How to Subtract Using Reverse Addition

This was requested by Jake’s Mom. Since she was taught to borrow, she was dumfounded at what Jake brought home. Happily, Jake is young enough and unscathed enough to not balk at a “different” method that what his mom was taught. He got it right away.

But Jake’s mom, on the other hand, is struggling.

If your kiddo is being taught this, here’s a way to look at it that might help you understand what’s going on.

First, a brief review on the relationship of subtraction to addition:

Here’s what “reverse addition” looks like in relation to our old friend “borrowing,” using the same example:

And here’s an example:

Another example (along with a special tip for you):

And a final example, just to help you get the hang of it.

Still have questions? Post them in the comments. Need something else? Request it and I’ll get to it as soon as I can.

Thanks, Jake’s Mom, for the question!

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8 Responses to How to Subtract Using Reverse Addition

Neal M says:

January 24, 2011 at 2:55 pm

Great videos, Bon! Keep it up – I look forward to seeing more.

Bon says:

January 26, 2011 at 10:43 am

Thanks, Neal. Glad you’re here!

janeyquiel says:

January 28, 2011 at 4:57 pm

I agree with your assumption.

- Bon says:
  
  February 2, 2011 at 9:52 am
  
  Thanks, Janeyquiel!
  
Tammy Jolley says:

March 7, 2011 at 1:36 pm

Thanks! I like this way better for myself. Jake doesn’t seem to mind either way but has obviously been taught this way. Appreciate the lesson so I know what he is doing:)

Shawn Urban says:

August 29, 2011 at 2:17 pm

Hi Bon,

One advantage I see with the reverse addition method is that it bleeds quite nicely into algebra, certainly more so than subtraction does.

I wonder how division via reverse multiplication looks. That might be interesting to play with to find out.

Shawn

- Bon says:
  
  September 4, 2011 at 7:39 am
  
  Thanks for your comment, Shawn.
  
  I hadn’t thought about the implications of reverse addition on algebra. Thanks for pointing it out.
  
  Reverse multiplication… I’m going to have to think on that one. Interesting.
  
Paul Gouin says:

March 28, 2016 at 8:04 pm

In France where I studied, kids learns to write the 4 operations without ANY additional scribbles (except sometimes large additions).

They think about the subtraction as subtraction (not reverse addition) but the layout of the operation is the same as the one presented above as reverse addition.
The EXPLANATION given is called “constant difference” : I do not change a difference if I ADD THE SAME AMOUNT to both terms of a subtraction: add 10 to the TOP number in any column, and then add 1 power of the next higher kind to the BOTTOM number of the next column.
63 – 25 = (63 + 10) – (25 + 10)
They don’t write the 1 carried over, they just remember it for a fraction of a second.