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http://www.math.com/school/subject2/lessons/S2U1L2GL.htmlOriginally Posted by Klipschorn
Originally Posted by kingcrux31
Originally Posted by Rocky437
do you even know how to do any math using your own head?
Apparently not.
http://www.purplemath.com/modules/orderops.htm
If you are asked to simplify something like "4 + 2Ã3", the question that naturally arises is "Which way do I do this? Because there are two options!":
It seems as though the answer depends on which way you look at the problem. But we can't have this kind of flexibility in mathematics; math won't work if you can't be sure of the answer, or if the exact same problem can calculate to two or more different answers. To eliminate this confusion, we have some rules of precedence, established at least as far back as the 1500s, called the "order of operations". The "operations" are addition, subtraction, multiplication, division, exponentiation, and grouping; the "order" of these operations states which operations take precedence (are taken care of) before which other operations.
Choice 1: 4 + 2Ã3 = (4 + 2)Ã3 = 6Ã3 = 18
Choice 2: 4 + 2Ã3 = 4 + (2Ã3) = 4 + 6 = 10
A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right. For instance, 15 ÷ 3 à 4 is not 15 ÷ 12, but is rather 5 à 4, because, going from left to right, you get to the division first. If you're not sure of this, test it in your calculator, which has been programmed with the Order of Operations hierarchy.
[font=Verdana, Arial, Helvetica, sans-serif][size=-1][/size][/font]
[font=Verdana, Arial, Helvetica, sans-serif][size=-1]When expressions have more than one operation, we have to follow rules for the order of operations:[/size][/font]
- [font=Verdana, Arial, Helvetica, sans-serif][size=-1]First do all operations that lie inside parentheses.[/size][/font]
- [font=Verdana, Arial, Helvetica, sans-serif][size=-1]Next, do any work with exponents or radicals.[/size][/font]
- [font=Verdana, Arial, Helvetica, sans-serif]Working from left to right, do all multiplication and division.[/font]
- [font=Verdana, Arial, Helvetica, sans-serif][size=-1]Finally, working from left to right, do all addition and subtraction[/size][/font]
http://mathforum.org/dr.math/faq/faq.order.operations.html
PEMDAS
(You might remember this as "Please excuse my dear Aunt Sally.")[sup]1[/sup]This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out.
- Parentheses
- Exponents
- Multiplication and Division
- Addition and Subtraction
[sup]1[/sup]Some people are taught to remember BEDMAS:
Brackets
Exponents
Division and Multiplication, left to right
Addition and Subtraction, left to right
Besides the obvious sources Google and Wolfram AND Bing.. THUS 288.
For emphasis.