Subtracting Tens from Two-Digit Numbers
In this video, we’re going to learn how to subtract a multiple of 10 from a two-digit number. We’re also going to find out how we can model this using place value equipment.
Let’s begin with this two-digit number, 36. And let’s imagine that we want to find 20 less than this number. We could write what we need to do as a subtraction. 36 subtract 20 equals what. Let’s think about the number that we’re taking away for a moment. What do we know about 20? We know that if we were modeling it out of place value blocks, we’d need two 10s blocks. If we wanted to show it using place value counters, we need two 10s counters. And if we used a place value grid to show our number, we need to write the digit two in the tens place. Of course, we would also need a zero in the ones place just to show that the two was in the tens place.
All these ways of showing how to model 20 tell us something very important about this number. 20 is a multiple of 10. It’s what we get when we multiply a number by 10. Two times 10 is 20, isn’t it? If we start at zero and count in tens, every number that we say will be a multiple of 10. zero, 10, 20, 30, 40, and so on. These are all multiples of 10 and they’re all the sorts of numbers that we’re going to be subtracting in this video. And it’s important that we remember what we’ve just learned. Each of these is a number of tens. It’s really going to help us when we have to take them away.
Right, let’s get back to our calculation. Now one way we can subtract a multiple of 10 from a two-digit number is by using place value blocks to help. What is our starting number 36 look like if we made it out of place value blocks? Well, it’s a two-digit number, so all we’re going to need are some tens and ones. It’s made up of three 10s, these have a value of 30, and six ones because 30 plus six equals 36. And we need to take away the number 20 from this, which we’ve said already is worth two 10s. There aren’t any ones at all. Let’s see how our two-digit number changes then as we subtract these two 10s. Now, we’ll start as we would do with any calculation like this, and that’s with the ones.
We’ve got six ones blocks here. But as we’ve said already, we’re taking away a number of tens. If we look at the number 20, there’s a zero in the ones place. We aren’t subtracting any ones at all. So we start with six ones, and we’re going to end with six ones. Our answer is going to have the digit six in the ones place because six take away zero equals six. Now it’s time to consider the tens. We’ve got three 10s blocks here because there are three 10s in 30. But we know because we need to take away 20, this is the same as taking away two of these 10s. Let’s cross two 10s blocks out, and as we do, watch how the digit underneath changes. One, two. We know that three take away two equals one, and so three 10s subtract two 10s is going to leave us with one 10. We’re left with one 10 and six ones.
To find 20 less than a number, we noticed that the ones digit didn’t change at all, but we’ve now got two less 10s. 36 subtract 20 equals 16. But what if we don’t have any place value blocks to help us? There are other ways we could model what we’re doing. Let’s try using place value counters. This time, we could begin with the number 62 and try to find out what’s going to happen if we subtract 40. 62 subtract 40 equals what. Let’s begin by modeling our starting number again. The six in 62 is worth six 10s or 60. So we could model this using six 10s counters. And then we’re also going to need two ones counters. Six 10s and two ones are the same as 62.
Now as soon as we look at the number that we’re taking away here, 40, we should be able to see that it’s a multiple of 10 again. Because it’s made up of the digit four in the tens place, we know that four 10s make 40. So as soon as it comes to actually working out the subtraction and looking at our ones column, we know there’s nothing we need to do. Because we’re taking away a multiple of 10, we just need to think about the tens. If we start with two ones and we take away zero ones, we’re going to be left with two ones. There’s been no change to our ones digit at all. But there will be a change to our tens digit. We’ve got six 10s counters here, but we need to take away four 10s. How many tens do you think we’re going to have left?
Let’s take away four of our 10s counters and watch how the digit changes. One, two, three, four. We know that six take away four equals two. And so six 10s subtract four 10s is going to leave us with two 10s. Although the ones digit hasn’t changed, our tens digit has decreased by four. 62 subtract 40 equals 22.
Hopefully, you’re getting the hang of this now and you’re able to spot that what we’re doing each time is concentrating on the tens digit. You know, we could solve a calculation like this using a pencil and paper or even just using our heads. Let’s see how quickly we can find the difference between 50 and the number on the card, which is 85. Do you remember that when we need to find the difference between two numbers, one way we can do so is by using subtraction. We start with the larger number, and we can find the difference between them both by subtracting the smaller.
85 subtract 50 equals what. And there should be no surprise to see we’re subtracting another number that ends in a zero. It’s a multiple of 10 again. Remember, we’re going to have to find the answer by focusing on the tens. So we need to think of our two-digit number in terms of its tens and ones. And we know that 85 is made up of eight 10s and five ones. And those eight 10s are going to be really important to us. Now we could just think about these in our heads. Or if we had a pencil and paper, we could just quickly sketch eight 10s and five ones. There we are. And the number that we’re subtracting is simply a number of tens, five 10s and zero ones.
So what do we know about how our starting number is going to change? Because we’re subtracting a number of tens, we’re not going to be taking away any ones. And so the number of ones that we had to start with, which is five ones, is still going to be five ones by the time we finished. Five subtract zero equals five. But we know that our tens are going to change. 85 has eight 10s, and if we want to take away 50, that’s five 10s we need to subtract. Now we could just work out eight take away five in our heads. If we’ve used a pencil and paper, perhaps you can see a quick way to spot how to subtract five. The way that we drew our eight 10s, we’ve actually partitioned them.
