[31 August 2022] I got back into a little maths study (it has only been two years...) and I opened up my text book and skimmed through the first chapter.

In it there are rules give for multiplying or dividing by negative or positive numbers and what result that will give, either positive or negative. But I have some queries:

• Why does multiplying negative numbers together result in a positive number? And,

• Why does dividing a negative number by another negative number result in a positive number?

We are given the BODMAS rules (PEMDAS if you are American). I remembered from highscool that the contents of brackets (parethesis) are calculated first, but who came up with this idea (it's merely a created rule and not a underlying thing of the universe)?

All that seems to exist is it was someone called Achilles Reselfelt in the 1800s.

Given that this is such a widely taught thing in mathematics is seems very odd that there is nothing about this person on the Wikipedia page, or a history of how things might have been done prior to the rule being defined. It appears from Wikipedia that Mathematical Notation began in the 16th century.

Further queries:

• What are the real world uses of prime factorizes? (i.e. prime factors of 12 are 2 x 6 = 2 x 2 x 3).

• What are the real world uses of 'Lowest Common Multiples' (L.C.M.)?

Fractions:

• Where do the terms numerator and denominator come from?

• Why does dividing a fraction by another involve inverting the second and then multiplying them?

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