How to Solve a PEMDAS (Order of Operations) Problem

Many of my students have tremendous difficulty with PEMDAS (Order of Operations) problems, but there is no reason for this. Just follow the simple steps and tips below, and you will get them all correct.

Difficulty:

Moderately Easy

Instructions

Things You'll Need

• Pen/Pencil
• Writing Paper
• The steps described below

1. First do anything that you see in parentheses. Ignore anything else that you see. If you have nested brackets, such as this pattern: [()], then work you way from the inner set to the outer, one step at a time.

2. Next, simplify exponents. Remember that an exponent tells you how many times to multiply the number times itself.

3. Next, do multiplication and division left to right. That right there is the key. You must do the division first, if it comes to the left of the multiplication. However, this step is always fully completed before the next one. For example, in the problem 4+15/5*2, we first do the division to get 3. Then we multiply 3 times 2 to get 6. Only then do we add 4 to get 10 (see below).

4. Finally, do addition and subtraction left to right. Again, the subtraction could come first, if it is to the left of the addition.

Tips & Warnings

• Do you work one step at a time.

• As you finish each step, carefully bring down all the remaining numbers and symbols

• Remember that multiplication and division are done left to right, and so are addition and subtraction

• Don't skip or combine any steps

• Work slowly and carefully, and check your work at each step.

• Avoid using your calculator. Advanced calculators will likely adhere to the PEMDAS rules, but simple calculators will just do calculations in the order that you enter them, which will likely be wrong.

Resources

• Math with Larry (Free Online Math Help)