Ars Calcula

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: