|
ADDING
is a Combining Process
a) the ORDER
of the terms does not matter
b) the GROUPING of the terms
does not matter
3 + (-5 + 6) = [3 +
(-5)] + 6 = 6 + (-5) + 3
Therefore, the algebraic expression:
17 + (-x + 4)
... can be re-written as:
[17 + (-x)] + 4
>> re-grouped
17 + (-x) +
4 >>un-grouped!
SUBTRACTING is a Removal Process
| N.B. ALL subtraction expressions can be re-written as addition by ADDING THE OPPOSITE NUMBER. |
| FOR SUBTRACTION: |
| ORDER MATTERS (which
are we removing from which?): |
| 3 - (-5) does NOT = -5 - 3 |
| GROUPING MATTERS: |
| 3 - (-5 + 6) does NOT = [3 - (-5)] + 6 |
| Understanding these rules will help you simplify
complex expressions involving parentheses |
| When subtracting a GROUP of two or more numbers or
terms, you can ADD THE OPPOSITES of EACH term:
Let's look at the following example: |
| 22 - (x + 4)
if you simply add the opposite of EACH term, you will
have the expression:
22 + (- x) + (- 4) which
also can be written as: 22 - x -
4
ANOTHER WAY to look at this problem is to view (x
+ 4) as a "package deal"... you are subtracting each term
inside the package (aka, the parentheses). So, subtracting the x
and the 4, the simplified
expression looks like this:
22 - (x + 4) = 22 - x - 4
Substitute any value for x to prove this rule
true (wow,
are you gonna be fun at parties or what?) |
| 9 - (4 - 8) = 9 + (-4) +
8 (when simplified:
13) |
| 10 - (-3 + x ) = 10 + 3 + (-x)
(when
simplified: 13 - x) |
| DO NOW: |
| 8 - (4 - 6) = |
| x - (-4 - x) = |
| -x - (-4 - x) = |
|