Math worksheet practicing order of operations (PEMDAS) with ten problems.

You're given a worksheet titled “Order of Operations - (PEMDAS)” with 10 problems. PEMDAS stands for:

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

We’ll solve each problem step by step, following PEMDAS.

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Problem 1: `((14 + 3) + (20 ÷ 2)²) + 5²`

1. Inner parentheses:
- `14 + 3 = 17`
- `20 ÷ 2 = 10` → then `10² = 100`
2. Now: `(17 + 100) + 5²` → `117 + 25`
3. Final: `117 + 25 = 142`

✔ Answer: 142

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Problem 2: `(12 ÷ 3)² + ((10 - 4) × 6²)`

1. Parentheses:
- `12 ÷ 3 = 4` → `4² = 16`
- `10 - 4 = 6`
- `6² = 36` → `6 × 36 = 216`
2. Add: `16 + 216 = 232`

✔ Answer: 232

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Problem 3: `(6² + (18 ÷ 9 + 5²)) - 3²`

1. Exponents first:
- `6² = 36`
- `5² = 25`
- `3² = 9`
2. Inside inner parentheses: `18 ÷ 9 = 2` → `2 + 25 = 27`
3. Now: `36 + 27 = 63` → `63 - 9 = 54`

✔ Answer: 54

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Problem 4: `(6² + (8 ÷ 4 + 3²)) - 4²`

1. Exponents:
- `6² = 36`
- `3² = 9`
- `4² = 16`
2. Inside parentheses: `8 ÷ 4 = 2` → `2 + 9 = 11`
3. Now: `36 + 11 = 47` → `47 - 16 = 31`

✔ Answer: 31

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Problem 5: `((18 - 3) - (20 + 2)²) × 7²`

1. Parentheses:
- `18 - 3 = 15`
- `20 + 2 = 22` → `22² = 484`
2. Now: `15 - 484 = -469`
3. `7² = 49`
4. Multiply: `-469 × 49`

Let’s compute:
`-469 × 49 = -469 × (50 - 1) = -469×50 + 469 = -23450 + 469 = -22981`

✔ Answer: -22981

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Problem 6: `((9 - 4)² + 4) + 13 + 5²`

1. `9 - 4 = 5` → `5² = 25`
2. `25 + 4 = 29`
3. `5² = 25`
4. Now: `29 + 13 + 25 = 67`

✔ Answer: 67

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Problem 7: `((10 - 3)² + 7) - 4 + 6²`

1. `10 - 3 = 7` → `7² = 49`
2. `49 + 7 = 56`
3. `6² = 36`
4. Now: `56 - 4 + 36` → left to right: `52 + 36 = 88`

✔ Answer: 88

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Problem 8: `10 + (10 + (10 - 5)²) + 6`

1. Innermost: `10 - 5 = 5` → `5² = 25`
2. Next: `10 + 25 = 35`
3. Now: `10 + 35 + 6 = 51`

✔ Answer: 51

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Problem 9: `7 + (5 + (9 - 6)²) - 9`

1. `9 - 6 = 3` → `3² = 9`
2. `5 + 9 = 14`
3. Now: `7 + 14 - 9 = 21 - 9 = 12`

✔ Answer: 12

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Problem 10: `(20 ÷ 4)² + ((16 - 3) × 5²)`

1. `20 ÷ 4 = 5` → `5² = 25`
2. `16 - 3 = 13`
3. `5² = 25` → `13 × 25 = 325`
4. Now: `25 + 325 = 350`

✔ Answer: 350

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## ✔ Final Answers:

1. 142
2. 232
3. 54
4. 31
5. -22981
6. 67
7. 88
8. 51
9. 12
10. 350

Let me know if you’d like these formatted as a completed worksheet or explained differently!