RE: Member Photos
September 21, 2017 at 6:45 am
(This post was last modified: September 21, 2017 at 6:46 am by pocaracas.)
(September 21, 2017 at 6:23 am)Nymphadora Wrote:(September 21, 2017 at 5:21 am)pocaracas Wrote: Yeah, like Kernel said, I don't think it's about being smart or anything... maths is just a set of rules, with its own language set. It's more similar to learning/knowing a different language, than being smart.Red mine.
Most of the times, it's about remembering the right words to make the full sentence.... there are so many words... so many.
Anyway, letters in maths should not be feared. They simply represent a number. They may represent a number we wish to discover, or any arbitrary number we may wish to assign.
The letters are like labels for numbers, when we are not sure which numbers should go in there. Even when we do know the numbers, they tend to be so weird that we prefer to use a letter in it's place, like the speed of light in vacuum, 'c' = 299 792 458 m s-1, or the famous π=3.141592653589793238462643383279...
So, anyway... I had to look up what this "foil" business was, because in Portuguese there's no such thing
a*(b+c) = a*b + a*c... simple enough, but if a itself is a sum
(a1+a2)*(b+c) = a1*b+a1*c + a2*b + a2*c, that's cool.... how about we add some more terms?
(a1+a2+a3)*(b+c) = a1*b+a1*c + a2*b+a2*c + a3*b+a3*c, just keep doing more of the same!
You had me clear up to that point. Then you lost me.
Gotcha... let's try with numbers, then!
3*(9 + 5) = ???
Because we have those parenthesis in there, we are saying that whatever is inside them must be calculated before what comes on the outside - this is part of the language I mentioned.
So that becomes:
3*14 = 42.
But that's the same as splitting the multiplication in two a*(b+c)= a*b + a*c:
3*9 + 3*5 = 27 + 15 = 42
and is substantially different from
3*9 + 5 = 27 + 5 = 33
The parenthesis make a difference in the order of the calculations.
As a general rule, multiplications and division are carried out before sums and subtractions. The parenthesis force us to carry out whatever is inside them first, regardless of the operators on the outside.
You can have enclosed expressions in parenthesis inside parenthesis. When that happens, you should process the innermost one first, and then work all the way to the outermost one.
For example:
3*(9*(4+2)+5) =
= 3 * ( 9*6 + 5) = { or 3 * (9*4 + 9*2 + 5) = 3 * (36 + 18 + 5) }
= 3 * (54 + 5) = {Note how the multiplication got calculated first, inside the parenthesis - general rule applies for each expression}
= 3 * 59 =
= 177