Video Transcript
Dividing by Seven
In this video, we’re going to learn
how to use different strategies to divide by seven. These are going to include things
like using models and also applying times tables facts that we already know to
help. Let’s begin by thinking about what
it means to divide by seven, and we’ll start with the question, “What’s 14 divided
by seven?”
Now whenever we’re dividing, it
doesn’t matter what number we’re dividing by. We can think of it in one of two
ways. We’re either sharing or
grouping. Let’s show what we mean by this
because it will really help us when it comes to working out the answer to
divisions. Here’s our starting number 14 as
represented by 14 fish. Now, if we think of 14 divided by
seven as sharing, we need to share our 14 fish into seven equal groups. When we divide by sharing, we’re
finding the number in each group. This is what the answer
represents. Let’s try splitting our fish into
seven equal groups then. What’s going to happen.
We could start off by sharing one
fish into each group. That would mean seven of our fish
were shared out, and if we share another fish into each group, that’s all 14 of
them. Two, four, six, eight, 10, 12,
14. So one way to think of our division
is us sharing 14 fish into seven equal groups. And we’ve found the number in each
group. There are two fish in each group,
aren’t there? 14 divided by seven equals two. But you know, we can also think of
our division in another way. We call this grouping. Instead of splitting themselves
into seven equal groups, our fish could decide to split themselves into groups of
seven. This time, we know how many
there’ll be in each group; there’ll be seven.
But we need to find the number of
equal groups. How many sevens are in 14? And we can find the answer by
counting in sevens. One group of seven is seven, and
two groups of seven are 14. If the fish split up into groups of
seven, they’ll make two equal groups. 14 divided by seven equals two. It’s exactly the same answer we’ve
found, but the number two means two different things depending on whether we’re
sharing or grouping. With this question, we’ve used
pictures to help us, but there are other strategies we could’ve used.
Let’s imagine that we want to find
the answer to 42 divided by seven. As we’ve seen already, one way that
we can think of dividing by seven is that we’re trying to find out how many sevens
there are in the number. So we could ask this division
slightly differently. How many sevens are in 42? We could find the answer by
counting in sevens. We could start at zero and count
forwards in sevens until we eventually get to the number 42. Or we could start with 42 and do
the same thing but backwards: keep subtracting seven until we eventually reach
zero. Let’s try this second method,
repeated subtraction.
Let’s start at 42 and see how many
sevens we need to take away to get back down to zero. 42 take away seven equals 35. 35 subtract seven equals 28. If we take away one more lot of
seven from 28, we have 21 left. 21 subtract seven equals 14. And we know from our last example
how many sevens there are in 14, don’t we? We need to subtract two more lots
of seven. And then we’ve reached zero. Did you notice how many sevens we
needed to subtract? One, two, three, four, five,
six. There are six sevens in 42, and so
we can say 42 divided by seven equals six.
Now, to find this answer, we’ve
just had to do quite a few subtractions, haven’t we? 42 take away seven, 35 take away
seven, and so on. But did you notice something about
the numbers that we reached each time? These are all numbers in the seven
times table. They’re all multiples of seven. And so, if we know our multiples of
seven, we don’t need to subtract. We just need to count backwards and
keep making jumps. And we call this skip counting. Let’s skip count six times just to
show how many sevens there are in 42. So we can say 42 and then 35, 28,
21, 14, seven, zero. If we know our multiples of seven,
skip counting is much quicker than repeated subtraction.
But you know there’s an even
quicker method that we could use to find out how many sevens there are in a
number. And it’s another strategy that we
could use. It’s probably fair to say that it’s
actually the quickest way to divide by seven, if we know how to. As I’m sure you know already,
addition and subtraction in maths are opposites. They’re what we call inverse
operations. But did you know the same is true
of multiplication and division? They’re opposite to each other. We could think of multiplication as
making lots of equal groups to find out the total. And we could think of division as
starting with the total and splitting it up into equal groups. And this means that when we’re
faced with a division question like this, we can use multiplication facts we already
know to help us.
And because in this video we’re
thinking about dividing by seven, we need to brush up on our seven times tables
facts. Let’s stick with the same question
where we’re dividing 42 by seven. And if we want to use
multiplication facts to help, we need to ask ourselves something. It’s a similar question to the one
the blue fish is asking, how many sevens are in 42? Except this question mentions
multiplication. What can I multiply by seven to
give the answer 42? Something times seven is 42. And if we know this fact, we can
solve the division. Now perhaps you know this fact
straightaway, but even if you don’t, we could start at one times seven and keep
working through until we get an answer of 42.
One times seven is seven, two
sevens are 14, three times seven equals 21, four times seven is 28, five times seven
is 35, and six times seven equals 42. Now that we’ve reminded ourselves
about this multiplication fact, let’s think what it means. If six times seven equals 42, this
means there are six lots of seven in 42. And if we want to start with 42 and
split it up into groups of seven, there’ll be six of them. What a quick way to find the
answer! If we know six times seven equals
42, then we know 42 divided by seven equals six. Now so far, we’ve just been
thinking about finding out how many sevens there are in 42. This is grouping.
But what if we were thinking of our
division as sharing. Well, we can use what we know about
multiplication here as well. If we know that six times seven
equals 42, we also know that seven times six equals 42. Because we can think of this as
seven groups of six, we know that if we share 42 into seven equal groups, there’ll
be six in each group.
We’re going to answer some
questions now where we need to put into practice everything we’ve learned about
dividing by seven. And let’s try some of the different
strategies we’ve learned too. We’ve learned how to divide by
seven by using repeated subtraction, also, how we can do this a little more quickly
if we skip count. We’ve used models to help us like
these arrays. And finally, we’ve seen how
important it is to know our seven times tables because we can use these
multiplication facts we already know to help us divide by seven. Let’s try some questions then.
