Why is it important to learn the order of operations?

Answer 1

Studying the order of operations and the laws governing the use of operations will permit us to apply them to solve problems and get correct data. If we do not master operations and the rules for their application, we can't work problems in a clear and consistent manner to arrive at the right answers. There are rules governing the order in which operations are performed so that they can be performed correctly. And there are also laws for the application of operations so that correct information can be discovered by applying them. Let's look at two examples, one for the order of operations and one for the laws of operations and see if it becomes clearer. In the problem 9 - 3 + 2 = ? we have to figure out which operation to perform first. Lacking any direction outside what we have been given, do we work 9 - 3 to get 6 and then do 6 + 2 to get 8? Or do we do 3 + 2 to get 5 and then do 9 - 5 to get 4 as an answer? It can't be both. The order of operations is important, and we add before we subtract. That means we second option is the correct one, and we solve to get 4 for an answer. In the problem 7 times the quantity 3 plus 2 we are asked to work 7 ( 3 + 2 ) = ? to find an answer. So do we multiply first and do 7 x 3 and get 21 and then add 2 to get 23, or do we add 3 plus 2 to get 5 and then multiply by 7 to get 35 as an answer? Or just what do we do to solve it? We've got parens to direct us here. But what's the scoop? There is a law we use called the distributive law of multiplication, and to resolve this expression by applying that law, we have to "distribute" the multiplication process to all the terms inside the parens. We distribute the 7 to the 3 and to the 2 by multiplying each of them by the 7 and then add to get 7 x 3 = 21 and 7 x 2 = 14 and then do 21 + 14 to get 35 for an answer. Note that in the above problem, we could have added inside the parens and then multiplied to get the same correct answer, but the net result is the same in that the 7 is "distributed" across all the terms inside the parens to find the right answer. There will be problems where the terms inside the parens are not the "same" and cannot be "combined" to move toward an answer. Like in 7 ( 3a + 2b ) = ? for an example, we can't combine 3a and 2b, so we distribute the 7 to get 21a + 14b for the answer. The order of operations is multiply, divide, add and subtract. It's easy to see with these two examples that there are different ways to work problems with multiple operations. But there is only one correct way. By applying the proper order and the right rules for operations, we get the answer to a problem - the correct one.