Thread: Multiplication by means of the distributive property Poll

Hello,
I am new this online forum, so hopefully I asked this in the right category. I been writing little math blogs about topics me and my friend like to discuss, most of it deals with concrete mathematics. Its a nice little hobby of mine, I like to research numbers and their patterns when ever I get a chance too. The question that I was wondering is do any of you mathematicians or non-mathematicians ever use the distributive property to do multiplication?

I wrote this article about using the distributive property to do multiplication a while back, and wondered does anyone actually use that method? If you are a none mathematician, how do you find multiplying numbers easier? I wrote this long article on how you could multiply in your head faster, but I not really sure if I can correctly state that it is faster.

To be more clear,
Do you multiply numbers like they teach in elementary school, line by line. Or do you use some other method to do multiplication faster.

Cheers,
Obitus

Given the nature of this particular forum, I'll allow the post even though it's spam for your methods. But I'm watching...

First, your poll needs another category: People who know the distributive property but don't use it.

And "your" is "you are" or "you're."

Heck, I just use my fancy calculator. I am a Physicist after all.

-Dan

I am sorry, did I do something I am not supposed too?

By spam, I assume you don't like my link to my article. If against the rules I can take it down. I just wanted people to know what I am talking about.
I can just post what I wrote on my blog into here, if that would help. I doubt any one would want to read that long of a post. Also, thanks for the grammar correction. It is still good to see people care about proper use of English (I mean that sincerely, not being sarcastic so please don't take it as so).

I don't know how to edit a poll, I am new to this forum posting. I will check the "edit post" option one more time.

What do you use when your calculator is not available?

Cheers,
Obitus

I was just checking different categories on your forums that interest me, I had no idea you guys actually get that much spam. No wonder your suspicious of me, but I am only interested in posting math topics here.

Originally Posted by obitus

What do you use when your calculator is not available?

Cheers,
Obitus

There is a joke about a Physicist, an Engineer, and a Mathematician at the horse races. A man comes up to them and asks them if they could predict which horse is going to win. The Engineer says, "The mass of the jockey and the horse will come to play and then there is the drag coefficient", etc. The Mathematician says "There are eight horses here and all but one of them has had injuries while racing", etc. The Physicist says "Let's start with a spherical horse..."

If I don't have access to a calculator then I shamelessly estimate using round numbers so I don't have to do "hard" math.

-Dan

Originally Posted by topsquark

If I don't have access to a calculator then I shamelessly estimate using round numbers so I don't have to do "hard" math.

-Dan

Well that is kind of what I was talking about in the article, I break down the multiplication in terms of the tenths place. Then I just do the multiplication of single digits, only some of the digits have extra "padded zeros". I guess people just don't think about multiplying as much any more, people are more comfortable using machines. Don't think I will find my answer here, but I appreciate your input.

On a side note, do you know what my professor calls a physicist? A "wanna be mathematician"

In higher mathematics, one rarely has to multiply big numbers. They say that in abstract algebra, even numbers have purely symbolic meaning. If I do need to multiply, say, 21 * 35 in my head, I indeed represent it as 20 * 35 + 35 = 735 (not sure if this is what you are talking about). But if it is, e.g., 24 * 37, then I would probably do a long multiplication.

Ok, I will give you an example: Lets take 24*37
I first pick the bigger number 37 and break it down by the tenths place and so on:


I do the same thing for 24:
[tex]24 = 20 + 4[\tex]

I then multiply each factor by the other factors:





Then I just add all the numbers:


I double check my work to see that I am right, and I am. Then I am done with the problem, this all of course happens much faster in one's own head.

I tried to explain that the best I could in my article, but then I realized people would get discouraged from ever using such a technique cause it looks long. Until I started to tutor in my undergraduate career, I found that none math majors found it easier to do this then relying on a calculator all the time. So, I figure I would ask on here to see who would use such a technique.

I did not come up with anything new or re-invent the wheel, all I did was break up the numbers to do simple multiplication. I try to get people to do mental math rather than rely on a machine, I can understand why you would use a calculator when you have to calculate big numbers.

i think of (positive integers) as polynomials in 10.

interestingly enough the way we multiply numbers "normally" (like we are taught, early in life) is somewhat "backwards", doing the 1's first, and "carrying 10's over (as 1's in the "ten's place")" leaves us totally in doubt as to what the answer is until we are completely finished.

it makes much more sense to, when multiplying 24*37, to multiply 20*30 FIRST. then we know our answer is more than 600.

the two "cross-terms" are 20*7 and 4*30, these are going to be the next largest contributors, in terms of size, contributing 140 and 120 to our total. now we're up to 860, and we are not more than 81 off, at this point.

in fact, we are exactly 28 from the desired total, which gives 888. the whole idea of doing it this way is "we keep getting closer" increasing our confidence in the final answer as we add more terms.

another "rough estimate" can be obtained by writing 24*37 = 25*37 - 37 < 25(4*9 + 1) = (25*4)*9 + 25 = 925, and since 50 > 37 > 25, we should be between 875 and 900.

5's and 2's are easy to work with in our decimal system, so finding a nearby multiple of 5 and/or 2 in our factors, reduces calculation with "hard numbers" (like 7, for example).

the distributive rule rocks. don't trust machines to think for you. fight the power!

Originally Posted by obitus

On a side note, do you know what my professor calls a physicist? A "wanna be mathematician"

Always remember that I can ban you...

When I was in High School I learned a similar method with the intention of doing it mentally. Every now and again I would work a problem. Of course people saw me gazing off into space and thought I had some kind of a problem. (If only they knew! Buwahahaha!) So I actually was doing that at one point.

-Dan

Originally Posted by topsquark

Always remember that I can ban you...

When I was in High School I learned a similar method with the intention of doing it mentally. Every now and again I would work a problem. Of course people saw me gazing off into space and thought I had some kind of a problem. (If only they knew! Buwahahaha!) So I actually was doing that at one point.

-Dan

Well played sir!
Yes, thats a new fad it seems. Students get all sorts of labels, not just from other students any more but from teachers as well.

At Deveno:
Yes, you get what I am talking about. I actually sometimes break down the numbers even more until I get 10 and 5 in the factors. For example with 24 and 37


sow now I only need to do two calculations:

I wonder why nobody teaches it this way?