PEMDAS, but for Emotions

By Steff Du Bois, PhD, author of I’m Not Okay and That’s Okay

Transport back with me, to Algebra class—seventh grade, eighth grade, or whenever that was for you. You’ve already learned how to solve more straightforward math equations—those with just subtraction or just division or just exponents. Now, you’re learning to solve more complex equations that include multiple of these.

Your algebra teacher shares with you something revelatory: Because these new, complicated equations have multiple types of math in them, you need something called an order of operations to work through them—a step-by-step approach to solving these multifaceted problems.

Enter PEMDAS. Aka, Please Excuse My Dear Aunt Sally. Aka, Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

It’s an acronym. It’s a mnemonic. It’s a guide. It’s a praxis. It’s basically everything you could ever want and need to solve life’s most challenging math problems. It reminds you to process problems one step at a time, and it gives you the step-by-step order to follow. It’s a religion.

Perhaps most excitingly, the underlying principle of PEMDAS extends far beyond algebra class, and indeed far beyond the field of math. (Thankfully, because I stopped understanding math when I got to geometry.)

This principle—that an order of operations can provide a helpful framework for solving complex problems—is one you can apply to yourself each day. Specifically, as you navigate the inevitable moments of feeling multiple negative emotions at once.

These moments are so deeply common. When you make a big mistake, you might feel distress, failure, and anxiety. When you’re underpaid at work, you might feel frustrated, inferior, and worried about paying the bills. When your romantic partner wrongs you, you might feel anger, sadness, and unsafe. When your child struggles in a way you can relate to, you might feel concerned about your kid, insecure about your parenting skills, and personally triggered.

These moments create unique challenges characterized by the broader sense of emotional overwhelm. All the emotions you’re feeling simultaneously—they can sort of glom together, into what seems like a big, heavy, amorphous emotional heap. You might think, “Where do I even start?”

In these moments, just as in algebra class, a clear order of operations can aid you. This emotional order of operations is a lot like PEMDAS, but also has a key difference.

Regarding how they’re alike: First, both require you to assess the problem you’re looking at, specifically by naming its components parts. For example, solving the math equation

X = (2+ 4) + 5² – 3 x 3 

requires you to first notice it includes Parentheses, an Exponent, Multiplication, Addition, and Subtraction. This step is as important to solving the math problem as it is to navigating complicated emotional moments. Simply put, labeling the multiple negative emotions you’re feeling in any moment sets you up to effectively and efficiently work through those emotions.

Another similarity between an order of operations for math and emotions, is that after you identify the key components of the current problem, it’s recommended to address each of those components singularly and in a stepwise fashion. In our equation

X = (2+ 4) + 5² – 3 x 3 

per PEMDAS, you’d first take care of what’s in the Parentheses: 2 + 4 = 6. You’d then address the Exponent: 5² = 25. Next, the Multiplication: 3 x 3 = 9. Finally, Addition and Subtraction, left to right: (6) + 25 – 9 = 22. Therefore, after taking things methodically and stepwise, you solve for X, as 22.

Same goes for those moments with multiple negative emotions: Address each component one at a time. Let’s use one of our earlier examples: When you make a big mistake, you might feel distress, failure, and anxiety.

After identifying these component emotional parts, attempt to process and respond to them one by one. I listed distress first because I recommend dealing with any general “distress” first. This is because experiencing general distress itself can be aversive and can compromise your ability to process other emotions. You may have heard of the related concept of distress intolerance, which is when we feel dysregulated simply because we’re distressed at all.

This makes sense; distress is distressing. But labeling general distress—and using a few microskills to reduce it—can help set you up to process other, more situation-specific emotions you’re feeling. Such distress tolerance microskills include breathing/relaxation exercises; visualizing something positive; splashing cold water on your face; grounding yourself in the present moment by connecting with your current sensory experiences; or repeating an empowering phrase to yourself, e.g., “You’ve got this.”

After you complete this important step in your emotional order of operations, move on to the next emotion—the one that feels most strong. I recommend this approach, because often if you can process a little or a lot of this strongest emotion, some of the other negative emotions you’re feeling may also dissipate.

Let’s say in our example, the remaining emotion you felt most strongly was failure. Using some microskills to address these failure feelings can go a long way. Such microskills include generating counterevidence to the feeling of failure—asking yourself, “When have I been successful, now or in the past?”; de-catastrophizing—reminding yourself that likely the worst outcome you’re imagining now will not manifest; and, self-compassion—generating compassionate contextual reasons for the mistake you made, “I was stressed, I did my best.”

Processing some general distress and failure hopefully would have you feeling better already. But, to the extent that you want, keep going in your emotional order of operations—aiming to process any remaining emotions one by one, until you feel better enough to move forward from whatever complex or challenging emotional experience you’re having.

For sure, each of your complex emotional experiences is unique—just like each algebra problem is. But, an order of operations will give you a broader, guiding framework to use across experiences.

Here’s where we get to that key difference between PEMDAS and our emotional order of operations: PEMDAS leads to you solve problems, whereas our new system leads you to process, but not necessarily “solve,” emotions.

This isn’t totally surprising, because while math is quantitative, life is qualitative. This qualitative richness of life is what makes it so beautiful, but also sometimes so gut-wrenching. We can simultaneously be grateful for both systems like PEMDAS that solve problems, and for more emotion-based orders of operations that don’t solve problems, but help us live a more fulfilling life.

Thanks, algebra teacher. Thanks, Aunt Sally. And now, thanks, new emotional order of operations.

Steff Du Bois, PhD, (he/they) is a clinician in private practice, and associate professor of psychology at the Illinois Institute of Technology (IIT). They lead the Du Bois Health Psychology Laboratory, where they mentor psychology students and conduct health psychology research.