The Division Symbol: Grouping
In this video, we’re going to learn
how to use the division symbol. And we’re going to use it to write
equations to find the number of equal groups when we put two, three, four, five, or
10 objects into a group. This is the division symbol. We use it when we want to divide or
share a number of objects. Now, one way we can use this symbol
is when we want to put the same number of objects in a group. Have you ever needed to do
that? For example, at school, your
teacher might pass you a box of pencils and say, “Can you give out these pencils,
please, so that every table gets three each?” There’s lots of sharing like this
goes on in schools, especially when it comes to sports lessons.
Here are 20 basketballs. Now, let’s imagine that we’ve been
asked to share these basketballs into equal groups so that there are five
basketballs in each group. If we share 20 into groups of five,
how many groups will we make? How many groups of five can we make
from 20 basketballs? Here’s one group of five and
another, three groups of five, and then there are five more. So we can say if we share 20 into
groups of five, we can make four groups. Let’s write what we’ve just done as
a number sentence or equation. We started with 20 basketballs, so
let’s write the number 20 to begin with. This is the number that we’re
splitting up or sharing.
Because we divided this number, we
now need to use the division symbol, which is two dots and a line in between, like
that. We divided or shared our group of
20 into smaller groups of five basketballs. So the calculation that we’ve
worked out here is 20 divided by five. In other words, how many groups of
five can we make from 20? How many did we make? We made four equal groups. 20 divided by five equals four.
Here are 18 tennis balls. Now, let’s imagine that we’ve been
asked to split up or divide our 18 tennis balls into equal groups of three. In other words, each of our groups
needs to have three tennis balls in it. If we divide 18 into groups of
three, how many groups will there be? Let’s take away groups of three
until we’ve got no more to take away. 18 take away three equals 15. If we take away another group of
three from 15, this leaves us with 12. If we take away another group of
three from 12, we’re left with nine. Nine take away three equals
six. If we take away a group of three
from six, we’re left with one more group of three. And if we take away this, we’re
left with zero.
How many groups of three then could
we take away from 18? We took away one, two, three, four,
five, six groups of three. If we divide 18 into groups of
three, there will be six groups. And again, we can use the division
symbol to write this as a number sentence. We started with 18. We divided it into equal groups of
three. And we made six groups. 18 divided by three equals six.
Let’s have a go now at answering
some questions where we have to use the division symbol. In each of the questions, we’re
going to need to divide or split up an amount of objects into equal groups of a
certain size. And each time, we’re going to be
looking to find how many groups we can make.
There are 12 fish. There are what fish in each
bowl. There are what bowls. Fill in the blank: 12 divided by
three equals what.
Our question begins by telling us
that there are 12 fish. Doesn’t look like there are 12
fish. Each bowl doesn’t have very many
fish in it at all. Where are the 12 fish? Well, it seems there were 12 fish
to begin with, but they’ve been split up or shared out between different bowls. This looks like it’s going to be a
question all about division, splitting up or sharing an amount of objects. Our next sentence gives us a little
clue as to what’s happened. There are what fish in each
bowl. If we look at the fish bowls, we
can see that they all contain the same number of fish. The fish have been divided into
equal groups. We can see that there are three
fish in each bowl.
The next sentence we need to
complete is the number of bowls. There are how many bowls. There are four bowls, aren’t
there? We can write what’s going on here
as a number sentence. And this is the last blank that
we’re asked to fill in. Now, let’s have a look at this
number sentence to see if we understand it. It begins with the number 12. What does the number 12 represent
in this situation? It’s the amount we started
with. We had 12 fish to begin with.
And what happened to those 12
fish? They were shared out so that there
were three fish in each bowl. That’s why we use the division
symbol here, two dots with a line in between. We’ve divided the amount we started
with. And we’ve divided, as we’ve said,
by three. Three is the number that we wanted
in each group or in each bowl. Now, the answer to our number
sentence is going to be the number of groups that we could make. In other words, the number of
bowls. If we start with an amount and we
divide it so that we have an equal number in each group, the answer will be the
number of groups that we can make.
There were 12 fish to begin
with. There are three fish in each
bowl. There are four bowls. 12 divided by three equals
four. The missing numbers are three,
four, and four.
Emma wants to put these 12 blocks
into groups so that there are three blocks in each group. Which of these is equal to the
number of groups she will make? 12 take away three, 12 multiplied
by three, 12 divided by three, or 12 plus three. How many groups will there be?
In this question, we’re told that
Emma has 12 blocks. We can see a picture of them. But we’re also told that Emma wants
to do something with her blocks. She wants to put them into groups
so that there are three blocks in each group. In other words, as the label to the
picture shows, she wants to make groups of three. In the first part of the question,
we’re given four different calculations. Can you see what’s the same and
what’s different about them? They each contain the numbers 12
and three, don’t they? But the symbol in between is
different. How do we find the number of groups
that Emma makes? Do we take away three from 12? Do we multiply 12 by three? Do we divide 12 by three? Or do we add three to 12?
To understand which symbol we need
to use, we need to think carefully about what Emma’s doing here and what the numbers
12 and three represent. We know that the number 12 is the
number of blocks that Emma begins with. And as we’ve said already, she does
something to this group of 12. She splits it up or shares it or
divides it into equal groups of three. This is where the number three
comes from. It’s the number of blocks that she
puts in each group. Now, because Emma is splitting up
the 12 blocks, she’s going to need to divide to find the answer. The division symbol is the one
that’s two dots with a line in between. We can find the number of groups
that Emma will make by dividing 12 by three.
So how many groups will there
be? Let’s use 12 counters and make
groups of three to find the answer. We can make one, two, three, four
groups of three. Emma has 12 blocks and sorts them
into groups so that there are three blocks in each group. The calculation that’s equal to the
number of groups she will make is 12 divided by three. And 12 divided by three equals
four. There will be four groups.
What have we’ve learned in this
video? We’ve learned how to use the
division symbol to write number sentences that help us find the number of groups
when we divide an amount into equal groups.