Can someone explain to me some algebraic rules I forgot?

Post Reply New Topic

Say we're solving -9-(-3)

Firstly, why can it become -9-1(-3)

And why don't we do -9-1= -8
-8* -3

I know the rule is change the sign of the subtrahend and add. But why?

Multiplication and division have higher priority than addition and substraction. You can't take 1 from 9 without first multiplying it by -3. The way to go about it would be:

-9 -1(-3)
-9+ (-1)(-3)
-9 + 3
-6

An explanation of why, from the top of my head, would be that addition and substraction are opposite operations, so adding a number would be the same as substracting it's opposite, and viceversa. There is probably a more formal explanation in Spivak's Calculus if that one is not enough though, I could look for it if necessary.

Last edited by Shatbat on 09 Aug 2012, 5:30 am, edited 1 time in total.

w - w = 0
substitute -x for w and get
-x - (-x) = 0

x + -x = 0

-x + x = 0

therefore +x = -(-x)

ruveyn

Maybe I'm being dumb but the operators don't make any sense to me.

How can it be minus and times all at once?

It's not times when it's done that way. It's just a way to write -9 - -3 , substract minus three from minus nine, and the parenthesis is there for clarity. The multiplication comes later when you multiply minus three times one, which by definition doesn't change the value of the original minus three.

Some of the rules are based on how numbers actually work, and some are just about how we happen to write things. One of the rules that's just how we write things is that multiplication (and division) gets done before addition (and subtraction). We could write it so that addition came before multiplication, but then we would have to put parentheses in different places for it to mean the same thing. We could also not have any rule about which comes first, but then we would have to use a whole lot more parentheses, and everything would be harder to read.

Because of the way we write things, -9-1 isn't actually in -9-1(-3), because the multiplication has to happen before the subtraction can know what is being subtracted. If you fully parenthesized -9-1(-3), it would be (-9)-(1(-3)).