Remainders Using Models
In this video, we’re going to learn
how to model division of two-digit numbers when they do not divide evenly. These children have 17 gel
pens. They want to share them
equally. How can we share these 17 gel pens
between three children? We need to divide them. Let’s give everyone one gel pen
each, two each. Now they have three gel pens
each. Now they have four gel pens
each. Each child has five gel pens, and
we have two gel pens left over. We can’t share these equally
between three children because one child wouldn’t get a gel pen.
To record how we worked this out,
we would say there were 17 pens to begin with. We shared them equally or divided
them between the three friends, which gave the children five gel pens each. And there were two gel pens left
over. When we divide, we have to divide
into equal groups. If we have an amount left over, we
call this the remainder. So the “r” in our number sentence
stands for remainder. There were 17 gel pens. We divided them or shared them
equally between three children. Each child got five gel pens. There were two left over. 17 divided by three equals five
remainder two. Let’s practice what we’ve learned
about dividing with remainders by answering some questions now.
Each of the milk bottles are sold
in crates of four. How many complete crates are there
and how many bottles are left over?
This is a division problem. We have to divide the milk bottles
into crates of four. In other words, we have to divide
the milk bottles into equal groups of four. We have to count how many crates or
groups of four there are and how many bottles are left over. This group has already been done
for us. It contains four milk bottles. Let’s continue dividing the milk
bottles into groups of four. Now we’ve got two groups of four,
three groups of four, four groups of four, and there’s one milk bottle left
over. We made four equal groups, and
there’s one milk bottle left over. If the milk bottles were sold in
crates of four, we could make four complete crates, and there would be one milk
bottle left over.
10 children want to play a
game. They need to be in teams of
two. Find how many teams of two there
will be and whether any child will be left out. Is it four teams, no one will be
left out; four teams, one will be left out; five teams, no one will be left out; or
five teams, one will be left out?
This question is all about
dividing. There are 10 children and they’re
trying to make teams of two. We have to work out two things: how
many teams of two they can make and whether or not any child will be left out. We could model the number of
children using blocks. We’ve got 10 blocks to represent
the 10 children. Now, we can divide our 10 children
or our 10 blocks into teams or groups of two: one, two groups of two, three groups
of two, four groups of two, five groups of two. We had 10 counters and we’ve shared
them or divided them equally into groups of two.
Can you see how many groups we
made? There are five, so we can cross out
these two possible answers. We didn’t make four teams. We made five. We made five groups, and there are
no bricks left over. So this is the correct answer. There are five teams, and no one
will be left out. If 10 children want to play a game
and they need to be in teams of two, they could make five teams, and no one will be
left out. To find the answer, we used 10
bricks and divided them into equal groups of two. And we found that there will be no
bricks left over.
A teacher has 22 pencils that they
want to share equally between four children. What is the maximum number of
pencils each child will receive? Some pens might be left over.
This problem is all about sharing
equally, which means it’s a division problem. The teacher wants to share 22
pencils equally between four children. We have to work out how many
pencils each child will receive. We’ve modeled the number 22 using
these bricks. Can you think of a way of sharing
these pencils equally between four children? That means each group has to
contain an equal number of bricks. There we go. We’ve made four groups, and each
group contains an equal amount of bricks. Can you see how many bricks are in
each group? We’ve made four groups of five, and
there are two bricks left over.
If we have 22 pencils and shared
them equally between four children, each child will have five pencils and there will
be two left over. 22 divided by four equals five
remainder two. So the maximum number of pencils
each child will receive is five. We can’t share the two that are
left over equally between four children. So the most pencils the children
can get is five each.
What have we learned in this
video? In this video, we have learned how
to divide with remainders using models.