Maths Question, not sure how to explain it.

Question

I am a student that is going to be taking his Pre-GCSE in School soon, I am not very good with Maths but I have been watching a few videos online trying to self teach myself. I have been good so far but I have hit an error in a sum I am trying to do. I am currently on the stage of learning how to take away using long numbers, I can do it in my head but apparently I must write it down on a piece of paper. I am using the borrowing method, but I have hit a glitch, I'll explain what I mean by this below.

So, I have this difference:

2939293 - 
2943929

Everything is great up until the last number!

Here is what I do...

So I start with 3-9, it can't be done so I borrow 1 off the 9, making the 9 an 8 and making 3 13 which is 4, so I write 4.

Moving onto the next, 8-2 which is easy, its 6

I then go onto 2 - 9, which can't be done so I borrow 1 from the 9 to the left, making that 9 an 8 and making 2 a 12, so 12 - 9 is 3.

I then do 8 - 3 which is 5

I then do 3-4, which can't be done so again I borrow from the 9 to the left, making that 9 an 8, and making the 3 a 13. 13 - 4 is 9

then I move on to the 8 - 9, I can't do it so again I make the 2 to the left a 1 and 8 becomes 18, so 18 - 9 is 9.

I am then left with 1 - 2 but I have no left numbers to borrow from, what do I do?

Answer 1

Note that the first number is smaller than the second number ($29{\color{red}3}9293$ vs. $29{\color{red}4}3929$) - this means that the answer will be negative. You've done nothing wrong.

So what's the answer? Well, up until the last digit you have $995364$. You then have $1-2$ in the remaining digit. Your answer is (what you have so far)-(how much you still need to borrow): that is, $$995364-1000000=-(1000000-995364)=-4636,$$ and if you plug the original difference into your calculator you'll see that this is correct.

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How should you approach a difference like this in general?

Well, remember how subtraction works: $A-B$ is the same thing as $-(B-A)$. E.g. $1-2=-(2-1)=-1.$ So if you have a difference $A-B$ that you want to compute, first check whether $A$ is bigger than $B$. If it is, then go ahead as usual; if it's not, then compute $B-A$ as usual, and take the negative of that.

Answer 2

When doing subtraction like this, it's helpful to note which of the two numbers is bigger. For simplicity, lets call the two numbers $a$ and $b$. Now we are trying to find $a-b$. If $a$ is bigger than $b$, then we're fine. If $b$ is bigger than $a$, then calculate $b-a$ instead, and put a minus sign on the answer. This makes sense as we should expect to get a negative answer when subtracting a bigger number from a smaller number.