What happens if the order of operations is not followed

I had no defence; a fee-paying student had made the claim so it must be true. Think of it as community service. The error illustrated above is caused by the fact that addition and subtraction should not necessarily happen in that order. If we have a string of these two operations it is called a sum and we should work from left to right:.

Similarly, division is no more important than multiplication. If we have a string of these two operations it is called a product and we will work from left to right again:. Even now, it is not too late to rid ourselves of bi-syllabled arithmetic acronyms.

Leave no trace of them. Allow BOPS to strike a victory blow for young mathematicians everywhere. You can follow him on Twitter at owenelton. Owen Elton. BODMAS rule This mathematical rule dictates the correct order of operations to be followed when you complete a mathematical number sentence question with different operations. For many students, PEMDAS implies that the order of operations consists of six steps, one for each letter of the acronym.

In fact, the order of operations consists of four steps:. Importantly, multiplication and division are evaluated as part of the same step, as are addition and subtraction in the next step.

I have encountered far too many students who misunderstand the order of operations in precisely this way. Fortunately, I have a solution to this problem: rather than beginning a lesson on the order of operations by introducing PEMDAS, it should only be introduced after working through many examples using the four-step order of operations as it is written above. Once students come to understand the order of operations through practice, only then may PEMDAS be introduced to serve its intended purpose: not as a set of instructions, but as a mnemonic device to assist with memory.

Eric Bennett is the author of Elementary Math for Computer Science with Python , a textbook for elementary-aged students. The order of operations is the rule for what operations should be done first when there are several operations within the same equation. The order of operations is like grammar rules for the language of math.

It explains how to interpret an equation to mean what it is supposed to mean. The order of operations says that operations must be done in the following order: parentheses, exponents, multiplication, division, addition, and subtraction.

When there are parentheses, whatever is inside must be done first. The stuff inside the parentheses may also need to be broken down according to the order of operations as well. It is even possible to have parentheses within parentheses.

In cases like this, work from the inside out. Multiplication and division can be done together. Addition and subtraction also work together. You can do subtraction first, or you can do addition first. They are part of the same step, however, they can only be done after items in parentheses, exponents, and any multiplication and division. Video Source mins Transcript. Remember to take it one step at a time and rewrite your equation after completing an operation.