8 June 2012Posted by Photius

The last two posts covered mental addition (both by using nearby numbers and by breaking things down -- which is really just a special case of repeatedly using nearby numbers). In this post, we'll talk a little about mental subtraction.

We won't be straying too far from the last post, though, since our first trick for mental subtraction is: Subtracting by adding.

Here's what the trick looks like in practice: To compute $$107 - 28$$, we think "$$107 - 30$$ is $$77$$, and $$77 + 2 = 79$$, so... $$79$$!"

Another example: To mentally compute $$254 - 119$$, we think "$$254 - 120 = 134$$, plus $$1$$ gives... $$135$$!"

Here's how the trick works. Suppose we wish to calculate $$512 - 385$$. Now, $$385$$ is a "complicated-looking" number, and it would be hard to subtract it from $$512$$ directly. So we replace $$385$$ with a larger number that looks easier: In this case, we'll choose $$400$$. Now we easily compute $$512 - 400 = 112$$. To get our final answer, we need to add $$400 - 385 = 15$$ to this. (This final addition is why the method is called "subtracting by adding.") So we get $$112 + 15 = 127$$ as our final answer.

Here are some more examples: