Complete the expression. 6269317 subtract what equals 3128031.
Here, we have a subtraction with a missing number. We don’t know the number that we’re taking away. But there are two ways we can work it out. The first method we could use is to apply our knowledge of subtraction and how it works. If we know the whole amount, we don’t know what number we subtract, but we do know what number we’re left with. Then, we can think of this as being like a part-part-whole model, where we only know one of the parts. So, to find the second part, we just subtract the part we do know. So, we could find the answer by calculating 6269317 take away 3128031. This would give us the missing number.
Now, there’s another method we could use. And if we look carefully, we can see that the calculation has been written using vertical subtraction, or column subtraction. What we could do is go through the subtraction column-by-column as if we were working out the answer. We might not know the digit we’re subtracting each time, but we do know the starting digit and the answer. And we can use these two pieces of information to work out what the missing digit each time is. This is using our reasoning skills. Let’s use this method to find the missing number.
In the ones column, we have seven take away something equals one. So, this is a case of just thinking what do we take away from seven that leaves us with one. Seven take away six equals one. Our missing number has a six in the ones place. In the tens column, we have one lot of 10 subtract something equals three lots of 10. Wait a moment! How can we subtract something from one lot of 10 and be left with three lots of 10?
Well, clearly the digit in the second number must be larger than one. And so, this means when calculating to find the answer, we’d need to exchange. And we take one lot of 100 and exchange it for 10 tens. This way, the number in the tens column is 11. And this way we can take away something and leave us with three tens. What do we subtract from 11 to get three? 11 tens take away eight tens leaves us with three tens. You know, it’s columns like this last one that make this an interesting way of trying to solve the problem. It turns it into a puzzle where we need to look for clues to try and solve it.
In our next column, we can see how important it is to write on the calculation as we go along. You remember we exchanged 100, and we were left now with two hundreds. If we hadn’t recorded that, the digit would be three hundreds, and we’d get the wrong answer. So, it was important that we write on our calculation as we go along. Two hundreds take away what leaves us with zero hundreds? Well, for us to be left with zero hundreds, we need to subtract those two hundreds. The next digit is two.
In the thousands column. We start with nine thousands, and our answer is eight thousands. So, the digit we must subtract is 1000. In the ten thousands column, we start with six lots of 10000, or 60000, and we end with two lots of 10000, or 20000. What do we subtract from 60000 to get to 20000? Six take away four equals two. So, this four has a value of 40000.
In the hundred thousands column, we start with 200000, and we end with 100000. To get there, we need to subtract 100000. So, the digit in the hundred thousands place is one. Finally, in the millions column, six million take away something leaves us with three million. Six million take away three million equals three million.
So, it seems most of the columns were quick to work out. There was only that one column where we needed to think about exchanging and required a little bit more thought. So, although we could’ve found the missing part by subtracting the answer from the starting number in our subtraction, we chose to apply our knowledge of column subtraction and to predict what each digit was going to be. The missing number in our calculation is 3141286