Write the four missing digits to make this addition correct.
And we’re given a vertical addition with four missing digits in it. But what’s the best way to find out what those missing digits are? We could start at the top and work our way through each missing digit downwards. But we know when we add two numbers vertically, we don’t add like this. We always start with the ones column and we work our way from right to left. Sometimes, what we add in one column will affect the next column along. So it’s important that we go about this in the same way.
Let’s consider the ones column to start with. Eight ones plus an unknown number of ones equals nine ones. It looks like the missing digit is one. But what if the answer is 19? That would still give us a nine in the ones place. Well, we know that eight plus 11 makes 19 and 11 is a two-digit number. We’re only looking for one missing digit. So the calculation must be eight ones plus one one equals nine ones.
Let’s think about the tens column. An unknown number of tens plus nine tens equals what seems to be one ten. How’s that possible? Well, it must be that the total is 11 tens. This would give us a one in the tens column. And it’s probably quite useful to put the one underneath in the hundreds column to remind ourselves when we get to the hundreds column to include it.
So what do we add to nine tens to give us 11 tens? We add two tens or 20. Now for the hundreds, six hundreds plus an unknown number of hundreds plus the one hundred that we exchange underneath equals zero hundreds. How is this possible? Well, this must be another example where we’ve exchanged. We’ve made a two-digit number.
If the calculation makes 10, then we can exchange 10 hundreds for 1000. And we still have a zero in the hundreds place. Six and the one hundred underneath makes seven hundreds. So to make 10 hundreds or 1000 we need to add three hundreds.
Now it would be very easy to make a mistake with the thousands column. Imagine we’d started off with the thousands. We’d have looked at it and said an unknown number plus three equals nine. The missing digit must be six. But because we work from right to left, we can see that we’ve exchanged 10 hundreds for 1000 and there’s 1000 underneath. What do we add to three plus one to make nine? Well, three plus one equals four. So what do we add to four to make nine? We add five.
5000 plus 3000 plus the 1000 we exchanged equals 9000. And that’s why it’s so important when we’re answering a question like this to include all the exchanged digits and also to always work from right to left.
Another quick tip is if we have time to do a quick check to see that the addition makes sense. Eight ones plus one one equals nine ones. Two tens plus nine tens equals 11 tens. Six hundreds plus three hundreds plus the one hundred we’d exchanged equals 10 hundreds, which of course is the same as 1000. Finally, 5000 plus 3000 plus the 1000 we’ve exchanged equals 9000. 9019, the answer is the same. So our missing digits must be correct.
From left to right and from top to bottom, the missing digits are five, two, three, and one.