Friday, June 30, 2006

Finger Arithmetic Part Seven

Continuing finger arithmetic from Part Six. This one is called Part Seven. It is the eighth part in the series.

Ten's Compliments. Back in Part Six, we added 7 + 8. We set 7, and added 8 by adding 3 then 5. Adding 3 involved a carry, generating an addition of 5 while remembering that we still have to add 5. Very complicated. This Ten's Compliments idea reduces the steps, and having to remember upcoming steps. It is similar to Five's Complements, introduced in Part Three.

The Ten's Compliment of a number is the number you add to get ten. For now, we'll only use the Ten's Compliment of numbers greater than five. So, the Ten's Compliment of six is four. The Ten's Compliment of seven is three. The Ten's Compliment of eight is two. And the Ten's Compliment of nine is one.

So how does this help? Let's return to the dreaded seven plus eight example. Start with two fists, then set two right hand fingers and the thumb. You'd like to add eight, which is five plus three, but you don't have three to add. Eight is ten minus two (the Ten's Compliment of eight is two). Subtract the Ten's Complement, which is done by subtracting both right fingers. Then add ten by adding a finger to the left hand. Read the result: fifteen. That's ten (the left finger), plus five (the right thumb) and zero (the right fingers). Again, we added 7 + 8, which is 7 - 2 + 10.

How about six plus seven from the last lesson? You do this the same way it was done in the previous lesson. When you have six set, you don't have three fingers to subtract, and you do have two fingers to add. The way it works is that you always have exactly one of these options.

The relevant examples are 6 + 9, 7 + 9, 8 + 9, 9 + 9, 7 + 8, 8 + 8, 9 + 8, 8 + 7, 9 + 7, 9 + 6.

Again, you are referred to the example generator, which can provide you with an infinite number of examples. Each time you click here, you get a new page. Use your back button to get back to the lesson. This is the same link as in the previous lesson.

Technically, we really introduced the Ten's Compliment of five, which is five in Part Five. It wasn't called that, and it just seems simpler to treat it as a special case.

Stay tuned for the introduction of two digit addition.

4 comments:

kitty said...

Are you referring to Chisenbop?

Stephen said...

Basically.

DWR said...

Thanks a bunch. I enjoyed learning the finger counting technique almost as much as I enjoyed your style of writing; it somehow appears wry though I can't explain why.

Stephen said...

Apparently, i somehow picked up my writing style from my mother. When i was in my 20s, she sent me a letter. I discovered two things. First, she's really funny. But then, on reflection, it became clear that she'd always been that way. Very dry humor. Every joke delivered with a perfect poker face. She didn't care if you got the joke or not, she just moved on. I say 'somehow'. I haven't seen much of it.