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## Main Question or Discussion Point

Without any rough work

- Thread starter jnbp13
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Without any rough work

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Forget 3-digit numbers. How would you multiply three 1-digit numbers "simultaneously"?

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Is there any method like crosswise method of multiplication of two numbers

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Three digits at time! In looking at an algorithm, which can be used in order to evaluate

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Do you understand the crosswise method? I mean understand why it works, not just how to execute the algorithm. Why does the crosswise method for computing the product of two numbers give the correct answer? If you think about that question, it might give you some insight for creating your own method for computing "bigger" products.

Mark44

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Okay then!

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@gopher

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I've made an algorithm myself to overcome this task

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But the thing is that it's too complex

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- Do you mean it's not clear how one is supposed to proceed? If so, you don't have a well-defined algorithm.

- Do you mean it requires too much working memory to use in practice? If so, change your algorithm to involve writing more things down, so you have less reliance on working memory.

- Do you mean it takes too long? If so, you may just be SOL. If I had to multiply three three-digit numbers without a calculator, it would take me quite a while. Maybe there's a more efficient (i.e. fewer steps, or easier steps) algorithm you can find, maybe not.

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why not?

(100*a+10*b+c)(100*d+10*e+f)(100*g+10*h+i) = 1000000 a d g+100000 a d h+10000 a d i+100000 a e g+10000 a e h+1000 a e i+10000 a f g+1000 a f h+100 a f i+100000 b d g+10000 b d h+1000 b d i+10000 b e g+1000 b e h+100 b e i+1000 b f g+100 b f h+10 b f i+10000 c d g+1000 c d h+100 c d i+1000 c e g+100 c e h+10 c e i+100 c f g+10 c f h+c f i

you can look up the one digit multiplications in a table.

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Put the calculator in your head.

That's how you do it.

That's how you do it.

Borek

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That's the first multiplication.1000000 a d g

That's the second multiplication.100000 a d h

That's third, and so on.10000 a d i

Three consecutive multiplications already, and we are still far from the final result.

Basically it depends on how you define "at the same time".

Mark44

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To multiply three numbers, you can use the fact that multiplication is associative (i.e., (ab)c = a(bc)) to multiply a pair of the numbers and then multiply that product by the third.

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If I multiply two 1 digit numbers, I just use memorized multiplication tables. You could do that with multiplying 3 1 digit numbers also. Mulitiplying with at million is just a left shift.

To multiply three numbers, you can use the fact that multiplication is associative (i.e., (ab)c = a(bc)) to multiply a pair of the numbers and then multiply that product by the third.

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