PEMDAS or order of operations is majorly important on the ACT®. Most students make small errors here and there that result in them missing points. The ACT® is banking on you making these errors. The answer choices often reflect common PEMDAS misapplications.
It benefits most students to ensure they're implementing this process really well. Knowing it is a good first start. Correcting your work in the right way is going to prevent you from making these mistakes. That translates into more points.
PEMDAS
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It's the order in which you should solve mathematical operations.
- P arentheses
- E xponents
- M ultiplication
- D ivision
- A ddition
- S ubtraction
The underlined E and D remind us that we evaluate multiplication and division from left to right, as they have equal priority. The same goes for addition and subtraction. First you do parentheses and exponents. Then, once both of those are done, you move on to evaluate multiplication and division. Once you deal with multiplication and division for the entire equation, then you can move on to the addition and subtraction.
How to Remember PEMDAS
The usual mnemonic Please Excuse My Dear Aunt Sally can help you remember PEMDAS. The phrase has nothing to do with anyone who existed. Mnemonics aid memory recall. While 'Please Excuse My Dear Aunt Sally' doesn't relate to math, it's a handy way to remember the order. On test day, don't hesitate to write PEMDAS at the top of your scratch paper if it helps you stay on track.
Practice Section
Question 1:
Solve the following equation using PEMDAS: 3 + 6 × (5 + 4) ÷ 3 − 7
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Solution:
- Parentheses: Evaluate inside the parentheses first. 3 + 6 × 9 ÷ 3 − 7
- Multiplication and Division: Perform these operations from left to right. 3 + 54 ÷ 3 − 7 = 3 + 18 − 7 = 14
Question 2:
Solve the following equation using PEMDAS: 8 ÷ 2 × (2 + 2)²
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Solution:
- Parentheses: Evaluate inside the parentheses first. 8 ÷ 2 × 4²
- Exponents: Evaluate the exponent. 8 ÷ 2 × 16
- Multiplication and Division: Perform these operations from left to right. 4 × 16 = 64
Question 3:
Solve the following equation using PEMDAS: 7 + (6 × 5² − 4) ÷ 2
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Solution:
- Parentheses: Evaluate inside the parentheses first. 7 + (6 × 25 − 4) ÷ 2
- Multiplication and Subtraction: Evaluate inside the parentheses. 7 + (150 − 4) ÷ 2 = 7 + 146 ÷ 2
- Division: Perform the division. 7 + 73 = 80
How is this going to show up on the ACT® Math?
Now that you've practiced some pure PEMDAS problems, let's talk about how this concept appears on the actual ACT® Math section.
While the ACT® math section gives you few questions, if any, that are just PEMDAS and PEMDAS alone, order of operations constitutes most of the questions on the test. This is due to something the ACT® calls "Depth of Knowledge."
The ACT® uses a concept called 'Depth of Knowledge' to increase question difficulty. In simple terms, harder questions often require more steps to solve. This is where PEMDAS becomes important - more steps mean more chances for order of operations mix-ups.
Conclusion
Getting a solid grip on PEMDAS and answering lots of multi-step problems will set you up for success on the ACT® Math section.