Question Video: Column Addition of Three-Digit Numbers with Partial Sums

Find 427 + 338. Hint: Make partial sums by adding the hundreds, adding the tens, and adding the ones.


Video Transcript

Find 427 plus 338. Hint: Make partial sums by adding the hundreds, adding the tens, and adding the ones.

Now although the table underneath this question might look complicated, all this question is really asking us to do is to add together two three-digit numbers. We need to add together 427 and 338. The grid is just there to help us. By writing the two numbers in a table like this, it can help us to see the different parts that make up these three-digit numbers. The hundreds are in a column on top of each other. So are the tens and the ones. Now, if somebody said to you, “What’s the total of 427 and 338?,” you might think to yourself, these numbers are really large. We can’t add them all up in one go.

Well, thankfully, we don’t have to do this. And our question shows us how to find the answer by adding each part separately: first, the hundreds, then the tens, and finally the ones. Let’s begin with the hundreds. The number 427 has a four in the hundreds place. And the number 338 has a three in the hundreds place. And so to find the sum of the hundreds, we need to add together 400 and 300. Four plus three equals seven, and so 400 plus 300 equals 700. Now let’s add the tens. And we can see from the side that the calculation is going to be 20 plus 30.

But where do these numbers come from? Well, in our first number, the digit two is in the tens place. And we know that two tens are worth 20. That’s where our 20 comes from. And in the second number, we have the digit three in the tens place, which is worth 30. So to find the sum of the tens, we need to add together 20 and 30. We know that two plus three equals five, and so two tens plus three tens equals five tens or 50. Onto the ones, what’s seven ones plus eight ones? We know that double seven is 14. So seven plus one more than this must be worth 15. And this is interesting because we can’t write the number 15 in the ones place. 15 is made of one ten and five ones.

So as we write the sum of our ones in our grid, we’re going to have to write one ten and five ones. And when it comes to finding the total of our tens in a second, we’re gonna have to remember that one extra 10. Now we found the sum of the hundreds, the tens, and the ones. But in order to find the overall total, we need to put these partial sums back together again. How many ones do we have? Zero plus zero plus five ones gives us a total of five ones. And if we look at the tens digits, there was zero tens in 700, five tens in 50. But don’t forget we had that one extra 10, didn’t we, when we added together our ones. So five tens plus one more ten equals six tens or 60.

And in the hundreds column, we’ve only got those seven hundreds to think about. So let’s put a seven in the hundreds place. We found a total of 427 and 338 by making partial sums. First, we added the hundreds, then the tens, then the ones. And to find the overall answer, we just added these three parts back together. 427 plus 338 equals 765.

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