Why is it important to follow the order of operations? What are some possible outcomes when the order of operations is ignored? If you invented a new notation where the order of operations was made clear, what would you do to make it clear?

In mathematics , the order of operation also known as precedence rule is a rule used to clarify which procedures should be performed first in a given mathematical expression. When there is more than one operation involved in a mathematical problem, it must be solved by using the correct order of operations. The rules are 1. Calculations must be done from left to right. 2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first ie starting our work with the innermost pair, moving outward. 3. Exponents (or radicals) must be done next.

4. Multiplication and division are done next .
5. Addition and subtraction must be done next.
The acronym which can be used to remember this order is
Big Elephants Destroy Mice And Snails (Brackets, Exponents, Divide, Multiply, Add, Subtract) If the order of operation is not followed, a lot of problem is created. we get different answers for the same problem. for example 15 + 5 X 10 -- Without following the correct order, we know that 15+5=20 multiplied by 10 gives me the answer of 200. 15 + 5 X 10 -- Following the order of operations, we know that 5X10 = 50 plus 15 = 65. This is the correct answer, where as the above is wrong. If I was to invent a new notation where the order of operation was made clear, I would have used colours. I would have assigned each operator a colour.

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