>>16866219
Try looking up why writing was invented in the first place before asking stupid questions.

>>16866219
I prefer it like this instead:
32 × 15
= 16 × 30
= 8 × 60
= 480

You are making a falce assumption that most blacks can count.
They can't even add together double digit numbers

>>16866219
In "the Joy of x" the Autor descipes how humans get to numbers and caluclating by observing patterns.
For multiplication picture a box of bottels. If you allready know numbers and addition it's quite intuitive to come up with "that is 3 times 4 bottels so 4 + 4 + 4 and than you go on a little more with that thought and abstract it and than you have general multiplication. As this is actually quite usefull people will do it frequent and because its hard to allway mentaly picture boxes if they get bigger someone comes up, by abstraction, with some algorithm to solve it.

>>16866398
I prefer it like this instead:
15 × 32
= 15 × 2 × 2 × 2 × 2 × 2
= 30 × 2 × 2 × 2 × 2
= 60 × 2 × 2 × 2
= 120 × 2 × 2
= 240 × 2
= 480

>>16866219
OP you sure about this? Symbolic expressions and abstract thinking in math, something all of us take for granted today, is a very recent thing in human history. Before that math was all in words and problems were tied to real life situations, not as separate abstract ideas. If you were to go back to the Middle Ages and ask the average person what "15 times 32" is, they probably won't know. Not cause they're dumb but cause those abstract mathematic concepts weren't really a thing. If you guys think I'm bullshitting, some languages in the past didn't even have words for big numbers.
>>16866231
Most of modern mathematics is only about 500 years old.

>>16866838
>If you were to go back to the Middle Ages and ask the average person what "15 times 32" is, they probably won't know.
People in the Middle Ages were regularly trading large quantities of goods, stocking inventory, maintaining supplies for their craft, kept livestock, counted their harvest, saved up money or dealt with military formations made from that amount of people. 15 x 32 is not a particularly large number that people wouldn't have come across in daily life.

>>16866219
never knew u could do this

>>16866828
You're in luck, that 32 = 2^5.
But one can lose track, when doubling many times.

And almost everyone has 8 × 6 = 48 memorized.

>>16866923
I was thinking more of peasant villagers than more educated classes. Math was just directly tied to their farm, not as some abstract theoretical field we see it as today. Acres, cartloads, stones, bushels, paces. Local agricultural units was basically what most of the world used as measurements before the metric system.

But yeah you're right more educated people like clergymen and merchants used bigger numbers & more complex math. But even for these educated people they had no Hindu-Arabic Numerals, no place value, no decimals, no systematic expressions, none of the stuff we teach to literal brain-rotted 8 year olds nowadays. Everything was written in words and math could be different in the same country, since there was no standardization back then. Mathematics was painfully slow and primitive before the Scientific Revolution.

>>16866219
>Even today in a poor african country people cannot read or write but can quickly multiply numbers in financial transactions
source?? evidence?

>>16866398
>>16866828
I prefer 15 x 3 x 10 + 15 x 2
450 + 30
480
you get to exercise your memory AND basic operations

>>16866219
Why wasn't I ever taught this in school?

>>16867709
it was. ever heard of associative property?
15 x 32 = 15 x (2 x 16)
= (15 x 2) x 16
= 30 x 16
guess what property was used here.
you were too retarded to get the point of it.

>>16866828

I prefer it like this:

15 x 32 = 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32

15 x 32 = 64 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32 + 32

... = 480

>>16866219
I don't know if what you're claiming is even true, but regardless... I bet it takes something of an intellectual leap to go from regarding speech as a stream of thoughts expressed by continuously modulating the air flowing through your speech organs, to thinking about it as a concatenation of words. Not to mention breaking it down further into letters that (imperfectly) represent sounds. If you think about it, meaning is mostly contextual. A word doesn't mean much on its own so it's not an obvious semantic unit. It's counter-intuitive, unlike language itself.

With multiplication, it's a simpler story: if you have a quantitative sense at all, you can easily learn to count and compare quantities. Once you start counting bundles of things, you're exploring multiplication. Since counting is inherently discreet and abstract, it translates into symbols far more naturally, so maybe if you have a population with at least a basic "sense" for multiplication, it's less of a leap for it to learn to do it symbolically.

>>16866219
You literally answered your own question.

15
* 32

=+ 10 2*5
=+ 20 2*1
=+ 150 3*5
=+ 300 3*1

= 480
i do the brainlet method

>>16866828
Since you like doubling, how would you evaluate the following?
n/5 = __?__
21/2.5 = __?__
1234/5 = __?__

>>16868006
15×32
= (10 + 5)×(30 + 2)
= 10×30 + 10×2 + 5×30 + 5×2
= 300 + 20 + 150 + 10

23×57
= (20 + 3)×(50 + 7)
= 20×50 + 20×7 + 3×50 + 3×7
= 1000 + 140 + 150 + 21

>>16867681
15×32
= (10 + 5)×(30 + 2)
= 10×30 + 10×2 + 5×30 + 5×2
= 300 + 20 + 150 + 10

23×57
= (20 + 3)×(50 + 7)
= 20×50 + 20×7 + 3×50 + 3×7
= 1000 + 140 + 150 + 21

>>16868006
Nevermind the previous reply.
I don't know how that happened.
Maybe I was sabotaged.