Math Problem Statement

Order of Operations Puzzle #1 with various arithmetic expressions to evaluate.

Solution

It looks like you’ve uploaded an "Order of Operations Puzzle" worksheet. The problems focus on evaluating expressions using the correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)).

Let’s walk through the worksheet’s problems:

  1. 15 - 3 × 4 = 3

    • The student wrote: 1512=315 - 12 = 3, which is correct. The order of operations was followed (multiplying before subtracting).
  2. (18 ÷ 4) × 2 = 11

    • Solution: (18÷4)×2=4.5×2=9(18 ÷ 4) × 2 = 4.5 × 2 = 9, but the student circled this as correct even though the final answer isn't 11.
  3. 20 - 8 + 3 = 9

    • This one looks fine: 208=1220 - 8 = 12 and then 12+3=1512 + 3 = 15, so the answer is 15, not 9. It was evaluated incorrectly.
  4. 56 ÷ 8 - 1 = 6

    • 56÷8=756 ÷ 8 = 7, and 71=67 - 1 = 6, which is correct.
  5. 20 + 10 × 2 = 4

    • The student incorrectly evaluated 20+10×2=420 + 10 × 2 = 4, which is wrong. The correct solution should follow multiplication first:
      • 10×2=2010 × 2 = 20, then 20+20=4020 + 20 = 40, not 4.
  6. (7 × 5) ÷ 2 = 49

    • Evaluating inside parentheses: 7×5=357 × 5 = 35, then 35÷2=17.535 ÷ 2 = 17.5, not 49. The answer provided is incorrect.
  7. 5 + 8 × 2 - 4 = 22

    • Correctly solved:
      • 8×2=168 × 2 = 16, then 5+16=215 + 16 = 21, and finally 214=1721 - 4 = 17, not 22.
  8. 36 ÷ 6 × 2 + 9 = 12

    • The correct order should be division and multiplication first:
      • 36÷6=636 ÷ 6 = 6, then 6×2=126 × 2 = 12, and 12+9=2112 + 9 = 21, not 12. The answer is incorrect.
  9. 4 × 10 ÷ 3 + 2 = 8

    • The student's scratch work shows 40÷3=13.3340 ÷ 3 = 13.33, so the final answer should be:
      • 13.33+2=15.3313.33 + 2 = 15.33, which does not equal 8. The answer is incorrect.
  10. 43 - 4 × 4 + 8 = 35

    • Correctly evaluated:
      • 4×4=164 × 4 = 16, then 4316=2743 - 16 = 27, and 27+8=3527 + 8 = 35, which is correct.
  11. 16 + 21 - 3 × 6 = 19

    • Multiplication first: 3×6=183 × 6 = 18, then 16+21=3716 + 21 = 37, and 3718=1937 - 18 = 19, which is correct.
  12. 11 + 10 - 4 × 9 = 65

    • The correct answer is:
      • 4×9=364 × 9 = 36, then 11+10=2111 + 10 = 21, and 2136=1521 - 36 = -15, so it does not equal 65. This is incorrect.

Would you like to go into more detail on any specific question?

Here are 5 related questions to practice:

  1. How do you handle parentheses in expressions like (2+3)×4(2 + 3) \times 4?
  2. What’s the result of 24÷4×3+224 \div 4 \times 3 + 2?
  3. If an equation has both addition and subtraction, which one should be done first?
  4. How do you solve 36+18÷6536 + 18 \div 6 - 5?
  5. Can you explain why 7+3×21=127 + 3 \times 2 - 1 = 12?

Tip: Always solve any operations inside parentheses first, then move on to exponents, and continue following the PEMDAS rule step by step!

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Math Problem Analysis

Mathematical Concepts

Order of Operations
Arithmetic Operations
PEMDAS

Formulas

Basic arithmetic operations: Addition, Subtraction, Multiplication, Division
Order of operations (PEMDAS)

Theorems

None specifically, but the order of operations rules are applied: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)

Suitable Grade Level

Grades 5-7