Order of Operations Worksheets - Free Printable

You’ve uploaded an image of a math worksheet titled “Using Order of Operations” with 10 expressions to evaluate, and the answer key is already filled in on the right side. The worksheet also shows step-by-step solutions for each problem using the correct order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right).

Since you asked to “solve the problem and explain the solution,” I’ll go through each problem, explain the steps clearly, and verify the given answers.

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✔ Problem 1: `(9 × 9) + 7 + 54 ÷ 9`

Step 1: Evaluate inside parentheses:
→ `9 × 9 = 81`

Step 2: Do division next:
→ `54 ÷ 9 = 6`

Step 3: Now add left to right:
→ `81 + 7 + 6 = 88 + 6 = 94`

✔ Answer: 94

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✔ Problem 2: `10(15 ÷ 5 + 6) + 9`

Step 1: Inside parentheses — do division first:
→ `15 ÷ 5 = 3`
→ Then `3 + 6 = 9`

Step 2: Multiply:
→ `10 × 9 = 90`

Step 3: Add:
→ `90 + 9 = 99`

✔ Answer: 99

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✔ Problem 3: `(8 + 20 ÷ 10) + 36 ÷ 4 + 3`

Step 1: Inside parentheses — division first:
→ `20 ÷ 10 = 2`
→ Then `8 + 2 = 10`

Step 2: Division outside:
→ `36 ÷ 4 = 9`

Step 3: Now add all:
→ `10 + 9 + 3 = 19 + 3 = 22`

✔ Answer: 22

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✔ Problem 4: `6 × 3(10 + 8)`

Note: This is often interpreted as `6 × 3 × (10 + 8)` — multiplication is associative and implied multiplication has same precedence as explicit.

Step 1: Parentheses:
→ `10 + 8 = 18`

Step 2: Multiply left to right:
→ `6 × 3 = 18`
→ `18 × 18 = 324`

✔ Answer: 324

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✔ Problem 5: `9 + 15 - 8(5 + 13 - 9)`

Step 1: Inside parentheses:
→ `5 + 13 = 18`, then `18 - 9 = 9`

Step 2: Multiply:
→ `8 × 9 = 72`

Step 3: Now left to right:
→ `9 + 15 = 24`, then `24 - 72 = -48`

✔ Answer: -48

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✔ Problem 6: `6(28 ÷ 7 + 14 ÷ 7) + 8`

Step 1: Inside parentheses — both divisions:
→ `28 ÷ 7 = 4`, `14 ÷ 7 = 2`
→ `4 + 2 = 6`

Step 2: Multiply:
→ `6 × 6 = 36`

Step 3: Add:
→ `36 + 8 = 44`

✔ Answer: 44

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✔ Problem 7: `7(5 × 2) + 8`

Step 1: Inside parentheses:
→ `5 × 2 = 10`

Step 2: Multiply:
→ `7 × 10 = 70`

Step 3: Add:
→ `70 + 8 = 78`

✔ Answer: 78

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✔ Problem 8: `4(6 - 5 + 4) × 9`

Step 1: Inside parentheses — left to right:
→ `6 - 5 = 1`, then `1 + 4 = 5`

Step 2: Multiply:
→ `4 × 5 = 20`, then `20 × 9 = 180`

✔ Answer: 180

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✔ Problem 9: `5 + 10(8 + 21 ÷ 3)`

Step 1: Inside parentheses — division first:
→ `21 ÷ 3 = 7`, then `8 + 7 = 15`

Step 2: Multiply:
→ `10 × 15 = 150`

Step 3: Add:
→ `5 + 150 = 155`

✔ Answer: 155

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✔ Problem 10: `(6 + 8) + 9 × 7`

Step 1: Parentheses:
→ `6 + 8 = 14`

Step 2: Multiplication:
→ `9 × 7 = 63`

Step 3: Add:
→ `14 + 63 = 77`

✔ Answer: 77

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## 📌 Summary:

All 10 problems were solved correctly according to order of operations (PEMDAS). The answer key provided in the image is accurate.

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## 💡 Key Takeaways:

- Always start with Parentheses.
- Then Exponents (none here).
- Then Multiplication and Division from left to right.
- Then Addition and Subtraction from left to right.
- Implied multiplication (like `3(4)`) is treated the same as `3 × 4`.

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✔ Final Answer: All 10 problems are correctly solved. Answers are:
1. 94 2. 99 3. 22 4. 324 5. -48 6. 44 7. 78 8. 180 9. 155 10. 77

Let me know if you’d like a printable version or more practice!