Operations are the actions taken to solve math problems: addition, subtraction, multiplication, and division. Order of Operations defines the way these operations should function in order to achieve the correct result.

The order of operations expression is MDAS, with each letter representing a different operation (listed below). These four operations together are:

**M**ultiplication**D**ivision**A**ddition**S**ubtraction

Based on MDAS, multiplication and division will always outrank addition and subtraction. However, multiplication does not outrank division, and addition does not outrank subtraction. Instead, the order between multiplication and division or between addition and subtraction is determined by what operation appears first going from left to right. Thus, it may be clearer to think of MDAS like this: MD - AS.

*Note that in the future when you learn about parantheses and exponents in higher levels of math, this pneumonic will expand to PEMDAS. *

**Example**

Since addition and subtraction are the same rank, you simply calculate moving left to right. However, in the next problem, you have to multiply before subtracting.

**Multi-Step Equation Example**

By order of operations, you now know that the solution is 13.

Order of operations can be difficult at first, and it can be easy to make some common mistakes. You are accustomed to solving a problem left to right, but now you have to recognize the operations in the problem and solve according to their order—multiplication/division before addition/subtraction. At the same time, remember that:

- Multiplication and division are equal to one another
- Addition and subtraction are equal to each other
- When you have multiplication/division or addition/subtraction next to each other, then you should solve left to right.
- Be careful not to use a number more than once as you go through each stage of the problem. One way to avoid this issue is to cross out numbers after using them in an operation so you can visually keep track of your steps.

- 3 x 4 + 6 = ?
- 3 + 4 x 6 = ?
- 4 x 7 - 6 x 2 = ?
- 25 + 8 x 3 - 12 = ?
- What is 17 - 3 x 4 ÷ 2 + 13 x 5?

- .067
- 18.67
- 76
- 205

**Answers to Practice Problems**

- 18
- 27
- 16
- 37
- 76

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