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

Find 263 + 219. Hint: Make partial sums.


Video Transcript

Find 263 plus 219. Hint: Make partial sums.

In this question, we need to add together two three-digit numbers, 263 and 219. Can you see them both written in this place-value table? You know, writing two numbers on top of each other in a place-value table like this can be really helpful when writing them. It helps us to think about each part of the numbers separately. The hundreds digits are above each other in a column. The tents digits are in their own column and so are the ones. Thinking about the hundreds, the tens, and the ones separately can help us find the overall total. We know this because we’re given a hint, and it tells us to make partial sums. In other words, we need to add together the different parts of our two numbers.

Step one, let’s add the hundreds. If we look at the digits in this column, we can see that both of our numbers have two hundreds. And we know that the total of 200 plus another 200 equals 400. That’s right, 400 as the sum of our hundreds. Step two, we need to add the tens part. The number 263 has six tens, which are worth 60, and the number 219 has one ten, which is worth 10. Six tens plus one more ten equals seven tens, which are worth 70. The sum of the tens part is 70. Step three, we need to add the ones. In 263, there are three ones, and in 219, there are nine ones. It might be easier if we start with a larger number here and work out nine plus three more. Nine plus three equals 12.

Now we can’t write 12 in the ones place because it’s made up of one ten and two ones. So we’re going to have to record our answer by writing a one in the tens column and a two in the ones column. It’s important to remember that we’ve done this because even though we’ve added the ones, we’ve given ourself an extra ten to add when it comes to adding up all the tens at the end. The sum of the ones part is 12. Step four, add the partial sums. We found the sum of the hundreds, the tens, and the ones. And now to find the overall answer, we need to combine these back together again.

How many ones do we have? Zero plus zero plus two makes a total of two ones. How many tens do we have? Zero tens plus seven tens equals seven tens. But let’s not forget we’ve got one more 10 to add onto. This was the 10 that we got when we added our ones together to make 12. So seven tens plus one more ten equals eight tens. And because the digit eight is in the tens place, it’s worth 80. Finally, we’ve only got the digit four in the hundreds place, so the total of our hundreds is four. We found the total of 263 and 219 by making partial sums. We found the sum of the hundreds part, the tens part, and the ones part and then finally added together these partial sums to find the overall total. 263 plus 219 equals 482.

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