Video Transcript
Subtracting Zero and All
In this video, we’re going to learn
how to subtract zero from a number and how to subtract all of a number from
itself. And we’re going to do this with
numbers up to 10. Here’s a group of bananas; they’re
dangling above a river. Let’s count how many there are. The whole group contains five
bananas. So we could say, all of the group
equals five bananas. And who’s this swimming along? This crocodile likes bananas but
isn’t very good at jumping. Looks like he spotted them. Will he? Won’t he? Oh, dear. Let’s write what’s just happened as
a subtraction.
There were five bananas to begin
with. Unfortunately, the crocodile hasn’t
managed to eat any, so we haven’t taken away any. We can say we’ve subtracted
zero. And that’s part of what this
video’s about. What happens when we subtract
zero? How many bananas are left? One, two, three, four, five. All of them are left. We started with a number, we
subtracted zero, and we were left with the same number. Five take away zero equals
five.
Looks like our crocodile might be
going for another try. This looks closer. He’s got them all. Let’s write this as a number
sentence. Again, we started with five
bananas. And this time, we’ve subtracted all
of them. Because there were five to start
with, we can say we’ve subtracted five. How many bananas are left? Of course, there are no bananas
left, zero. Our crocodile has taught us two
important facts about subtracting zero and subtracting all. When we subtract zero, how many are
left? Well, firstly, when we subtract
zero, all are left. Taking away zero is the same as
taking away nothing. So we’re left with the same number
we start with. We can see this in our first number
sentence, five take away zero equals five. The number doesn’t change.
Now, what happens when we take away
everything? If we subtract all, how many are
left? Well, this is the second fact our
crocodile has taught us. When we subtract all, we have zero
left. And we can see this in our second
number sentence, five take away five leaves us with nothing or zero. If we take away all that we have,
we have nothing left. And this is what we mean by
subtracting zero and subtracting all. Let’s have a go at answering some
questions that involve subtracting zero and all. Hopefully, we won’t meet any
crocodiles along the way.
There are four balloons, and
all of them have popped. How many are left? Write the equation that
explains this situation. Four take away zero equals
four, five take away four equals one, four take away four equals zero, or five
take away five equals zero.
The first piece of information
we’re told in this problem is that there are four balloons, although perhaps we
should say there were four balloons because we’re then told that all of them
have popped. And we can see this in the
picture. Now, there’s a very important
word in this sentence and that’s the word “all.” We’re told, all of them have
popped. What does the word “all”
mean? Well, it means every single one
of them. And in this question, the word
“all” represents the number four. We had four balloons and all of
them have popped. So that means four of them have
popped. And of course, we can see if we
count the remains of the balloons in the picture that four of them have
popped.
And we’re asked how many are
left. Well, perhaps we know what the
answer is already. But let’s model the question
using counters just to be sure. These four counters can
represent our four balloons. Now, let’s take away counters
to represent the balloons popping. Remember, we need to show that
all of them have popped, so we need to take away one, two, three, four. Four take away four leaves us
with nothing. And so if all of the balloons
popped, we’re left with zero.
The next part of the problem
asks us to write the equation or the number sentence that explains the
situation. Which of these number sentences
shows us that there will be zero balloons left if we pop all four of them? Well, if there is zero balloons
left, then we’re looking for an answer that is zero. So that means we can ignore the
first and the second number sentences here. Both of our two remaining
number sentences have an answer of zero. But which one is correct? Four subtract four equals zero
or five subtract five equals zero. There were four balloons and
all four of them popped. So the equation that explains
this is four take away four equals zero. When we subtract all of a
number from itself, we’re left with nothing or zero.
There are five apples, and none
of them has been eaten. How many apples are left? Write the equation that
explains this situation.
We begin this problem with five
apples. In fact, we can see a picture
of our five apples underneath. The next piece of information
we’re told is that none of the apples has been eaten. And this word “none” is really
important. It represents a number. And that number is zero. Zero apples have been
eaten. Our first question asks us, how
many apples are left? If we’ve eaten none of them, we
know that all of them are going to be left. And we can see in the picture
this isn’t a picture before; this is a picture afterwards. Yes, we started with five
apples. But because none of them have
been eaten, we’ve ended with five apples too. And so we can say the number of
apples that are left is five.
In the next part of the
problem, we’re asked to write the equation or the number sentence that explains
the situation. What number shall we start with
in our number sentence? Well, we know that there were
five apples to begin with. So we’ll start with the number
five. Because this is to do with
eating apples, it’s going to be a take-away number sentence or a
subtraction. Now, what number are we going
to subtract? How many apples were eaten? None of the apples were
eaten. So we can put a zero there. This is all about subtracting
zero from a number.
And what happens when we
subtract zero from a number? Well, as we’ve said already,
when we take away zero, we’re left with all. The number that we started with
doesn’t change. And we can see that we’re left
with five apples still. The equation that explains the
situation is five take away zero equals five.
Complete the subtraction
sentence. Six take away what equals
zero.
As part of this question, we’re
given a subtraction number sentence. But it’s got a missing number
in it. Six take away what equal
zero. To help us understand what the
question is asking, we’ve also got a picture. And if we count them, we can
see that the picture shows six sweets. But each of the sweets has been
crossed through; it’s been taken away. And there aren’t any sweets
left. Let’s try modeling this using
cubes. Here’s a line of six cubes to
begin with. Now, how many do we need to
subtract so that we’re left with zero or none?
We’ll take away one, two,
three, four, five, six. We’ve taken away all of
them. Six take away six equals
zero. If we start with a number, we
take away something, and we’re left with nothing, the number that we’ve taken
away must be all of the number we started with. So in this number sentence, the
missing number is six. Six subtract six leaves us with
zero.
What is nine take away
zero?
We know that the number zero
stands for nothing. But what happens when we take
away nothing from another number? This question asks us, what
happens when we take away zero or nothing from nine? Let’s model this number
sentence. Perhaps we could use a ten
frame.
Now, the first number in our
subtraction is nine. So let’s represent this by
putting nine counters on our ten frame. Now, we don’t need to count
these out. Nine is only one less than
10. So we need to almost fill our
ten frame, just leave one space. Here are our nine counters. And in our subtraction, we’re
told to subtract or take away zero. So let’s pick up the number of
counters that we’re told to subtract.
Here we go. Watch the counters. Done. Of course, if we take away
zero, we’ve taken away nothing. We didn’t need to pick up any
counters at all. When we subtract zero from a
number, that number will stay the same. And so if we subtract zero from
nine, the answer is going to be the same as the number we started with. The answer’s nine. Nine take away zero leaves us
with all of the amount we started with. The answer is nine.
So what have we learned in this
video? Well, we’ve learned two things. We’ve learned how to subtract zero
from a number and also how to subtract all of a number from itself. And we found out two rules. When we subtract zero, all is left
and the number doesn’t change. And when we subtract all of a
number, we have zero left.
