Order of Operations
Order of Operations
When expressions have more than one operation, we have to follow rules for the order of operations:
1. First do all calculations inside the parentheses.
2. Now calculate any exponents.
3. Next do all multiplication and division from left to right.
4. Last, from left to right, do all addition and subtraction.
You should now have calculated the answer. Why do we have to solve problems in this order? Can we solve these problems in a different “order?” If so, do we arrive at the same answer?
Let’s look at the problem: 20 + 4 x 10
20 + 4 x 10 -- Without following the correct order, I know that 20+4 =24 multiplied by 10 gives me the answer of 240.
20 + 4 x 10 -- Following the order of operations, I know that 4 x 10 = 40. I add 40 + 20 = 60.
60 would be the correct answer to the expression 20 +4 x 10 not 240.
Mathematicians have spent considerable time and thought when they developed the order of operations. So why the order? I am not exactly sure but from what I understand it would appear as if the order is based upon the importance or power of the operation. Multiplication is more “powerful” than addition because of the distributive property. If you look at the problem 12 x 34, you can distribute the 34 by multiplying (12 x 30) and adding it to (12 x 4). As you can also see you must complete the operations inside the parentheses which leads you to believe that they are more powerful then multiplication and addition. If you would like to learn more, check out these sites:
http://mathforum.org/library/drmath/view/52582.html
http://mathforum.org/library/drmath/view/57199.html
http://mathforum.org/library/drmath/view/57031.html
http://en.wikipedia.org/wiki/Order_of_operations
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