Order of Operations worksheet focusing on multiplication, division, addition, and subtraction with examples and exercises.

Let's solve this Order of Operations worksheet step by step, following the PEMDAS rule:

> Parentheses
> Exponents
> Multiplication and Division (from left to right)
> Addition and Subtraction (from left to right)

We'll go through each section carefully.

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🔷 Section A: Underline which part to do first

We underline the operation that comes first based on PEMDAS.

1) 9 + 4 × 6
→ Multiplication first: 4 × 6
✔ Underline: `4 × 6`

2) 6 - 10 ÷ 5
→ Division first: 10 ÷ 5
✔ Underline: `10 ÷ 5`

3) 4 × 21 ÷ 3
→ Multiplication and division from left to right. First: 4 × 21
✔ Underline: `4 × 21`

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🔷 Section B: Underline first and second operations

1) 30 ÷ 6 - 15 ÷ 5
- First: 30 ÷ 6 and 15 ÷ 5 (both divisions) — do them in order from left to right.
- So first: 30 ÷ 6, then 15 ÷ 5
✔ Underline: `30 ÷ 6`, then `15 ÷ 5`

2) 2 × 8 - 18 ÷ 3
- First: 2 × 8 and 18 ÷ 3 (multiplication and division)
- Left to right: 2 × 8 first
- Then 18 ÷ 3
✔ Underline: `2 × 8`, then `18 ÷ 3`

3) 13 + 11 - 4 × 2
- First: 4 × 2 (multiplication)
- Then: 13 + 11 or 13 + 11 - ... — addition/subtraction left to right
✔ Underline: `4 × 2`, then `13 + 11`

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🔷 Section C: Choose correct answer

We’ll evaluate each expression using order of operations.

1) 12 - 2 × 4
= 12 - 8 = 4
✔ Answer: 4

2) 16 + 32 ÷ 8
= 16 + 4 = 20
✔ Answer: 20

3) 5 × 9 - 11 × 2
= 45 - 22 = 23
✔ Answer: 23

4) 4 + 3 × 10 ÷ 5
→ Multiply and divide left to right:
3 × 10 = 30 → 30 ÷ 5 = 6
Then: 4 + 6 = 10
✔ Answer: 10

5) 72 + 30 - 25 × 4
→ 25 × 4 = 100
Then: 72 + 30 = 102 → 102 - 100 = 2
✔ Answer: 2

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🔷 Section D: Calculate without a calculator

We apply PEMDAS.

1) 8 - 3 × 2
= 8 - 6 = 2

2) 4 + 6 ÷ 2
= 4 + 3 = 7

3) 5 + 4 × 4
= 5 + 16 = 21

4) 5 - 12 ÷ 3
= 5 - 4 = 1

5) 2 + 7 × 3
= 2 + 21 = 23

6) 7 - 1 × 6
= 7 - 6 = 1

7) 31 - 3 × 8
= 31 - 24 = 7

8) 6 - 10 ÷ 5
= 6 - 2 = 4

9) 8 ÷ 4 + 14
= 2 + 14 = 16

10) 8 + 7 + 2 × 6
→ 2 × 6 = 12
Then: 8 + 7 + 12 = 27

11) 5 × 5 + 20 ÷ 10
= 25 + 2 = 27

12) 49 ÷ 7 + 18 ÷ 3
= 7 + 6 = 13

13) 8 × 6 + 77 ÷ 7
= 48 + 11 = 59

14) 10 + 7 - 2 × 6
= 10 + 7 - 12 = 17 - 12 = 5

15) 18 - 6 × 15 ÷ 5
→ 6 × 15 = 90 → 90 ÷ 5 = 18
Then: 18 - 18 = 0

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🔷 Section E: Spot and correct mistakes

1) 3 + 5 × 7 = 56 ✘
→ Wrong: Did 3 + 5 = 8, then 8 × 7 = 56
But correct: 5 × 7 = 35, then 3 + 35 = 38
✔ Corrected: 3 + 5 × 7 = 38

2) 11 + 3 × 9 - 8 = 14 ✘
→ Wrong: Probably did left to right: 11+3=14, 14×9=126, 126−8=118
But correct:
- 3 × 9 = 27
- 11 + 27 = 38
- 38 - 8 = 30
✔ Corrected: 11 + 3 × 9 - 8 = 30

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✔ Final Answers Summary

#### Section A:
1) Underline: 4 × 6
2) Underline: 10 ÷ 5
3) Underline: 4 × 21

#### Section B:
1) First: 30 ÷ 6, Second: 15 ÷ 5
2) First: 2 × 8, Second: 18 ÷ 3
3) First: 4 × 2, Second: 13 + 11

#### Section C:
1) 4
2) 20
3) 23
4) 10
5) 2

#### Section D:
1) 2
2) 7
3) 21
4) 1
5) 23
6) 1
7) 7
8) 4
9) 16
10) 27
11) 27
12) 13
13) 59
14) 5
15) 0

#### Section E:
1) 3 + 5 × 7 = 38 (not 56)
2) 11 + 3 × 9 - 8 = 30 (not 14)

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📌 Key Takeaway:

Always follow PEMDAS:
- Do multiplication and division left to right
- Then addition and subtraction left to right

This avoids common mistakes like doing operations in left-to-right order when it’s not correct.

Let me know if you'd like this as a printable PDF or need help with any specific problem!