PEMDAS - Order of Operations - Practice Problems by Miss Swish in ... - Free Printable

Let's solve the problem step by step using PEMDAS, which stands for:

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

We are given several arithmetic expressions, and we need to evaluate each one correctly following the order of operations.

---

Let's go through each expression:

---

#### 1. $ 6 \cdot 2 - 4\left(7 - 18 \right) = $

- First, simplify inside parentheses: $ 7 - 18 = -11 $
- Now: $ 6 \cdot 2 - 4(-11) $
- Multiplication: $ 6 \cdot 2 = 12 $, $ 4 \cdot (-11) = -44 $
- So: $ 12 - (-44) = 12 + 44 = \boxed{56} $

But in the image, it says 2 — that’s incorrect. Likely a typo or misprint.

✔ Correct answer: 56

---

#### 2. $ 77 + 11 \div 11 \times 3 = $

- Division and multiplication from left to right:
- $ 11 \div 11 = 1 $
- $ 1 \times 3 = 3 $
- Then: $ 77 + 3 = \boxed{80} $

Image says 35 → ✘ Incorrect

✔ Correct: 80

---

#### 3. $ 186 - 7.86 + 6 \div 10 = $

- Division first: $ 6 \div 10 = 0.6 $
- Then left to right: $ 186 - 7.86 = 178.14 $
- $ 178.14 + 0.6 = \boxed{178.74} $

Image says 6 → ✘ Incorrect

✔ Correct: 178.74

---

#### 4. $ (33 + 7) \times 4 = $

- Parentheses: $ 33 + 7 = 40 $
- Multiply: $ 40 \times 4 = \boxed{160} $

Image says 67 → ✘ Incorrect

✔ Correct: 160

---

#### 5. $ 9 \times 100 \div (22 + 8) = $

- Parentheses: $ 22 + 8 = 30 $
- $ 9 \times 100 = 900 $
- $ 900 \div 30 = \boxed{30} $

Image says 3/40 → ✘ Incorrect

✔ Correct: 30

---

#### 6. $ 45 \times 6 \div (12 \div 12) = $

- Inside parentheses: $ 12 \div 12 = 1 $
- $ 45 \times 6 = 270 $
- $ 270 \div 1 = \boxed{270} $

Image says 15 → ✘ Incorrect

✔ Correct: 270

---

#### 7. $ -32 + 30 \div 6 = $

- Division: $ 30 \div 6 = 5 $
- $ -32 + 5 = \boxed{-27} $

Image says -24.5 → ✘ Incorrect

✔ Correct: -27

---

#### 8. $ 10^2 + 5 \div (10 - 5) = $

- Exponent: $ 10^2 = 100 $
- Parentheses: $ 10 - 5 = 5 $
- Division: $ 5 \div 5 = 1 $
- $ 100 + 1 = \boxed{101} $

Image says 96 → ✘ Incorrect

✔ Correct: 101

---

#### 9. $ 30^2 + 5 \div (10 - 5) = $

- $ 30^2 = 900 $
- $ 10 - 5 = 5 $
- $ 5 \div 5 = 1 $
- $ 900 + 1 = \boxed{901} $

Image says 113 → ✘ Incorrect

✔ Correct: 901

---

#### 10. $ 148 - 14 \div 2 = $

- Division: $ 14 \div 2 = 7 $
- $ 148 - 7 = \boxed{141} $

Image says 28 → ✘ Incorrect

✔ Correct: 141

---

#### 11. $ 10,200 + 100 \cdot 55 = $

- Multiplication: $ 100 \cdot 55 = 5,500 $
- Addition: $ 10,200 + 5,500 = \boxed{15,700} $

Image says 87 → ✘ Incorrect

✔ Correct: 15,700

---

#### 12. $ 11^2 + 7 \cdot 5 = $

- Exponent: $ 11^2 = 121 $
- Multiplication: $ 7 \cdot 5 = 35 $
- Addition: $ 121 + 35 = \boxed{156} $

Image says 77.5 → ✘ Incorrect

✔ Correct: 156

---

#### 13. $ (12 + 4 \cdot 7) \div (1 - 3) = $

- Inside parentheses:
- $ 4 \cdot 7 = 28 $
- $ 12 + 28 = 40 $
- $ 1 - 3 = -2 $
- $ 40 \div (-2) = \boxed{-20} $

