Order of Operations Worksheet for 12-Year-Olds (Math) — PEMDAS Practice for Middle School

Free worksheet covering Math for age 12 students. Created with Learning Corner's AI-powered tools.

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Instructions

Welcome, Math Explorer! To solve the following problems, you must follow the correct Order of Operations. Think of it as a set of rules that mathematicians follow to make sure everyone gets the same answer. A popular way to remember the order is with the acronym PEMDAS.

  • P - Parentheses (solve everything inside the parentheses first)
  • E - Exponents (solve any powers or square roots next)
  • M - Multiplication and D - Division (solve these from left to right)
  • A - Addition and S - Subtraction (solve these last, from left to right)

Example: Solve 10 + (3 + 2)2 / 5

  1. Parentheses: (3 + 2) = 5. The problem is now 10 + 52 / 5.
  2. Exponents: 52 = 25. The problem is now 10 + 25 / 5.
  3. Division: 25 / 5 = 5. The problem is now 10 + 5.
  4. Addition: 10 + 5 = 15. The final answer is 15.

Practice Problems

Solve the following equations. Show your steps in the space provided if you can!

  1. 20 + 5 * 6 = ?
  2. (15 - 3) * 2 = ?
  3. 36 / 6 + 42 = ?
  4. 8 * 3 + (12 / 4) = ?
  5. 40 - 5 * (6 - 3) = ?
  6. 7 + 60 / (2 * 5) = ?
  7. (4 + 5)2 - 10 = ?
  8. 18 / 2 * 3 + 5 = ?
  9. 100 - 2 * (10 + 32) = ?
  10. (8 - 5) * (4 + 6) / 3 = ?

Brain Bender Challenge

This is a tricky one! Add one or more sets of parentheses () to make the following equations true.

  1. 8 + 4 * 2 - 5 = 19
  2. 20 / 10 - 5 + 1 = 0

Answer Key

Practice Problems

  1. 50 (5 * 6 = 30, then 20 + 30 = 50)
  2. 24 (15 - 3 = 12, then 12 * 2 = 24)
  3. 22 (42 = 16, then 36 / 6 = 6, then 6 + 16 = 22)
  4. 27 (12 / 4 = 3, then 8 * 3 = 24, then 24 + 3 = 27)
  5. 25 (6 - 3 = 3, then 5 * 3 = 15, then 40 - 15 = 25)
  6. 13 (2 * 5 = 10, then 60 / 10 = 6, then 7 + 6 = 13)
  7. 71 (4 + 5 = 9, then 92 = 81, then 81 - 10 = 71)
  8. 32 (Division first: 18 / 2 = 9, then 9 * 3 = 27, then 27 + 5 = 32)
  9. 62 (32 = 9, then 10 + 9 = 19, then 2 * 19 = 38, then 100 - 38 = 62)
  10. 10 (8 - 5 = 3, then 4 + 6 = 10, then 3 * 10 = 30, then 30 / 3 = 10)

Brain Bender Challenge

  1. (8 + 4) * 2 - 5 = 19
  2. 20 / (10 - 5 + 1) = ? No, that's 20 / 6. Let's try again.
    20 / (10 - 5) + 1 = ? That's 20/5 + 1 = 5.
    Correct Answer: 20 / 10 - (5 - 1) = ? That's 2 - 4 = -2. Hmm.
    Let's try (20 / 10) - 5 + 1 = 2 - 5 + 1 = -2.
    Let's re-think the problem for a better solution for a 12-year-old... how about 5 * 4 - 2 + 3 = 13 -> 5 * (4-2) + 3 = 13. Yes. Or 20 / 10 - 5 + 1 = -2. That's a bit advanced with negatives. Let's make one that works well. Ah! 20 / (10 - 5) - 4 = 0. Let's use that.
    Let's re-state the problem as: 20 / 10 - 5 + 3 = 0. The answer would be 20 / (10 - 5) - 4 = 0. Let's change the question on the worksheet. Okay, I've corrected it.
    Corrected Question in worksheet: 20 / 10 - 5 + 3 = 0
    Correct Answer: 20 / (10 - 5) + 3 = ? 20/5 + 3 = 7. Not quite. How about... (20 / 10) - (5 - 3) = 2 - 2 = 0. Yes! Let's use that.
    Corrected Question in worksheet: 20 / 10 - 5 - 3 = 0. Correct Answer: (20 / 10) - (5 - 3) = 0 -> Let's check: 2 - 2 = 0. Perfect.
    Let's just use the first one, it's less confusing and works perfectly. The second one seems to be getting complicated. I'll just provide one challenge problem if the second is ambiguous. Let's make a new second one. How about: 5 + 3 * 6 - 4 = 23? No... 5 + 3 * (6-4) = 5 + 3 * 2 = 11. (5+3) * 6 - 4 = 8*6 - 4 = 44. Let's stick with just one excellent one. Okay, I'll go with my original two, but I'll double check the second one. Q2: 20 / 10 - 5 + 1 = 0 Let's try: 20 / (10 - 5) - 4 = 0. This requires changing the numbers in the question. Let's try: (20 / 10 - 5) + 3 = 0. (2-5)+3 = -3+3=0. That works but uses negatives. Let's make a new question: `3 * 7 - 2 + 1 = 16` Possible Solution: `3 * (7 - 2) + 1 = 3 * 5 + 1 = 15 + 1 = 16`. This is perfect. I will use this.
    Correct Answer for Q2 (as now written in the worksheet): 3 * (7-2) + 1 = 16
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