Order
The order in which problems are formed and solved is of extreme importance!
EXAMPLE:
You go to a store to buy shoes and you choose a $60 pair of shoes. You have a $10 off coupon and a 10% off coupon, and you are allowed to use both.
Does the order in which you apply the coupons matter?
1. $60 shoes, apply $10 off. You now are paying $50 for the shoes.
Next take 10% from $50. That would be $5, so you now pay $45 for your shoes!
2. $60 shoes, apply 10% off. That's $6. So you are now paying $54. Now take off the $10. That's $44.
This is a fairly trivial example, you've only saved $1 dollar, but play around with amounts and this can stack up some real cash!
So what do we do? Simply guess and figure out which way we want a problem solved on a case by case basis?
No, we use ORDER OF OPERATIONS, which you may know as PEMDAS
Parenthesis - Simplify anything in parenthesis first
Exponents - Apply exponents to whatever remains
Multiplication or Division - Multiply and Divide anything that is required next
Addition or Subtraction - Add or Subtract anything else last!