Can you Subtract by Adding?

[Trekker4747]

My SiL's taking a low-level college math course. One of the things, among many others, her instructor is doing is trying to teach her students to 'subtract by adding."

This practice confused my SiL so she was asking me about it, I researched it and I must admit that while the method of doing this is "fun" it also seems needlessly complex.

What do you think?

Here's how you do it:

We'll take two fairly large numbers: 346 and 297. For the sake of complexity I've made it so the number we subtracting has higher 10s and 1s digits than the 10s and 1s of the larger digit.

:steep inhale:

346 - 297

So what you do it you take the number we are subtracting and find its compliment - the number needed to make it into 1000. (Or 10 for a 1 digit number, 100 for a two digit number, etc.)

Finding the compliment is done by seeing what number is needed to turn the number in the one's place into a 10 - 3 in this case. And the number needed to turn the number into a 9 in the other places.

In 297's case, its compliment is 703.

Now we add 703 to 346 and get 1049. We then drop the one on the left and we end up with an answer of 49.

There, we've subtracted by adding. (In cases where the complimented number has fewer digits we "pad" it by adding nines.)

Do you perceive this as being easer than borrowing and carrying or just needlessly silly?

 

[The Sneeze Police]

Borrowing and carrying has worked for me for 40+ years.

The Subtract by Adding method seems a mildly entertaining but unnecessary.

 

[Trekker4747]

Borrowing and carrying has worked for me for 40+ years.

The Subtract by Adding method seems a mildly entertaining but unnecessary.

Kind of my thoughts. But darn if it isn't a bit fun.

I guess the "rationale" is that the borrowing and carrying mehtod is "messy looking" on paper. This, however, is the same mathclass that was teaching my SiL to do fraction work by drawing pictures.

 

[Starkers]

Ok my head hurts

One can also subtract by adding minus numbers of course

 

[Nerys Ghemor]

Borrowing and carrying has worked for me for 40+ years.

The Subtract by Adding method seems a mildly entertaining but unnecessary.

Kind of my thoughts. But darn if it isn't a bit fun.

I guess the "rationale" is that the borrowing and carrying mehtod is "messy looking" on paper. This, however, is the same mathclass that was teaching my SiL to do fraction work by drawing pictures.

I do something similar to this sometimes...but to be honest I'm not exactly sure WHAT it is I'm doing and I'd only be able to explain if I had a pencil and paper with a problem in front of me.

 

[nx1701g]

I subtract by adding by using negative numbers.

 

[Lookingglassman]

I declare myself king of the world and my first decree is that
2-2=4 just because I said so!

 

[trekkiedane]

I seem to recall something like this, well; the exact same thing really, but then I did go to school back in the day where electronic calculators were the size of dishwashers…

I declare myself king of the world and my first decree is that
2-2=4 just because I said so!

But if 1+1=3 for large values of 1, then what happens in your kingdom with 2-2?

 

[Omnius]

346 - 297

If I had to mentally calculate that, I'd do it like this:
346 - 297 = 346 - 300 + 3

(so I substract by adding.. a bit)
Your sample from your SiL seems indeed a bit too complex.

 

[JAG]

That is how I would do it as well^^^

 

[RobertVA]

The whole thing is nonsense!!!

It's adding complexity.
You still end up subtracting (297 from 1000 to get 703)!

 

[Jadzia]

I expect it's so you can work three digit subtractions out in your head more easily. Borrowing and carrying is hard to visualize for many people. But Omnius method is good too, providing one of the numbers is easy to round up or down.

 

[The Borg Queen]

So what you do it you take the number we are subtracting and find its compliment - the number needed to make it into 1000. (Or 10 for a 1 digit number, 100 for a two digit number, etc.)

And how do you work out what you need to make 1000 without subtracting that number from 1000 to begin with?

 

[thestrangequark]

Borrowing and carrying has worked for me for 40+ years.

It hasn't worked very well for most people, though.

There are many different ways to add, subtract, multiply, and divide; stacking with borrowing and carrying is just one way, and it works well for some. However, it is pretty inefficient and overly time consuming -- especially when one is doing math in one's head. It is also unnecessarily complex -- especially when teaching math to young children.
As a teacher you learn quickly that not every child learns the same way. I've found that students who are taught a variety of ways to perform a function vastly outscore their peers, not only on math tests, but also in other problem-solving situations. I was taught math the classic stacking, borrowing, and carrying way, and it worked well enough for me. However, when I started teaching I had to re-learn math the way it is taught today, and because of that, my math skills have vastly improved. I can do mental math (addition, subtraction, multiplication, division, percentages, fractions, and proportions) much faster than I could before, and with fewer errors.

It'll take some time, but as more schools adopt different approaches to teaching math (personally, I think using TERK and Everyday Math together makes for an exceptional math curriculum), the math scores of American students will greatly improve.

Oh, and drawing pictures is one of the best ways to teach fractions.

 

[RJDiogenes]

I do math in my head using Omnius' system as well. I sort of break it into easier chunks. It takes a fraction of a second.

This system does sound vaguely similar to some system I read about that was used by an ancient culture; I can't quite remember, though....

 

[Trekker4747]

So what you do it you take the number we are subtracting and find its compliment - the number needed to make it into 1000. (Or 10 for a 1 digit number, 100 for a two digit number, etc.)

And how do you work out what you need to make 1000 without subtracting that number from 1000 to begin with?

You find the complient for a number by figuring what number you need to make the number in the One's place a "10" and the rest of the numbers a 9 (including any 0's that may be there to fleshout the number you're subtracting so that it has the same number of places as the one you're subtracting from)

One should be able to find the compliment of a number without doing any math at all -that is just by "knowing" the compliment.

 

[The Borg Queen]

Hmm... I'm still not convinced that this method is any easier.

There seem to be more steps, for one thing.

 

[Trekker4747]

Hmm... I'm still not convinced that this method is any easier.

There seem to be more steps, for one thing.

Sure, there's more steps, but I'm not sure that necessairly makes it harder.

Keeping track of carrying numbers and such could likely confuse people, I dunno. It's kind of neat to me, but I like silly stuff like this.

 

[JuanBolio]

I subtract by adding by using negative numbers.

This is my preferred method as well.

 

[PKTrekGirl]

346 - 297

If I had to mentally calculate that, I'd do it like this:
346 - 297 = 346 - 300 + 3

(so I substract by adding.. a bit)
Your sample from your SiL seems indeed a bit too complex.

I do this too. And it makes sense, I think. Why do all of that borrowing and carrying when you can make it easy on yourself.

But those contortions that Trekker when through in the first post? Nah...I don't do that.