Find 28 divided by seven using the
cubes shown.
This question tests whether we know
how to divide by seven, and we’re told how to find the answer. We need to use the cubes that are
shown. Now these cubes, and there are 28
of them, aren’t just set out any way. They’ve been laid out in an
array. And we can use arrays like this to
help us solve division problems. Let’s think for a moment about what
dividing by seven means. We can think of the division in two
different ways, and we can use the array to show these two ways. Firstly, we can think of our
calculation as 28 shared into seven equal groups. Can you see a way to share our
array into seven equal groups? If we look closely, we can see that
there are seven columns in our array. So we could think of each column as
being one of our seven equal groups. And the answer to our division is
going to be the number of cubes in each group. Can you see how many there are?
If we share 28 cubes into seven
equal groups, there’ll be four cubes in each group. 28 divided by seven equals
four. But you know, we can use our array
to find the answer a different way. We can think of it as 28 grouped
into sevens. And once again, we can use our
array to help us. As we’ve seen already, our array
has seven columns, but we could think of this fact a different way. If we concentrate on the rows and
not the columns, we can say that each row contains seven cubes. So we can see that there are one,
two, three, four groups of seven.
This time, we know the number in
each group, but our answer tells us the number of sevens there are in 28. We found the answer to 28 divided
by seven by using the array. And we’ve shown that we can think
of this division in two different ways but still get the same answer. If we share 28 into seven equal
groups, there’ll be four cubes in each group. Or if we group 28 into sevens,
there’ll be four equal groups. 28 divided by seven equals
four.
Find 56 divided by seven using the
given number line.
How can we divide a number by
seven? In this question, we need to divide
56 by seven. But we’re also given something to
help us because one way we can divide by seven is by using a number line. Where do you think our number line
begins? Well, if we’re looking at it from
left to right, we could say it begins at zero. But if we’re thinking about what’s
happening on our number line, we can see that the action begins at the number
56. We can see that we start at the
number 56 and then keep subtracting seven again and again, until eventually we
arrive back at zero.
Why might we want to take away lots
and lots of sevens from 56? Well, we can think of our question
as asking us, how many sevens are there in 56? And we can count these sevens by
starting at 56 and keeping subtracting seven. Let’s see how many jumps backwards
of seven it takes us to get from 56 to zero. 56 take away seven equals 49. If we take away another lot of
seven, we’ll have 42. 42 subtract seven equals 35. 35 subtract seven equals 28. If we take away another lot of
seven, we’ll have 21 left. 21 take away seven equals 14. 14 subtract seven equals seven. And this leaves us with one more
lot of seven we can take away before we get back to zero.
We’ve subtracted sevens eight
times. And this took us from 56 to
zero. So we can say that there are eight
sevens in 56. We could even make eight jumps in
the opposite direction from zero up to 56. So we could say zero and then
seven, 14, 21, 28, 35, 42, 49, 56. We’ve used repeated subtraction on
the number line to help us find the number of sevens that there are in 56. 56 divided by seven equals
eight.
Find the quotient.
This is a really interesting
question because although we can see some numbers, we can’t see any of the four
symbols we’d often see when we’re doing a calculation. There’s also a tricky word. Find the “quotient.” So before we start, let’s go over
what this tricky word means and also why these numbers are being written this
way. The word “quotient” means the
result when one number is divided by another. You know how we use the word
“total” when we add two numbers together, and the answer is the total. Or “product,” when we multiply two
numbers together, the answer is the product. Well, if we divide two numbers, the
answer to that is the quotient.
So the first thing we can say about
this question is that it’s a division calculation. And the way that it’s been written
is just a way that we can sometimes write divisions. This is the number we’re starting
with, 35. And the number on the left is
always the number we’re dividing by. This question is just another way
of asking us, what’s 35 divided by seven? Or if you want to read the numbers
from left to right, how many sevens are there in 35? We can use our knowledge of
multiplication to help us here because division and multiplication are inverse
operations. They’re opposites. If we know the number that we
multiply by seven to get 35, then we know the number of sevens there are in 35.
Let’s go through our seven times
tables facts. One times seven is seven, two
sevens are 14, three sevens are 21, four times seven equals 28. And here’s the fact we’re looking
for: five sevens are 35. And if we know that five times
seven equals 35, we also know that the number of sevens that there are in 35 is
five. In this question, we’ve used our
knowledge of a seven times tables fact to help us divide by seven. Five times seven equals 35. And so we know 35 divided by seven
equals five.
Complete the missing number. What divided by seven equals
nine.
In this question, we’re given a
number sentence that’s all about dividing by seven. But we don’t have to divide by
seven to find the quotient or the answer. We already know it. Our missing number is the dividend;
it’s the first number in the division, the number that we divide. What number, if we divide it by
seven, will give us nine? To help us, we could use
multiplication facts and our knowledge of the seven times table. If we start with a number divided
by seven and the answer is nine, can you see how you might find the starting
number? Bar models are so useful, aren’t
they?
And we can see with this one that
to find our starting number or our dividend, we need to find seven lots of nine. What is seven multiplied by
nine? Well, we know that seven multiplied
by 10 or 10 lots of seven equals 70. And so seven lots of nine or nine
lots of seven is going to be seven less than this. And seven less than 70 equals
63. We found our multiplication fact to
help us solve the problem. Because we know that nine times
seven equals 63, we know that 63 divided by seven equals nine. Our missing number is 63.
What have we learned in this
video? We’ve learned different strategies
to help us divide by seven. These have included using models,
using repeated subtraction or skip counting, and applying multiplication facts we
already know to help.
