the whole idea is to resolve the innermost parentheses first.
then you resolve the next innermost parentheses.
then the next until you've resolved all parentheses that need to be resolved.
if your set of parentheses are not nested within each other, you resolve the leftmost set of parentheses first and then move on to the next leftmost until you've resolved them all.
this is all part of the properties of arithmetic operations.
what does this mean?
assume an operation of -(a - (b-c))
you need to resolve the innermost set of parentheses first.
this is (b-c).
there is nothing in (b-c) itself that can be resolved so you move on to the operation that is being performed on that innermost set of parentheses.
the operation that is being performed on that innermost set of parentheses is subtraction because there's a minus sign in front of it.
- (b-c) is equivalent to -1 * (b-c).
you use the distributive law of multiplication to get:
-1 * (b - c) is equal to -1 * b - (-1 * c)
this results in -b + c
your original expression of -(a - (b-c)) becomes:
-(a - b + c)
now you operate on the next most inner set of parentheses.
there is nothing within the set of parentheses that can be resolved so you move on to the operation that is being performed on that set of parentheses.
again, we have subtraction.
-(a - b + c) is equivalent to -1 * (a - b + c).
you use the distributive law go get:
-1 * (a - b + c) is equal to -1 * a - (-1 * b) + (-1 * c)
this results in -a + b - c
all parentheses have been resolved and you move on to the next set of parentheses in order from left to right.
the worksheet above follows this procedure.
the shortcut rule says that, if you have -(a - b - c), you simply reverse the signs within the set of parentheses and reverse the signs.
the shortcut rule says that -(a - b - c) is equal to -a + b + c
