Question Video: Understanding Place Value When Adding Multidigit Numbers Involving the Expanded Form of Numbers Mathematics • 4th Grade

Pick the sum equal to 3,324 + 5,564. [A] 9,000 + 800 + 80 + 8 [B] 8,000 + 900 + 80 + 8 [C] 8,000 + 800 + 80 + 9 [D] 8,000 + 800 + 80 + 8 [E] 8,000 + 800 + 90 + 8


Video Transcript

Pick the sum equal to 3,324 plus 5,564. Is it 9,000 plus 800 plus 80 plus eight, 8,000 plus 900 plus 80 plus eight, 8,000 plus 800 plus 80 plus nine, 8,000 plus 800 plus 80 plus eight, or 8,000 plus 800 plus 90 plus eight?

In this question, we’re given a pair of four-digit numbers to add together. But instead of finding a number that’s equal to their total, we’re asked to pick a sum. Our five possible answers are all additions, and only one of them makes a total that’s exactly the same as the total of the two numbers in the question. One way to find the answer could be to start off by adding our two numbers together and then go through each of our five possible answers adding them to see which one has the same total. But that’s a lot of addition we’d need to do. And there’s a quicker way to find the answer.

Can you spot anything interesting about the five additions that are listed? Well, they each show a number of thousands plus a number of hundreds plus a number of tens plus a number of ones. It’s almost as if our total of 3,324 and 5,564 has been split up into its thousands, hundreds, tens, and ones. Let’s try seeing how many thousands, hundreds, tens, and ones there’ll be in our answer. Let’s break apart the two four-digit numbers we’re given. Now, this is the sort of addition we can do in our heads, but we’re going to make a note of everything that we do so that it’s clear what strategies we’ve used.

So to begin with, let’s see how many 1,000s there’re going to be in our answer. Our first number contains three 1,000s and there’s a five in the thousands place of our second number, and 3,000 plus 5,000 equals 8,000. Looks like the number of 1,000s in our answer is going to be eight. And if we look at each of the possible additions, we can see that one stands out. The first one has nine 1,000s, not eight. So let’s cross this one through. It’s not the right answer. The others though could be. Let’s break apart the hundreds. Our first number contains three 100s and our second number contains five 100s. This is a very similar addition to the one we’ve just done, isn’t it? 300 plus 500 equals 800.

Now, if we look at our remaining possible answers, we can see that most of them do have 800 as the hundreds number in the addition. But can you spot one of them doesn’t? The first one on our list has 900. So we’re gonna cross this through. This one is not correct. Now it’s time to look at the tens. Our first number contains two 10s or 20 and our second number contains six 10s or 60, and 20 plus 60 equals 80. Now, if we look at our remaining answers, we can see that two of them do have 80 in them. But if we look at the last answer, we can see 8,000 plus 800 plus 90.

Let’s cross this one through. We want to be adding 80 not 90. Finally, we can break off the ones in both of our numbers and add those. Four ones plus another four ones makes a total of eight ones. We’ve found the total of 3,324 and 5,564 by breaking these two numbers apart, adding the thousands, then the hundreds, then the tens, then the ones.

Now, if we were to find the actual total, we’d combine all our answers together again. But of course, our question doesn’t ask us to do this. We’re just looking for a sum that represents 8,000 plus 800 plus 80 plus eight, and here it is. It would make an interesting answer, wouldn’t it? 8,888. The sum that’s equal to 3,324 plus 5,564 is 8,000 plus 800 plus 80 plus eight.

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