There’s a group of five at the top and then three more underneath. So we can see straightaway that five and three go together to make eight. If we want to subtract five from eight, we’re going to be left with three. Eight 10s subtract five 10s leaves us with three 10s. Our ones digit may not have changed, but our tens digit has decreased by five 10s. Another way we could have found the same answer in our heads is by counting back five 10s. We will show what we mean on a number line, but you could just count backwards in your head. So we’ll start with 85 and then count back five 10s. 75, 65, 55, 45, 35. Did you notice how each number we said as we counted had five ones? 85, 75, 65, and so on. Just goes to show how that tens digit changes, doesn’t it? The difference between 85 and 50 is 35.
Let’s answer some questions now where we have to put into practice everything that we’ve learned about subtracting multiples of 10 from two-digit numbers.
63 is six 10s and three ones. Take away one 10 to find 63 subtract 10. What is 63 subtract 30? Think: How many tens should you take away?
As we read through this question, did you notice two calculations that we need to work out? We’ve got 63 subtract 10 and then 63 subtract 30. Both of these calculations involve the number 63. And our question starts off by showing us how to model this number. We’re told that 63 is six 10s and three ones. And the place value grid underneath shows six 10s and three ones, both using place value blocks and also digits in the correct columns. In the first part of the problem then, we’re asked to find 63 subtract 10. And we’re told to take away one 10 to do this. Now this might sound obvious.
Of course, we have to take away one 10 if we want to find 63 take away 10. But understanding that the 10 that we need to subtract is the same as one 10s block is going to help us later on. Let’s see what happens then, when we take away one 10. Here are our six 10s and three ones, just like they are in the place value grid. If we’re taking away one 10, we don’t need to do anything to the ones blocks, but we do need to subtract one of our six 10s. This leaves us with five 10s. Our answer has five 10s and three ones. 63 subtract 10 equals 53.
In the second part of the problem, we need to find the answer to 63 subtract 30. What’s this got to do with subtracting 10? How is what we’ve just done going to help us? Well, we’re given a clue underneath. We’re asked, “How many tens should you take away?” When we look at the number 30, we can see a three in the tens place, but a zero in the ones place. This tells us that it’s a multiple of 10: three 10s are 30, 10, 20, 30. So just like we subtracted one 10 in the first part of the question, we now need to subtract three 10s.
And because we’re only taking away a number of tens again, we’re going to have three ones when we’re finished. There’s going to be no change there, but our tens digit is going to change. We need to subtract three 10s from the six 10s we already have. One, two, three. We know that six take away three leaves us with three, and so six 10s take away three 10s is going to leave us with three 10s. Our answer has three 10s and three ones. It’s the number 33. In this question, we modeled a two-digit number out of place value blocks. First, we subtracted one 10 and then, we had a go at subtracting three 10s. 63 take away 10 equals 53. And 63 take away 30 equals 33.
Take away 20 from 68.
In this question, we’ve got a subtraction we need to work out. We need to start with 68 and then take away 20 from it. 68 subtract 20 equals what. Can you see that both the numbers in this calculation have been written in a place value table for us? This allows us to think of the tens and the ones separately because they’ve been written in separate columns. We can see that the number we’re starting with, 68, is made up of six 10s and eight ones. But there’s something interesting about the number that we’re taking away. 20 doesn’t have any ones. It’s a multiple of 10; it’s what we get when we multiply a number by 10. Can you think how many tens there are in 20?
Perhaps you can recall the fact two times 10 equals 20. Or maybe you find the two digit in the tens place helpful. Whatever you use to help you, we can see that 20 is the same as two 10s. But because we’re subtracting zero ones, we can fill in part of our answer already. We started with eight ones in 68 and we’re going to end up with eight ones. We don’t have to take away any ones. Eight subtract zero equals eight. But whilst we don’t have any ones to take away, we do have to take away some tens. 68 has six 10s, and we need to subtract two of them.
Now there’s a simple number fact that we could use to help us here. Six take away two equals four. And if we know this, we also know that six 10s subtract two 10s equals four 10s. Our answer is going to have the digit four in the tens place. We found the answer by understanding that to take away 20 from a number is the same as to subtract two of its 10s. If we take away 20 from 68, we’ll be left with 48.
Fill in the blank: 93 subtract what equals 23.
Do you notice anything about the numbers that we’ve been given in this subtraction? We have the starting number and also the answer, but we don’t know what we have to take away to get there. To help us work out what’s being subtracted, let’s look at how our numbers change. We could write our starting number in a place value table. 93 is made up of nine 10s and three ones. 90 and three make 93. Now, we don’t know what we’re subtracting here. This is the number we need to find. But there is something interesting about the number that we get when we take it away. Our answer is 23 which is the same as two 10s and three ones.
What do you notice about these two numbers if we compare them? Well, they both contain three ones, don’t they? We’ve started off with three ones in 93, and we’ve ended up with a number with three ones, 23. The number that we’ve subtracted can’t contain any ones at all. It must have a zero in the ones place. But if we look at the number of tens we have, they do get less. We’re subtracting a number of tens here. And so the number that we’re taking away must be a multiple of 10.
Now, if we start with nine 10s and we end up with two 10s, how many tens have we taken away? Well, we know that two and seven are two parts that go together to make up nine. And so if we start with nine and we end up with two, we must have subtract seven. Nine 10s subtract seven 10s equals two 10s. In this subtraction, we noticed that the ones digit didn’t change, but the tens digit did. So we knew we were subtracting a multiple of 10. 93 subtract 70 equals 23. Our missing multiple of 10 is 70.
So what have we learned in this video? We’ve learned how to subtract a multiple of 10 from a two-digit number using different strategies to help. These have included things like modeling using place value blocks, completing place value tables, and working out the answer in our heads.