Video: Understanding Place Value When Comparing Numbers

Is 200 + 90 + 8 <, = or > 200 + 30?


Video Transcript

Is 200 plus 90 plus eight less than, equal to, or greater than 200 plus 30?

In this problem, we’ve got two additions to compare. The first one contains three numbers, 200 plus 90 plus eight. And the second calculation just contains two numbers, 200 plus 30. Is the first addition less than the second one? Are they both worth the same? Or is the answer to the first addition worth more than the second one? We need to choose the correct symbol to use in between them.

Now, one way to find out the answer here would be to calculate the total of both additions and then just to compare the two totals. Which one is larger? And we will do this. But there is another way to find the answer. And that’s to use reasoning, to look at the numbers that we have in our additions and to think carefully about which one might be larger. What’s the same about our two additions and what’s different?

Well, the first thing that we can spot that’s the same about our two additions is that they both contain a number of hundreds and a number of tens. Although in our first addition, we’ve also got a number of ones too. But because we’re thinking about a number of hundreds and a number of tens, we can use a place value grid to help us. Something else that our two additions have got in common, if we look carefully, is that they both start off with 200. And this is where the reasoning part comes in. Both additions show an amount that’s been added to 200. So in a way, we could forget the number 200 in both additions and just concentrate on what’s being added. Which is larger, 90 plus eight or 30?

Well, we know that 90 plus eight has a value of 98, and 98 is larger than 30. So even though we haven’t found the actual totals, we can say that the first expression is going to be larger than the second one. Let’s put our two hundreds back in and find the totals to see if we are right.

Our first addition is 200 plus 90 plus eight. In other words, two hundreds plus nine tens plus eight ones. The total of 200 plus 90 plus eight is 298. And in our second addition, we’re adding 200 and 30. In other words, two hundreds and three tens. We don’t have any ones to add. The total is 230. Both numbers have the same amount of hundreds. But if we compare the tens digits, nine tens is greater than three tens. And so, we were right. The first expression is greater than the second. 200 plus 90 plus eight is greater than 200 plus 30. The correct symbol is: is greater than.

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