This Lesson (HOW TO WORK WITH + AND - for addition and subtraction) was created by by longjonsilver(2297)  : View Source, ShowAbout longjonsilver: I have a new job in September, teaching
ADDITION and SUBTRACTION
The trouble that most students have with + and -, is in not understanding that they are actually used for 2 things:
+ can mean either a POSITIVE number or mean ADD.
- can mean either a NEGATIVE number or mean SUBTRACT.
So, you need to be aware of that.
Basically, where you have 2 signs written together, one will mean ADD or SUBTRACT and the other will mean you have a positive or negative number. The rules for dealing with 2 signs written next to each other, to combine them, are:
SAME signs --> combine them as a +
DIFFERENT signs --> combine them as a -
EXAMPLES: (the use of brackets here is just to make things more readable. As such, they should be employed in your work to, to keep things separated).
(+3)+(+2) --> +3 + 2 = +5
(+3)+(-2) --> +3 - 2 = +1
(-3)+(+2) --> -3 + 2 = -1
(-3)+(-2) --> -3 - 2 = -5
Subtraction is identical:
(+3)-(+2) --> +3 - 2 = +1
(+3)-(-2) --> +3 + 2 = +5
(-3)-(+2) --> -3 - 2 = -5
(-3)-(-2) --> -3 + 2 = -1
Note, once you have used the above rules, to combine any +- signs together, what you are left with is a straight forward addition/subtraction calculation, where you do not have to think about the "rules" --> just do the calculation.
Also, note that a 3 and 2 added or subtract will only ever give a 1 or a 5 as the answer, so -3-+2 will never be -6 for example.
MORE EXAMPLES
4a + (-3b) + (-2b) + a - 5ab + 2ab
OK, on this, we are adding (or subtracting) terms. You can only add or subtract LIKE terms...so 2 apples + 3 apples is 5 apples. However, 2 apples + 3 bananas is still 2 apples + 3 bananas.
so we have 3 different THINGS here: a, b and ab. we treat them all separately as:
4a + a --> 5a
-3b + (-2b) --> -3b - 2b --> -5b
-5ab + 2ab --> -3ab
(Note that the -5ab should really be written as - (+5ab), which simplifies to just -5ab). So we get the answer 5a - 5b - 3ab
Final example:
Now, this has multiplication in several places together with addition and subtraction. What rules do we follow for this? What do we do first?
BODMAS
B - o - DM - AS
If you have Brackets, do whatever you can inside them first. This is why you will see lots of brackets in your maths careers --> mathematicians use them to group things together to tell you that they should be done first.
Then follows any Division or multiplication.
Then follows any Addition or subtraction.
So, i shall simplify the above, step by step:
--> look inside the brackets to see if you can do anything... we cannot add any of the terms together. The reason for the brackets is to tell you that everything inside the second bracket needs to be multiplied by -1 (the minus sign in front of it is actually there as -1*(3b+1) but we do not write the 1 or the multiply sign... both are implied), so multiply the +3b and the +1 each by -1...
-1x+3b = -3b
-1x+1 = -1
so,
Now, we can do stuff in the larger bracket...collect like terms, to give
And now we multiply everything in this bracket by the -2a, to give
I hope this is all fairly clear and structured and that it lifts some of the mysteries in + and - numbers. To be honest, none of it is difficult, you just have to understand te very basic rules and the practice and practice and make mistakes and ten practice and make fewer mistakes. Practice DOES make perfect.
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