Practicing and Checking Multiplication With Playing Cards (2)

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To check multiplication of single digits by longer numbers with playing cards:

We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining.

It also pays to know why checking with nines-remainders works. Both of those things are beyond the scope of this article, but I’m working on a booklet and a video about how to check your answers for all of the basic operations of math using “number crunching”. There are lots of tips and shortcuts that make this method absolutely simple and effective. Let me know if you’re interested by using the “Contact” box near the upper right hand corner of this page.

(This video will be re-edited and uploaded by the end of Wednesday, April 30)

If you know about crunching, you’ll be interested to know that practicing with cards like this is perfect for checking with crunching. It turns out that if you crunch all the digits from zero to nine, you get a crunch number of 0.

Since we’ll always use sets of cards to represent the digits from zero to ten, we’ll always get a crunch number of 0.

So take whatever digit you were multiplying by, you’d have to multiply it by 0 to get your final check number. As you know, anything times zero is zero, so whenever you practice with cards like this, your check number will always be zero!

So if the crunch number of your answer is anything but zero, you have made a mistake somewhere.

Starting with ten cards is pretty easy. It turns out that as long as you use complete sets of all ten digits from 0 to 10, you will always have a check number of 0, no matter how many sets you use. So you can use ace to ten of as many suits as you like (as long as you remember that the tens count as zeros, and aces as ones).

That makes sense, doesn’t it? Because if a single set of zero to nine crunches to 0, then two sets must also crunch to 0, because 0 + 0 still equals 0.

In a very few days you should be able to work yourself up to multiplying any single digit number by a full set of forty cards (four sets of ace to ten, with all suits) within a few minutes. And then another minute or so to check them.

One of the benefits of doing it like this is that you are going to have to do all the additions and subtractions to get the nines-remainder of a forty or forty-one digit number in order to check it. That’s great practice in those two operations.

This is a fantastic morning exercise for children or adults. When you do something like this before breakfast, your mind becomes much more awake than it would have been.

Watch the video, then try it.

By the way, you may have noticed that at some point in video, I say, “The number has to crunch to nine,” where you may have thought I meant to say, “zero.” But remember, in Mod 9 (nines-remaindering, or “crunching”) zero is nine.

Did you know that technically, you can use any digit-remainder to crunch with, not just the nines-remainder? Most of the shortcuts (ask me about them) don’t work with nines-remainders other than nines, though, so that’s why we use nines, mostly.

Elevens-remainders are good to use as well. They have some shortcuts, just not as many as the nines, though. If you need to be absolutely sure of your answer, it’s best to check with the nines, and the elevens. I’ll have more posts up soon about each of them, and they’ll be thoroughly covered in the booklet that will be out soon.

Remember, a little bit of knowledge can be dangerous; so when you use numbers-crunching, be aware that it is “just a trick” until you understand it more deeply.


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