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.