Lesson Video: Multiplying a One-Digit Number by a Multiple of 10 Mathematics • 3rd Grade

In this video, we will learn how to multiply one-digit numbers by multiples of 10.

16:58

Video Transcript

Multiplying a One-Digit Number by a Multiple of 10

In this video, we’re going to learn how to multiply together single-digit numbers by numbers that are multiples of 10.

We know that multiples of 10 are what we get if we multiply any number by 10. They’re what we say when we start at zero and count on in tens. 10, 20, 30, 40, 50, and so on. These are all multiples of 10. And in this video, we’re going to be taking multiples of 10 like these and multiplying them by one-digit numbers. So the sorts of calculations we’re going to be thinking about are things like 50 multiplied by three, seven times 20, or maybe even 80 times four. These are all examples of a multiple of 10 being multiplied by a single digit.

Let’s imagine that there’s a big concert and some music fans need to travel to get there. So they’ve booked six taxis and also six coaches. Obviously, the taxis hold a lot less people than the coaches. Five people can travel in a taxi, but 10 times this can travel on a coach. These hold 50 people. So to work out the number of people that will be traveling by taxi, we need to find the answer to six lots of five. And if we wanted to work out the number of people that are traveling by coach, we’d need to calculate six multiplied by 50. And before we start to work out these numbers, can you see that this calculation here is exactly the sort of calculation we said we’d be looking at in this video? We’re multiplying a one-digit number by a multiple of 10.

Let’s use number lines to show how we can work out both amounts. Let’s start with the taxis. And we’re going to count in fives six times, one for each taxi. Five, 10, 15, 20, 25, 30. We know that six lots of five ones equals 30. And so we know that we’ve 30 people traveling to the concert by taxi. Now let’s work out how many people are going to travel by coach. And because each of our six coaches contain 50 people, we can find the answer by counting in fifties six times. 50, 100, 150, 200, 250, 300. By counting in fifties six times, we found that six lots of five 10s equals 300. 300 people are going to travel to the concert by coach.

Now what’s all of this got to do with our video aim of multiplying a one-digit number by a multiple of 10? Well, do you remember we said our second calculation, which was six multiplied by 50, is exactly the sort of calculation we’re going to be thinking about. And let’s imagine for a moment that you’ve been asked to work out the answer to six times 50. Of course, you could count in 50 six times like we’ve done here. But is there a quicker way to find the answer?

Well, there is, you know. And we can find it by comparing our two number lines together. With the first number line, we skip counted in fives or five ones. But with the second calculation, we skip counted by 10 times this amount, five 10s. And I don’t know if you’ve compared the jumps we’ve made on both number lines, but if we look at the numbers we’ve landed on each time, we can see a pattern. The bottom number is 10 times as large as the top number. One lot of five is five, but one lot of 50 is 10 times this. It’s 50. Two lots of five are 10, but two lots of 50 are worth 10 times 10. They’re worth 100.

And we keep on seeing this all the way down the number line. 150 is 10 times as large as 15. 200 is 10 times as large as 20, and so on, until we get to the very last answer, where 300 is 10 times as large as 30. If we want to find the answer to six times 50 or six times five 10s, we can first find the answer to six times five or six times five ones and then just multiply the answer by 10. Let’s try a couple more examples and show what we mean.

What if we want to find the answer to 60 multiplied by four? Can you spot the number fact that we’re going to use to help us? We know that 60 is worth six 10s. And so if we know the answer to six times four or six ones times four, we can use this to help us. We know that six times four equals 24. And so six 10s times four equals 24 10s. And to find out what 24 10s are worth, we just need to multiply 24 by 10. And we know that to multiply any number by 10, we simply shift all of its digits one place to the left. 24 10s are worth 240. Six times four equals 24, so we know 60 times four equals 240.

So far, we’ve used place value blocks quite a lot to help us understand what’s happening. But we can also use what we know about the properties of multiplication to help. Let’s imagine that we want to find the answer to three times 50. And of course, we know that 50 is worth five times 10. And so we know that the properties of multiplication tell us that three times 50 is going to be the same as three lots of five times 10. We also know something called the associative property, which tells us that we can group the factors in a multiplication in different ways. So if we want to find out the answer to three times five times 10, we could work out three times five first and then multiply the answer by 10.

Let’s read that calculation again, and we’ll model it with place value counters. Watch what happens. So we find three times five, and then we multiply by 10. And can you see this is going to give us exactly the same answer as three times 50? So that’s how we’re going to multiply one-digit numbers by multiples of 10. We’re going to use facts we already know to help us. To find the answer to 20 times six, we’ll be using two times six to help us. Three times 60 is made a lot easier if we know what three times six is. We can find 90 multiplied by five if we know what nine times five is, and so on. Hopefully, you’re starting to be able to spot the calculations that can help you. Let’s put into practice what we’ve learned now. We’re going to try multiplying some one-digit numbers by multiples of 10.

Find the value of 90 multiplied by three.

In this question, we’re being asked to multiply a multiple of 10 by a one-digit number. We know 90 is a multiple of 10 because it ends in a zero. That’s always a good way to spot them. And multiples of 10 are what we get when we multiply a number by 10. And 90 is nine 10s, isn’t it? This is a fact that we can use to help us find out the answer. And we can use place value blocks to help see how. So firstly, if we think of 90 as nine 10s, we can write our calculation as nine 10s multiplied by three, or in other words three lots of nine 10s.

