groups of dots. The first one’s a little bit
different because the two groups of dots we can see are different numbers. But it’s interesting that in all
the other pictures, we can see lots of groups of three dots. And we’re told that we need to pick
the picture where the total number of dots is the same value as the one that we’ve
Now, we know what eight and three
mean, but do you know what the symbol in between them means? It looks like a small letter x,
doesn’t it? Well, if you were listening
carefully as the question was read out, you might have heard. This symbol is the multiplication
symbol. And that’s why when the question
was read out, we said eight multiplied by three. Another way of saying the same
thing would be eight times three. We can think of the multiplication
symbol as showing a few lots of the same number or a few groups of the same
If we look at our first picture, we
can’t see any groups of the same number. But interestingly, we can see the
numbers eight and three. But this doesn’t show eight lots of
three or eight groups of three. I think we need the addition symbol
for this picture. It shows eight plus three. This isn’t what we’re looking
for. In this question, where we write
eight times three or eight multiplied by three, eight represents the number of
groups that we want and three represents the number of dots in each group.
We’ve already noticed some of the
pictures that have lots of groups of three, but which one has eight groups of
three? In the second picture, there are
one, two, three, four, five, six, seven, eight, nine groups of three. This doesn’t show eight times
three; it shows nine times three. Our third picture shows one, two,
three, four, five, six, seven, eight times three. It seems this is the picture we
were looking for.
And if we just check the last
picture, it’s always good to do this, we can see that it shows seven groups of
three. We know when we write eight
multiplied by three, this represents eight groups of three or eight lots of
three. So the picture that shows the total
number of dots that’s the same as eight times three is the one that shows eight
groups with three dots in each group.
Which of these can we read as two
groups of eight objects? Two plus eight, two divided by
eight, eight take away two, or two multiplied by eight.
We’re given four different possible
answers here. What’s the same about them and
what’s different? What can you see? They all contain the numbers two
and eight. This is interesting because our
question mentions the numbers two and eight too. But we can see each of our answers
has a different symbol. There’s an addition symbol, a
division symbol, a subtraction symbol, and a multiplication symbol.
To answer the question, we need to
think then about what these symbols mean because one of our possible answers is a
way of representing two groups of eight objects. We might expect two groups of eight
to look something like this. There are two groups, and each of
them has got eight dots. Now, which of our symbols could we
use to represent groups of something? We know if we add two numbers
together, we combine them. So two plus eight would mean the
total of two and another eight.
When we subtract one number from
another, the first number gets smaller. This isn’t a way of showing groups
of a number either. And we know we use the division
symbol when we want to share a number or split it up or divide it. But we know we can use the
multiplication symbol to represent several lots of a number or several groups of the
same number. So when we see two multiplied by
eight written out, we know this means two lots of eight or, as it says in the
question, two groups of eight objects. We can represent two groups of
eight objects by writing two multiplied by eight.
There are five bananas in one
bunch. Eight multiplied by five is the
total number of bananas in what bunches?
The first fact that we’re told in
this question is that there are five bananas in one bunch. We’re given a picture to help
us. And if you count them, you’ll see
that there are five. In a way, we can think about this
bunch of bananas as being a group of bananas. We’ve then got a sentence that we
need to complete. It is “eight multiplied by five is
the total number of bananas in what bunches.” Can you see an interesting symbol
in this sentence? It’s in between the number eight
and the number five, isn’t it? And it looks like a small letter
It is not a letter x at all
though. This is the multiplication
symbol. And when we write it in between the
numbers eight and five like this, we could say eight multiplied by five, eight times
five, eight lots of five. These are all ways of saying the
same thing. As we’ve said already, our bunch of
bananas is really a group of five. So what do you think eight times
five means if we’re talking about bananas? It means eight lots of five
bananas, doesn’t it? And because there are five bananas
in a bunch, we know that it means eight bunches of bananas. Eight multiplied by five is the
total number of bananas in eight bunches.
William is baking pies. He wants to make six multiplied by
eight pies. Pick one way he could do this. A tray of six pies and another of
eight pies or six trays with eight pies on each tray?
Can you picture what’s happening in
this question? We’ve got William who must be in
the kitchen and he’s baking some pies. He knows how many he wants to bake,
but he doesn’t know how to do it. We’re told that he wants to make
six multiplied by eight pies. This symbol in between the number
six and eight is the multiplication symbol. We could also say six times
Now, for William to make six times
eight pies, he’s gonna have to understand what the multiplication symbol means. We’re given two possible ways he
could make his pies. Let’s sketch them quickly so we
understand what they’re talking about. The first answer says that he could
make a tray of six pies and then another with eight pies on it. It might look something like
this. The second answer says six trays
with eight pies on each tray. So, that’s six trays and then eight
pies on each of them.
Now, if we look at our first
picture, what can we see? We can see six pies and another
eight pies. And if we were going to use a
symbol in between six and eight here, we’d use the addition symbol, wouldn’t we? We’d say we have six plus eight
pies. This is not the same as
multiplying. But if we look at our second
picture, we could say we have six groups of eight or six lots of eight or even six
times eight. This is the same as multiplying,
isn’t it? If William wants to make six
multiplied by eight pies, we know he can do this by taking six trays with eight pies
on each tray.
What have we learned in this
video? We’ve learned how to use the