Order of Operations worksheets | Worsheets library - Free Printable

Let's solve each problem step by step using the order of operations, often remembered by the acronym PEMDAS:

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

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1. $(14^2 \times 15) - (2^2 + 20)$

Step-by-step:
- $14^2 = 196$
- $196 \times 15 = 2940$
- $2^2 = 4$, so $4 + 20 = 24$
- Now: $2940 - 24 = 2916$

✔ Answer: 2916

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2. $8^2 \times 2 - 14 - 12$

Step-by-step:
- $8^2 = 64$
- $64 \times 2 = 128$
- $128 - 14 = 114$
- $114 - 12 = 102$

✔ Answer: 102

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3. $(6^2 + 18 - 8) \div 2$

Step-by-step:
- $6^2 = 36$
- $36 + 18 = 54$
- $54 - 8 = 46$
- $46 \div 2 = 23$

✔ Answer: 23

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4. $(14 + 2 \times 2)^2 - 16^2$

Step-by-step:
- Inside parentheses: $2 \times 2 = 4$
- $14 + 4 = 18$
- $18^2 = 324$
- $16^2 = 256$
- $324 - 256 = 68$

✔ Answer: 68

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5. $(19 + 7^2 \times 8) - 5$

Step-by-step:
- $7^2 = 49$
- $49 \times 8 = 392$
- $19 + 392 = 411$
- $411 - 5 = 406$

✔ Answer: 406

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6. $(12^2 - 15 + 17) \times 16$

Step-by-step:
- $12^2 = 144$
- $144 - 15 = 129$
- $129 + 17 = 146$
- $146 \times 16 = 2336$

✔ Answer: 2336

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7. $11 \times (5^2 + 3) - 5$

Step-by-step:
- $5^2 = 25$
- $25 + 3 = 28$
- $11 \times 28 = 308$
- $308 - 5 = 303$

✔ Answer: 303

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8. $(16^2 \times 8) \div 3 - 7$

Step-by-step:
- $16^2 = 256$
- $256 \times 8 = 2048$
- $2048 \div 3 = 682.\overline{6}$ → But let's keep it as a fraction or decimal?
- $682.666... - 7 = 675.666...$

But since this is likely meant for whole numbers, let's check if we made a mistake.

Wait — actually, $2048 \div 3$ is not a whole number. Let's compute exactly:

- $2048 \div 3 = 682\frac{2}{3}$
- Then $682\frac{2}{3} - 7 = 675\frac{2}{3}$

But perhaps we should leave it as a decimal or mixed number?

Alternatively, maybe the problem expects exact fractional form.

✔ Answer: $675\frac{2}{3}$ or $675.67$ (approx)

But let’s double-check: Is there a typo? Or is this acceptable?

Actually, no typo. So final answer is:

✔ Answer: $675\frac{2}{3}$ or $675.\overline{6}$

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9. $(6^3 - 12) \div (20 - 8)$

Step-by-step:
- $6^3 = 216$
- $216 - 12 = 204$
- $20 - 8 = 12$
- $204 \div 12 = 17$

✔ Answer: 17

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10. $15^2 + (18 + 9) - 19$

Step-by-step:
- $15^2 = 225$
- $18 + 9 = 27$
- $225 + 27 = 252$
- $252 - 19 = 233$

✔ Answer: 233

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11. $4^2 + (8 - 2)^2 \div 4$

Step-by-step:
- $4^2 = 16$
- $8 - 2 = 6$
- $6^2 = 36$
- $36 \div 4 = 9$
- $16 + 9 = 25$

✔ Answer: 25

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12. $10 + (16^2 - 14) \times 19$

Step-by-step:
- $16^2 = 256$
- $256 - 14 = 242$
- $242 \times 19 = ?$

Let’s compute $242 \times 19$:

Break it down:
- $242 \times 20 = 4840$
- $242 \times 1 = 242$
- So $4840 - 242 = 4598$

Then: $10 + 4598 = 4608$

✔ Answer: 4608

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✔ Final Answers:

1. 2916
2. 102
3. 23
4. 68
5. 406
6. 2336
7. 303
8. 675⅔ (or $675.\overline{6}$)
9. 17
10. 233
11. 25
12. 4608

Let me know if you'd like these formatted neatly or printed!