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Order of Operations Worksheet

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Order of Operations Worksheet worksheet preview

Order of Operations Worksheet

Mathematical operations symbols

📚 Part 1: Understanding GEMA

1. What does the mnemonic GEMA stand for? Fill in the blanks:

G - _________________ (parentheses/brackets)

E - _________________

M - _________________ (× and ÷)

A - _________________ (+ and −)

2. Write each expression as repeated multiplication:

a) 4² = _________________

b) 2³ = _________________

c) 5⁴ = _________________

3. Calculate these expressions using GEMA. Show your working steps:

a) 2 + 3 × 4

b) (5 + 2)²

✏️ Part 2: Practice Problems

4. Solve these expressions step by step. Remember to follow GEMA!

a) 8 ÷ 4 + 2³

b) (3 + 1) × 2³ − 5

c) (4 + 3)² ÷ 7 + 6

5. Challenge Problem: Solve this complex expression:

2 × (3³ − 4) + 10 ÷ (1 + 1)

6. Circle the correct answer for each expression:

a) 6 + 2 × 3 = ?

24

12

18

b) (8 − 3)² = ?

10

25

11

🤔 Part 3: Reflection

7. Explain in your own words why we need to follow the order of operations (GEMA):
8. What would happen if we solved 2 + 3 × 4 from left to right instead of using GEMA? Show both methods:

Using GEMA:

Left to right:

Why are the answers different?

9. Create your own expression that uses all parts of GEMA (grouped symbols, exponents, multiplication/division, and addition/subtraction). Then solve it:

My expression: ________________________

Solution:

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