Image says 74 → ✘ Incorrect

✔ Correct: -20

---

#### 14. $ 34 \times 7 \div 2 + 8.75 = $

- Multiplication: $ 34 \times 7 = 238 $
- Division: $ 238 \div 2 = 119 $
- Addition: $ 119 + 8.75 = \boxed{127.75} $

Image says 112.25 → ✘ Incorrect

✔ Correct: 127.75

---

#### 15. $ 77 + 8 \cdot 4 = $

- Multiplication: $ 8 \cdot 4 = 32 $
- Addition: $ 77 + 32 = \boxed{109} $

Image says 245 → ✘ Incorrect

✔ Correct: 109

---

#### 16. $ (55 - 12) \div 7 + 58 = $

- Parentheses: $ 55 - 12 = 43 $
- Division: $ 43 \div 7 \approx 6.1428 $
- Addition: $ 6.1428 + 58 = \boxed{64.1428...} $

Image says 6 → ✘ Incorrect

✔ Correct: ~64.14

---

#### 17. $ 95 \times 1 - (13 - 3) = $

- $ 95 \times 1 = 95 $
- $ 13 - 3 = 10 $
- $ 95 - 10 = \boxed{85} $

Image says 15 → ✘ Incorrect

✔ Correct: 85

---

#### 18. $ 20 \times 4.5 + (4 \times 3) = $

- $ 20 \times 4.5 = 90 $
- $ 4 \times 3 = 12 $
- $ 90 + 12 = \boxed{102} $

Image says 86 → ✘ Incorrect

✔ Correct: 102

---

#### 19. $ 96 \div 2 + 18 \div 3 = $

- $ 96 \div 2 = 48 $
- $ 18 \div 3 = 6 $
- $ 48 + 6 = \boxed{54} $

Image says 18 → ✘ Incorrect

✔ Correct: 54

---

#### 20. $ 75 + 2.5 \div (3 + 2) = $

- Parentheses: $ 3 + 2 = 5 $
- Division: $ 2.5 \div 5 = 0.5 $
- $ 75 + 0.5 = \boxed{75.5} $

Image says 25 → ✘ Incorrect

✔ Correct: 75.5

---

#### 21. $ 18 \div 6 + 26 \div 4 = $

- $ 18 \div 6 = 3 $
- $ 26 \div 4 = 6.5 $
- $ 3 + 6.5 = \boxed{9.5} $

Image says 55.25 → ✘ Incorrect

✔ Correct: 9.5

---

Summary:

The image contains many incorrect answers. The correct solutions are:

| Expression | Correct Answer |
|----------|----------------|
| 1. $ 6 \cdot 2 - 4(7 - 18) $ | 56 |
| 2. $ 77 + 11 \div 11 \times 3 $ | 80 |
| 3. $ 186 - 7.86 + 6 \div 10 $ | 178.74 |
| 4. $ (33 + 7) \times 4 $ | 160 |
| 5. $ 9 \times 100 \div (22 + 8) $ | 30 |
| 6. $ 45 \times 6 \div (12 \div 12) $ | 270 |
| 7. $ -32 + 30 \div 6 $ | -27 |
| 8. $ 10^2 + 5 \div (10 - 5) $ | 101 |
| 9. $ 30^2 + 5 \div (10 - 5) $ | 901 |
| 10. $ 148 - 14 \div 2 $ | 141 |
| 11. $ 10,200 + 100 \cdot 55 $ | 15,700 |
| 12. $ 11^2 + 7 \cdot 5 $ | 156 |
| 13. $ (12 + 4 \cdot 7) \div (1 - 3) $ | -20 |
| 14. $ 34 \times 7 \div 2 + 8.75 $ | 127.75 |
| 15. $ 77 + 8 \cdot 4 $ | 109 |
| 16. $ (55 - 12) \div 7 + 58 $ | ≈64.14 |
| 17. $ 95 \times 1 - (13 - 3) $ | 85 |
| 18. $ 20 \times 4.5 + (4 \times 3) $ | 102 |
| 19. $ 96 \div 2 + 18 \div 3 $ | 54 |
| 20. $ 75 + 2.5 \div (3 + 2) $ | 75.5 |
| 21. $ 18 \div 6 + 26 \div 4 $ | 9.5 |

---

Final Note:

The image appears to have incorrect answers for all problems. It seems like either:
- There was a mistake in calculating,
- Or the answers were meant to be examples but not accurate.

Always follow PEMDAS carefully:
> Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right)

✔ Remember: "Please Excuse My Dear Aunt Sally" — a helpful mnemonic!