# Is there a name for this method of column addition and subtraction?

Suppose I want to subtract 46 from 52. Instead of the borrowing method, I can use this method: $$\begin{array}{r} & 5 & 2\\ -\!\!\!\!\!\!& 4 & 6 \\ \hline & & -4 \\ +\!\!\!\!\!\!& 1 & 0 \\ \hline & & 6 \end{array}$$ where I am essentially adding the difference in the ones place (-4) to the difference in the tens place (10). Similarly, suppose that I want to add 79 to 52. I can write $$\begin{array}{r} & & 5 & 2\\ +\!\!\!\!\!\!& & 7 & 9 \\ \hline & & 1 & 1 \\ +\!\!\!\!\!\!& 1 & 2 & 0 \\ \hline & 1 & 3 & 1 \end{array}$$ where I am adding the numbers in the ones place together to get 11 and the numbers in the tens place together to get 120. I then add these two results together to get the final answer. Is there a name for this method of column addition and subtraction?

## 3 Answers

The method of addition and subtraction that you mention is not new. For now, I provide one reference, but I'm sure there are others. Note that your method of subtraction makes one big assumption that is not needed for the traditional method: you assume that students are familiar with negative integers.

The website Knowledge Over Grades uses a slight variant of your subtraction method: instead of "subtracting from right to left" it does the subtraction of larger powers of 10 first. It calls the method "subtraction of multi-digit numbers without regrouping or borrowing." (It assumes that the student is familiar with place values and negative integers.)

Note that there seems to be a typo in the image. (It uses the word carrying instead of borrowing.)

The website calls the addition method you mention "addition of multi-digit numbers without regrouping or carrying."

• Thank you for your answer! Sep 12 at 9:30
• Is there a reason why we don't teach younger students about negative numbers early on? Sep 12 at 10:34
• @mhdadk Perhaps because negative numbers are more difficult to understand. You can post that as a new question, but you'll have to specify what you mean by "younger students" and "early on." Sep 12 at 13:00

I don't know if your idea has a name, but it feels weird when you try to apply it to something like 10-4:

$$\begin{array}{r} & 1 & 0\\ -\!\!\!\!\!\!& \! & 4 \\ \hline & & -4 \\ +\!\!\!\!\!\!& 1 & 0 \\ \hline & {\color{red}1} & {\color{red}-}{\color{red}4} \end{array}$$

Since the sum of the ones place (-4+0 = -4) and the sum of the tens place (0+1=1), the "6" you put on your example seems to be forced, at least to me. I mean, if you want to teach this to kids, you will have to give a second thought on the rules.

• "the "6" you put on your example seems to be forced, at least to me." Fair enough. It also seemed a bit forced for me as well, and I was hoping there is a cleaner way of doing it. Sep 8 at 13:31
• so 0 is the only exception? @mhdadk
– BCLC
Sep 12 at 7:27

Your method is circular. Try:

1000000
−     1
−−−−−−−
100000
−1


Now what??

• This was posted as an answer, but it does not attempt to answer the question. It should possibly be an edit, a comment, another question, or deleted altogether. Sep 12 at 5:46
• @JoelReyesNoche: It is an answer. Why should a circularity in the method not be pointed out? Also, it's quite ridiculous that you criticize my answer although it is a clearer depiction of the problem than FormerMath's answer (which has 4 upvotes). Sep 12 at 5:52
• The question is "Is there a name for this method of column addition and subtraction?" I can't see how your post answers it. Sep 12 at 7:52
• But you have a point. FormerMath's post also does not answer the question. (That is why I did not upvote it.) I will now flag that post as "not an answer." Sep 12 at 7:55
• I tried converting these two answers to comments but the formatting doesn't work well in comments and the information is lost. It would certainly be better if both of them were comments, but I'm just going to leave them for now because they seem to be the best way this platform has of highlighting an important issue to the original poster. To be clear, I think the flags and discussion here were useful and helpful. Sep 12 at 14:52