Algebra Step by Step

PEMDAS! This simple yet powerful acronym is your key to mastering any mathematical expression. It’s a straightforward set of rules laying out the sequence for solving math problems. By following PEMDAS, you’re guaranteed to arrive at the correct answer every time, eliminating any potential confusion and boosting your confidence in your mathematical abilities!

Here’s the PEMDAS breakdown:

• P is for Parentheses: They come first! Always tackle any calculations inside grouping symbols before moving on. Parentheses can group the four basic operations (addition, subtraction, multiplication, and division).
• E is for Exponents: These little superscript numbers tell you how many times to multiply a base number by itself. Simplify all exponents before moving on.
• M is for Multiplication: Once parentheses and exponents are out of the way, it’s multiplication time! Perform all multiplications from left to right in the order they appear.
• D is for Division: Division follows the same rule as multiplication. Solve all division problems from left to right.
• A is for Addition: Now that multiplication and division are done, we can add! Again, work your way from left to right, adding each term in the expression.
• S is for Subtraction: We tackle any remaining subtractions, working from left to right.

Remember, PEMDAS is the secret to keeping order and accuracy in math. Following these steps correctly will solve any problem quickly and precisely!

Use PEMDAS to solve this problem.  In the space below, work on this problem. The steps will be explained on the next page.  

Problem: Solve the equation: 14  (3 * 2)  2

PEMDAS Breakdown:

1. Parentheses: We tackle what’s inside the parentheses first. 3 * 2 = 6.
2. Multiplication and division (from left to right): Since multiplication and division have equal weight in PEMDAS, we go from left to right. 6  2 = 3
3. Addition and subtractions. Add 14 to 3 to get 17.

Final Answer: 10

Explanation:

• We didn’t meet any exponents in this example, but if we did, they would be solved before multiplication and division.
• Even though the addition sign comes before the division sign in this example, we perform the division first because of the order of operations.

Another Example (with Exponents): Solve the equation: 2^3 – (5 + 1) x 4. This time, we will use the graphic below to organize our work.

Parentheses 5 + 1 = 6 So, now we have: 2^3 – 6(4)	Exponents 2^3 = 2*2*2 = 8  So, now we have: 8 – 6(4)	Multiplication/Division  6 x 4 = 24 So, now we have: 8 – 24
Multiplication/Division No division	Addition/Subtraction No Addition	Addition/Subtraction 8 – 24 = -18
Final answer:  -18

Example 3 (with all operations): Solve the equation: ²

Parentheses (3 – 1) = 2 So, now we have: 2	Exponents 32 = 3 * 3 = 9 So, now we have:	Multiplication/Division  24/8 = 3 So, now we have:
Multiplication/Division 2 * 2 = 4 So, now we have:	Addition/Subtraction 9 + 3 + 4 = 16 So, now we have:	Addition/Subtraction 16 – 8 = 8 So, now we have:
Final answer:  8

I love using this PEMDAS table because it organizes my work. I think of it as a problem-solving roadmap. Each box tells me precisely what to do next so I don’t forget any steps. To stay on track, I rewrite the problem after each step. I’ve discovered that breaking down problems and showing my work is incredibly helpful as I tackle more complex math concepts. Not only does this method help me stay organized and avoid errors, but it also provides valuable insights into the problem-solving process as I observe how the equation transforms with each step. Most importantly, it helps me stay on track and ensures I’m not missing anything.

Remember: Multiplication and division are like twins – they have the same importance in the order of operations. That’s why they are listed together in the PEMDAS table. The same goes for addition and subtraction – they’re also equal partners! We’ve given you plenty of space to work out each step so you can focus on getting it right.

Now, get ready to practice some problems! Each problem will have a graphic organizer to guide you. There are answers provided, but try to solve the problems yourself first. Then, you can check your work and see how you did.

Problem 1:

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Problem 2:  

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Problem 3:

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Problem 4: :

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Problem 5:

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Problem 6:

Parentheses	Exponents	Multiplication/Division
Multiplication/Division	Addition/Subtraction	Addition/Subtraction
Final answer:

Ready to master PEMDAS? Dive deeper with our comprehensive book available on Amazon, packed with practice problems and detailed, step-by-step explanations to guide you every step of the way. For an even more immersive learning experience, enroll in our interactive course at AlgebraHelpDesk.com and take your algebra skills to the next level. Start your journey to math confidence today!