Lesson Video: Subtracting Two-Digit Numbers on Number Lines Mathematics • 2nd Grade

In this video, we will learn how to use a number line to subtract two-digit numbers from two-digit numbers by making jumps of ten and one.

12:06

Video Transcript

Subtracting Two-Digit Numbers on Number Lines

In this video, we’re going to learn how to use a number line to subtract two-digit numbers from other two-digit numbers by making jumps of 10 and jumps of one.

Let’s imagine that we’ve been asked to subtract this pair of two-digit numbers. How are we going to find the answer to 98 take away 52? We know that we can find the answer to subtractions by counting backwards. So, we could mark the number 98 at one end of a number line and then count back 52 ones. One, two, three. Do you think this is going to be a quick way of finding the answer? We need to count back 52. We’ve only got as far as three. We’ve got a long way to go. There’s got to be a quicker way to find the answer.

To help us, we can think about the number that we’re subtracting, 52. We know that the number 52 can be broken up into five 10s and two ones. We know how to skip count in 10s. So, instead of making 52 little jumps of one, why don’t we jump back five 10s and then two ones? This is the same as counting back 52. We’re taking away from the number 98. So, the first thing we need to do is to place the number 98 on a number line.

We can use a blank number line rather than one with all the numbers already labeled on it. Because we’re going to be skip counting in 10s to begin with, we don’t need a lot of the numbers. We’re going to jump over them. So, let’s just label our number line as we go. To begin with then, let’s make five jumps of 10. We’ll skip count backwards in 10s five times. 98, 88, 78, 68. So far, we’ve jumped back three 10s. Let’s keep going. 58, 48. We’ve made five jumps of 10, which is the same as counting back five 10s or 50.

Did you find this easy to do? All we had to do each time is to change the number of 10s, didn’t we? The number of ones stayed the same. 98, 88, 78, 68, 58, 48. It’s very quick to skip count in 10s, and it saves a lot of time. Now that we’ve counted back five 10s, we just need to count back the remaining two ones. So, we’ll start with 48 and we’ll count back in ones twice. 48, 47, 46. We’ve found the answer by counting back, but instead of counting back 52 times, we split the number 52 into five 10s and two ones.

First, we made five quick jumps of 10 and then we made two smaller jumps of one. Can you see that altogether we’ve counted back 52? And so, we can say 98 take away 52 equals 46. We’re going to look at some questions now where we have to subtract a pair of two-digit numbers. At each time, we’re going to think about the jumps of 10s and ones that we can make to help us find the answer.

Which subtraction sentence matches the calculation on this number line? 80 take away 35 equals 27, 80 take away 53 equals 27, or 80 take away 63 equals 27.

If we’re ever asked to subtract two numbers, we can often find the answer by counting backwards. In this question, we’re shown a number line and it’s got some jumps marked on it, some in orange and some in red. Can you see all the minus signs? This tells us that we’re taking away 10s or ones each time. In other words, we’re counting backwards. To help us remember this, let’s draw little arrow heads on the end of each jump. This will show us the direction that we’re going. So, which number do you think we started with?

If we’re counting backwards along our number line in this direction, we must have started with the number 80. So, we know the first number in our calculation must be 80. And we know that it’s a subtraction sentence because we’re told so in the question. And also we can see that we’re counting backwards. Now, where do we end up? What’s the answer to our subtraction sentence? The answer is the number we finished on, and we can see this is 27. The subtraction sentence we’re looking for is going to be 80 take away something which equals 27. But if we look at our three possible answers, this doesn’t help us. They all begin with 80. They’re all subtractions, and they all have an answer of 27.

To find the correct answer, we need to think about the amount that’s being subtracted on the number line. There are one, two, three, four, five jumps of 10. So, we’ve counted back five 10s and then one, two, three ones. We know that five 10s are worth 50 and three ones are worth three. If we’ve subtracted 50 and then three, have we taken away 35, 53, or 63? The answer is 53, isn’t it? The number line shows that we started with the number 80 and then we subtracted five 10s and three ones, or 53. And we can see that the number we ended on was 27. The correct subtraction sentence is 80 take away 53 equals 27.

By counting back in 10s and ones on a number line, find 54 take away 29.

In this question, we need to subtract two two-digit numbers. We need to find the answer to 54 take away 29. And we’re told how to find the answer. We need to count back in 10s and ones on a number line. And we can see part of a number line below where the answer has started to be worked out. What’s being marked on the number line already? Well, firstly, we can see the number 54. This is the number that we’re beginning with. We need to take away 29 from this number. So we need to count backwards from 54.

And we’re told that we need to count back in 10s and ones. Now, if we’re subtracting 29, how many 10s and how many ones do we need to jump back? We know that 29 is the same as two 10s or 20 and nine ones. And this tells us the number of jumps we need to make. We need to count back two 10s and then nine ones. Let’s count back two 10s to begin with. So, we’re gonna start with the number 54. And we can see that our first jump of 10 is marked on the number line already. If we count back 10 from 54, we get 44.

Now, we can see part of the next jump of 10, but we can’t see it all. So let’s complete this next jump of 10. There, we go. We’ll label it minus 10 to remind ourselves what we’ve done. And if we count back 10 from 44, we reach 34. We’ve counted backwards two 10s, and we’ve gone from 54 to 34. Now, we just need to count back nine ones. One, two, three. Can you see how we’re labeling the number line by taking away one each time? 34, 33, 32, 31. Four, five, six, seven, eight, nine. 34, 33, 32, 31, 30, 29, 28, 27, 26, 25.

To find the answer to 54 take away 29, we started on a number line with 54 and then we subtracted 29 by jumping back two 10s and nine ones. The number we ended up on was 25. 54 take away 29 equals 25.

Use a number line to find 78 take away 45.

We need to find the answer to a subtraction here, 78 take away 45. And on the number line, we can already see the number 78 is marked on there for us. Now, if we’re going to take away 45, we need to count backwards. Now, we could count back in ones 45 times, but that’s gonna take us quite a long time. Instead, let’s break up the number 45 into 10s and ones, and then we can count back in 10s and then ones. 45 is the same as 40 plus five.

We know that 40 is the same as four 10s and five is equal to five ones. So, if we’re going to take away 45, we need to make four jumps of 10 and then five jumps of one. Let’s begin by counting back four jumps of 10. We’ll start with the number 78. 78, 68, 58, 48, 38. We’ve counted back four 10s and we’ve gone from 78 to 38. Now, we just need to take away five ones. So, we need to make five jumps of one, and we’ll start counting back from the number 38. 37, 36, 35, 34, 33.

We started with the number 78. And because we had to take away 45, we jump back four 10s and then five ones because four 10s and five ones are the same as 45. But by skip counting in 10s for some of the subtraction, it speeds things up a bit. The number we ended on was 33. So, we can say 78 take away 45 equals 33.

What have we learned in this video? We’ve learned how to use a number line to subtract a pair of two-digit numbers. We did this by counting back in 10s and then ones.

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