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Arithmos
Arithmos
Arithmos

Station  I
Wild Exploration 

Here are some “big question” ideas you might want to explore, or just think about.
Have fun!

Question 1

THERE IS NOTHING SPECIAL ABOUT BASE TEN FOR ADDITION

Here is an addition problem in a 151\leftarrow 5 machine. (That is, it is a problem in base five.) This is not a 1101\leftarrow 10 machine addition.

What number has code 2041320413 in a 151\leftarrow 5 machine?
What number has code 1324413244 in a 151\leftarrow 5 machine?

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What is the 151\leftarrow 5 machine answer?

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Question 2

THERE IS NOTHING SPECIAL ABOUT BASE TEN FOR MULTIPLICATION

Let’s now work with a 131\leftarrow 3 machine.

Find 1202×31202\times 3 as a base three problem.

Also, what are 111×3111\times 3 and 2002×32002\times 3?

Can you explain what you notice?

(In base three we should really be writing 1010 rather than 33 in each of these problems.)

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Question 3

Let’s now work with a 141\leftarrow 4 machine.

What is 133×4133\times 4?
What is 2011×42011\times 4?
What is 22×422\times 4?

Can you explain what you notice?

(In base four we should really be writing 1010 rather than 44 in each of these problems.)

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In general, if we are in a 1b1 \leftarrow b machine, can you explain why multiplying a number in base bb by bb returns the original number with a zero tacked on to its right?

Arithmos
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