Write the three missing digits to make this addition correct. Fifty-three thousand two hundred and what nine plus seven thousand four hundred and twenty what equals what tens of thousands six hundred and seventy-six?
It’s difficult to read the calculation with those gaps in it. There are three missing digits from the calculation. But we’re given enough information here to be able to work out what those missing digits are. And the way to find the answer is to go through each column as if we were adding it normally. And when we come across a missing digit, we’re going to think very carefully about what it could be.
First, we’ll add the ones. Nine plus what equals six? If we write this out by the side, we can see how strange this looks. We can’t add anything to nine to make six. So where does the digit six in the answer come from? What if it’s part of the number 16? That would give us a six in the ones column. What do we add to nine to get 16? Nine plus seven equals 16.
Some good advice is to include the one ten that we exchange in the tens column, because when we look at adding the tens column, we need to remember to include this. Now we can look at the tens column. What plus two tens equals seven tens?
Well, we know that five plus two equals seven. So could the answer be five tens plus two tens equals seven tens? No, because we’ve got one ten that we exchanged underneath that we need to include too. This is why it was such a good idea to make a note of it underneath. Instead of five, the missing digit is four. Four tens plus two tens equals six tens, but remembering the one that we exchanged equals our total of seven tens.
Even though there aren’t any gaps, it’s worth looking at the hundreds column just to check it makes sense. Two hundreds plus four hundreds equals six hundreds. Three thousands plus seven thousands equals 10 thousands. Again, this is an example where writing the small one underneath is a very good idea. We’ll see why when we get to the next column.
Five lots of 10000 plus nothing equals what? An easy mistake to make here would be to write the digit five in the ten thousands place. Five ten thousands plus nothing equals five ten thousands. And that’s why it’s so important that we remembered to exchange one lot of 10000 and to write it down underneath to remind ourselves. We’re not just adding five ten thousands and nothing. We’re adding another one lot of 10000 too. And so the missing digit is six.
We don’t have to write the small ones underneath to get the answer correct. All we have to do is write the correct missing digits. But it’s so easy to forget about them and make a mistake if we don’t write them down. So it’s a good idea just to include them in a question like this. 53249 plus 7427 equals 60676.
We used reasoning to find the three missing digits. We started with the ones column. And we looked at each column as if we were adding normally. And we thought very carefully about what each missing digit should be. So from top to bottom, the three missing digits are four, seven, and six.