In math, we have to have a set way of solving problems, otherwise everyone could get different answers. “Order of Operations” is simply a list of steps to use when solving problems with multiple operations (operations are adding, subtracting, multiplying, dividing).
The easiest way to remember the order is to use this acronym:
These letters stand for:
Multiplying and dividing go as a pair: if you have both of these operations, solve them from left to right. The same is true for adding and subtracting; if you have both, solve from left to right.
We will use the letters P, E, M, D, A, S as shorthand for the operations.
Example math problems related to order of operations:
- 5 + 7(4 – 2)
- First, identify the operations: we have A, M, S, and P. According to the order of operations, we must first start with the parentheses, which is where the subtraction is:
- 5 + 7(2)
- Now we multiply:
- 5 + 14
- Finish up by adding:
- 18 ÷ 3 + 5(7 – 4) x 2
- Identify the operations: D, A, M, P, S, and M.
- Start with the parentheses:
- 18 ÷ 3 + 5(3) x 2
- Now we see that we have D, A, M, and M.
- Since we have both dividing and multiplying, we will do those from left to right:
- 6 + 15 x 2
- 6 + 30
- Then add:
- To avoid confusion, first look for parentheses. Solve those parts, then look for exponents. After that, dividing and multiplying, and finally, adding and subtracting.
- 4 x 52 + 16 ÷ 2
- This time we have exponents, so start with that:
- 4 x 25 + 16 ÷ 2
- Now we’ll do multiplying and dividing:
- 100 + 8
- Then add: