Video: Comparing Two-Digit Numbers Using the Number Lines

Compare the numbers on the cards. Which symbol is missing? Hint: Use the number line. 84 _ 48. [A] < [B] = [C] >

04:16

Video Transcript

Compare the numbers on the cards. Which symbol is missing? 84 what 48. Hint: use the number line.

At the very bottom of this problem, we’re given three symbols. We’ll go through what each one means later on. We use these symbols to compare numbers together. And we’re given two two-digit numbers. We need to decide which of the three symbols goes in between these numbers. The two numbers that we need to compare on the cards are 84 and 48. We need to think about whether 84 is less than 48, whether it’s greater than 48, or whether the two numbers are the same.

Now, there are different ways we could do this. But in this particular question, we’re told how to find the answer. We’re given a hint and it says, use the number line. Now, when we’re given a hint in a question, it usually means “do this.” So let’s use the number line to help us. I can’t see the number 84 on this number line, can you? Where do you think it belongs? Well, I can see the number 80 here. The number 90 comes after this, and we know that 84 is in between 80 and 90. Can you see this notch halfway between 80 and 90? Because it’s halfway, we know that it stands for 85. And 84 comes just before 85.

So let’s draw an arrow just before this middle notch. And we’ll label it 84 just to remind us what we’re labeling. Now, let’s label our second number. Where’s the number 48 on the number line? Can you see the number 40? And we can see the number 50 after it. The halfway point in between must be 45. And we know that 48 comes after 45. It’s nearly 50. So let’s draw an arrow just before 50, and we’ll label it 48. This is a good question, isn’t it, because it’s already got us thinking about number lines and we haven’t even started comparing these two numbers yet.

But now that we’ve labeled our numbers, we can compare them. Where’s the number 84 compared to 48? We can see that it’s in this direction. It’s to the right of the number 48. We know as we move to the right along this number line, we go from smaller to larger. We can see this if we look at the numbers as a label, can’t we? We start at zero, and as we move to the right, we go on to 10, 20, 30, 40, and so on. These numbers are getting bigger and bigger. So because 84 is to the right of 48, it’s a larger number. 84 is greater than 48.

Now, we just need to choose the correct symbol to use in between the two numbers. Which symbol means is greater than? Well, we know that this symbol means is equal to or is the same as. So let’s cross out this symbol. We know this isn’t right. Now, we’re left with these two symbols that look a little bit like arrows. It’s often easy to get confused. Which one means is greater than? The way we can remember which is which is that the narrow part of each arrow always points to a smaller number, the wider part of each symbol always points towards the larger number. And the other thing to remember is that we always read from left to right.

So if we look at this first symbol, we can see that we start with a smaller number, end with a larger number. The smaller number is less than the larger number. So this symbol means is less than. And if we read the second symbol from left to right, we can see that we start with a larger number. The larger number is greater than the smaller number, so this symbol means is greater than. Hopefully, we’ve reminded ourselves which symbol we need to use. 84 is to the right of the number 48 on our number line. And we know that all numbers to the right of another number are larger numbers. The correct symbol to use in between 84 and 48 is the one that represents is greater than. 84 is greater than 48.

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