Answer key for a math worksheet on order of operations, displaying problems and their solutions.

You've uploaded an image of a math worksheet titled “Using Order of Operations” with 10 problems, and it includes the Answer Key on the right side. The student’s work is shown in red ink next to each problem, and the correct answers are listed vertically on the right.

Let’s go through each problem, verify the solution using the Order of Operations (PEMDAS/BODMAS), and explain why each answer is correct or incorrect.

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🔢 Order of Operations Reminder:

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

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## ✔ Problem 1:
Expression: `10 + 32 ÷ 8 × (14 - 8 + 3)`

✔ Student’s Work:
- `(14 - 8 + 3)` → `6 + 3` = `9` ✔️
- `32 ÷ 8 × 9` → `4 × 9` = `36` ✔️ (Left to right: division then multiplication)
- `10 + 36` = `46` ✔️

✔ Correct Answer: 46

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## ✔ Problem 2:
Expression: `(7 + 2) × 5 × 8`

✔ Student’s Work:
- `(7 + 2)` = `9` ✔️
- `9 × 5 × 8` → `45 × 8` = `360` ✔️

✔ Correct Answer: 360

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## ✔ Problem 3:
Expression: `6(6 - 2 + 36 ÷ 4) × 9`

✔ Student’s Work:
- Inside parentheses: `6 - 2 + 36 ÷ 4`
- `36 ÷ 4` = `9`
- `6 - 2 + 9` = `4 + 9` = `13` ✔️
- `6 × 13 × 9` → `78 × 9` = `702` ✔️

✔ Correct Answer: 702

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## ✔ Problem 4:
Expression: `(9 × 6) + 56 ÷ 8 + 40 ÷ 10`

✔ Student’s Work:
- `9 × 6` = `54`
- `56 ÷ 8` = `7`
- `40 ÷ 10` = `4`
- `54 + 7 + 4` = `65` ✔️

✔ Correct Answer: 65

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## ✔ Problem 5:
Expression: `7(13 - 4 + 36 ÷ 6) × 9`

✔ Student’s Work:
- Inside parentheses: `13 - 4 + 36 ÷ 6`
- `36 ÷ 6` = `6`
- `13 - 4 + 6` = `9 + 6` = `15` ✔️
- `7 × 15 × 9` → `105 × 9` = `945` ✔️

✔ Correct Answer: 945

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## ✔ Problem 6:
Expression: `4 + 16 ÷ 4 × (72 ÷ 9 + 10)`

✔ Student’s Work:
- Inner parentheses: `72 ÷ 9 + 10` = `8 + 10` = `18` ✔️
- Now: `4 + 16 ÷ 4 × 18`
- `16 ÷ 4` = `4`
- `4 × 18` = `72`
- `4 + 72` = `76` ✔️

✔ Correct Answer: 76

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## ✔ Problem 7:
Expression: `(4 + 20 ÷ 4) + 60 ÷ 10 + 10`

✔ Student’s Work:
- Parentheses: `4 + 20 ÷ 4` → `4 + 5` = `9` ✔️
- `60 ÷ 10` = `6`
- So: `9 + 6 + 10` = `25` ✔️

✔ Correct Answer: 25

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## ✔ Problem 8:
Expression: `3(8 + 9) × 4`

✔ Student’s Work:
- `(8 + 9)` = `17`
- `3 × 17 × 4` → `51 × 4` = `204` ✔️

✔ Correct Answer: 204

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## ✔ Problem 9:
Expression: `(2 + 2) × 5 × 3`

✔ Student’s Work:
- `(2 + 2)` = `4`
- `4 × 5 × 3` → `20 × 3` = `60` ✔️

✔ Correct Answer: 60

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## ✔ Problem 10:
Expression: `(9 + 54 ÷ 6) × 4 × 5`

✔ Student’s Work:
- Inside parentheses: `9 + 54 ÷ 6` → `9 + 9` = `18` ✔️
- `18 × 4 × 5` → `72 × 5` = `360` ✔️

✔ Correct Answer: 360

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## 📌 Final Summary:

✔ All 10 problems were solved correctly by the student.

The student followed Order of Operations properly:
- Solved inside parentheses first.
- Handled multiplication/division left to right.
- Then addition/subtraction.

The Answer Key on the right matches all solutions.

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## 🎯 Conclusion:

This worksheet demonstrates excellent understanding of the Order of Operations. Every step is logically sound and mathematically accurate.

✔️ All answers are correct.

If this was submitted as homework or a quiz — full credit! 🎉

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