Arithmetic understanding

[Probability]

If a question asks to subtract 243 from 126, then written out like this;

126 - 243 = - 117

What I don't understand is why the math writer wrote the sum out like this;

243
-126
117

If the solution is supposed to be negative, how can the mathematician produce a positive solution?

Surely it should be wrote like;

-243
126
-117

I thought it was a mistake at first, but many examples are wrote this way, is there a mathematical reason for this?

I'm not a mathematician.

 

[Ishuda]

If a question asks to subtract 243 from 126, then written out like this;

126 - 243 = - 117

What I don't understand is why the math writer wrote the sum out like this;

243
-126
117

If the solution is supposed to be negative, how can the mathematician produce a positive solution?

Surely it should be wrote like;

-243
126
-117

I thought it was a mistake at first, but many examples are wrote this way, is there a mathematical reason for this?

I'm not a mathematician.

I can't thing of a mathematical reason and don't know the particular reason here. However many people are 'more comfortable' subtracting smaller numbers from bigger numbers and would do the
243
-126
117
and then add the minus sign to the 117. That is 126-243=-(243-126)=-(117)=-117.

So maybe they are not going through that last step of 'adding the minus sign to the answer'.

 

[Probability]

I can't thing of a mathematical reason and don't know the particular reason here. However many people are 'more comfortable' subtracting smaller numbers from bigger numbers and would do the
243
-126
117
and then add the minus sign to the 117. That is 126-243=-(243-126)=-(117)=-117.

So maybe they are not going through that last step of 'adding the minus sign to the answer'.

Thank you for your reply. Your explanation above I also worked that out, the parentheses became confusing to me, how would one know to include them to make the answer correct?

I understand how to get the 126 to the RHS which becomes - 126, and I also understand how to get the negative 243 from the LHS to the RHS and that is negative also, then - 243 - 126 = incorrect solution unless parentheses are used, and I can see why they are used when you multiply out the parentheses which brings back the -126 to a positive 126, what I don't know is how I know to include them?

 

[Ishuda]

Thank you for your reply. Your explanation above I also worked that out, the parentheses became confusing to me, how would one know to include them to make the answer correct?

I understand how to get the 126 to the RHS which becomes - 126, and I also understand how to get the negative 243 from the LHS to the RHS and that is negative also, then - 243 - 126 = incorrect solution unless parentheses are used, and I can see why they are used when you multiply out the parentheses which brings back the -126 to a positive 126, what I don't know is how I know to include them?

I'm not quite sure what you are asking. Do you mean how do you write
243
-126
117
to indicate that what you really want is to subtract 243 from 126? If so I suspect your
-243
+126
-117
is what you want.

Maybe what you want is
c = a - b
- c = - (a - b) = b - a
so
c = - ( b - a)