Let’s model these using place value blocks. One, two, three lots of nine 10s. How many 10s blocks have we got here? Let’s use our knowledge of the three times table to help. Here we’ve got three lots of nine ones. And if we know how many ones blocks we’ve got, we also know how many 10s blocks we’ve got. Let’s count in nines three times. Nine, 18, 27. We’ve got 27 ones blocks. And because we’ve got nine 10s multiplied by three, we’ve also got 27 10s blocks.

But they’re not worth 27, are they? Remember, each of our 10s blocks is worth 10. And so to solve this problem, we need to take our answer to nine times three and multiply it by 10. The diagram on the right is 10 times as large as the one on the left because each of the blocks we’ve used is worth 10 times as much. So what’s 27 multiplied by 10? Well, we know when we multiply any number by 10, each of its digits becomes 10 times as large. And so it shifts one place to the left. Instead of the two in 27 being worth two 10s, it shifts one place to the left and is now worth two 100s. Instead of the seven in 27 being worth seven ones, that also shifts one place to the left and is now worth seven 10s. And we need to include a zero to show that we’ve got an empty ones column. 27 multiplied by 10 equals 270.

We’ve found the answer to 90 multiplied by three by thinking of the calculation as nine 10s multiplied by three. We know that nine 10s are 10 times as large as nine ones. So first, we found the answer to nine ones multiplied by three, which was a lot easier. Nine times three equals 27. And then we just found the number that was 10 times as large as this by multiplying 27 by 10. The value of 90 times three equals 270.

Use the number line to find the value of 20 multiplied by four. Then we’ve got five possible answers: 24, 60, 80, 100, or 40.

In this question, we’re being asked to multiply a multiple of 10 by a one-digit number. And we’re told to use the number line to help us. Let’s take a moment to look at this number line. We can see that it’s labeled from zero all the way up to 100. And each interval is worth 10. That’s why each of the numbers that’s marked is a multiple of 10: zero, 10, 20, and so on.

Now, how can we use this number line to help us find the answer to 20 times four? Well, we can think of this question as asking us to find four jumps of 20 on our number line. Now, how many intervals of 10 would we need to cross to make one jump of 20? How many numbers would we have to count along our number line? One, two. Because each interval is worth 10, we move along two numbers for every 20. Now, the reason why we’re saying this and not just counting along the number line is that we can actually work out the answer before we start.

If we move along two numbers for every jump of 20 and we need to find four 20s, then the number of numbers that we’re going to move along our number line is the same as two times four. We’re going to end up eight numbers along, which is the same as eight intervals along. And because as we’ve said already each interval is worth 10, we’re going to arrive at a number that’s worth eight times 10. We can predict we’re going to end up at the number 80. Let’s actually use our number line the way it’s supposed to be used. We’re going to count along in 20s four times. And let’s see whether we end up at 80.

So we’ll say zero and then 20, 40, 60, 80. We were right! We predicted that we’d need to move eight numbers along our number line to find the answer. And because our numbers increase by 10 each time, we predicted that the number we’d end on would be worth eight times 10. If two times four equals eight, we know 20 times four must have a value of 80.

Calculate two times three. Use the answer to the previous question to help you calculate two times 30. From the answers to the previous questions, which of the following is equal to two times 30? Two times three, two times three times zero, two times three times two, two times three times 10, or six plus 10.

This question has three steps to it. And to start with, you might look at it and think to yourself, what have all these steps got to do with each other? They’re asking three different things, aren’t they? Well, yes, each part does ask us to do something different, but they’re all related. And hopefully, by the end of this question, you’ll be able to see how they’re linked and importantly how this very first, quite easy fact can help us work out something much harder.

So to begin with, we’re asked to calculate two times three. Hopefully, we don’t have to think too much about this, do we? Two threes are six. On to the next part. We’re now asked to use the answer to the previous question, so that’s the number six, to help us calculate two times 30. How can we use the answer to that simple multiplication to find the answer to this one, which is a lot harder? Well, let’s take a moment to look at this calculation. We’re being asked to multiply a single-digit number, two, by a multiple of 10, 30. We know the number 30 is a multiple of 10 because it’s a number in the 10 times table. It’s worth three 10s. And knowing this is going to help us.

Two times 30 is the same as saying two times three 10s. So how many tens is that? Maybe now you can see how the answer to the previous question can help us. If two times three is six, then two times three 10s is six 10s. And what are six 10s worth? We just need to multiply our first answer by 10. Six times 10 equals 60. Our second answer is 10 times as large as the first one.

In the third part of this question, we’re asked to use what we’ve done previously in those first two calculations to help us find a calculation that’s equal to two times 30. So let’s go back right to the start and talk through what we’ve done. We wanted to find two times 30. We know that 30 is worth three 10s. So first, we found two times three. This gave us the number of tens in our answer. And to find the value of our answer, we then multiplied this by 10. Can you see which one of the calculations is the same as this? Let’s write it out as we say it.

First, we found the value of two times three. As we’ve just said, this gave us the number of 10s in our answer. And to find the value of our tens in the answer to our question, we need to multiply this by 10. Two times three times 10 is the same as two times 30, and we can see why. The number 30 is simply being split up into three times 10.

In this question, we’ve found how we could use a fact we already know to help us multiply a one-digit number by a multiple of 10. If we know two times three, we can use this to help us find two times 30 because we know our answer will be 10 times greater. Two times three equals six. And so we know two times 30 must be equal to 60, which is the same as two times three times 10.

So what have we learned in this video? We’ve learned how to multiply one-digit numbers by multiples of 10 using multiplication facts we already know to help.

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