Lesson HOW TO WORK WITH + AND - for multiplication and division

Source code of 'HOW TO WORK WITH + AND - for multiplication and division'

This Lesson (HOW TO WORK WITH + AND - for multiplication and division) was created by by longjonsilver(2297)

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About longjonsilver: I have a new job in September, teaching

There are 2 parts to understanding how to use signs correctly in maths. These are when dealing with ADDITION and SUBTRACTION and then with MULTIPLICATION and DIVISION. I cannot offer proofs of what I say or derivations, as basically I do not know them. They are also beyond the level of most courses. Also, they are quite boring, in my opinion. Sorry purists :-). However some other sites do offer potentially helpful examples, such as http://www.tpub.com/math1/4b.htm. However, for me they do my head in.

Multiplication and Division

MULTIPLICATION

This is the easier part to do first, so here goes with some examples:

(+2)*(+3) = +6
(+2)*(-3) = -6
(-2)*(+3) = -6
(-2)*(-3) = +6

(+5)*(+4) = +20
(+5)*(-4) = -20
(-5)*(+4) = -20
(-5)*(-4) = +20

OK, basically multiplipying (or dividing) 2 numbers then following these rules:

if the 2 numbers have the SAME sign, then the answer is +
if the 2 numbers have the DIFFERENT sign, then the answer is -

so, {{{(-2x)*(-3y) = +6xy}}}.

Get into the habit of breaking the question down. Do not think of -2x as one thing and -3y as the other. Instead think of the signs first... - and - give a +...so that is done. Next the numbers, 2x3 is 6. That is done. Then x... no other x terms to multiply with, so it is still x and then similarly the y..it has no other y terms to multiply with, so it remains y.

EXAMPLE:

3ab * -2a = {{{-6a^2b}}} So, I look at this as follows:

+ and - --> -
3x2 --> 6
axa --> {{{a^2}}}
b --> b

How about (2ab)*(-4b)*(-3ab)?

Remember, the sign rules above apply to ONLY 2 signs at a time, so initially do the above in 2 steps:

{{{(2ab)*(-4b) = -8ab^2}}}

then {{{(-8ab^2)*(-3ab) = 24a^2b^3}}}

Once you are happy with multiplication of many terms, you can do the signs in your head in one go: so for the above example, I would say + and - (from the 2 and the -4) is a -. Then this - and the - (from the -3) is a +.

DIVISION

This follows the exact same rule as multiplication, as you would expect since they are two sides of the same thing (ie 2*4=8 or 8/2=4 --> opposite processes).

So, I shall just do some examples:

(+12)/(+3) = +4
(+12)/(-3) = -4
(-12)/(+3) = -4
(-12)/(-3) = +4

And algebraic examples:

{{{(-12a)/(-4) = 3a}}}. Again, do the 2 signs. Then do the 12 and 4 then do the letters, in this case we only have one.

{{{(6a^3)/(-12ab) = (-a^2)/2b}}}. Again, do the signs, then the numbers, then the a-terms and then the b-term.

How about multiplication and division? Which should i do first? It doesn't matter, since as I said earlier, they are 2 sides of the same coin.

EXAMPLE: Simplify {{{((6a^2bc^3)*(-4a^2c))/(-2a^3b^3c^2)}}}

You can do any of this in any order, as the terms are all connected by either multiplication or divide. Realistically, to stop yourself getting in a muddle, you would probably pick the multiplication on the top first, to get that into one combined term, as follows:

{{{(-24a^4bc^4)/(-2a^3b^3c^2)}}}

and now we can do the division, to give {{{12ac^2/b^2}}}

In all this, if there is no sign written, then it is assumed to be a +, so the last answer is in fact +{{{12ac^2/b^2}}}