Grade 5 Order of Operations Worksheet focusing on PEMDAS with nested parentheses.

Explanation:
We are solving 10 problems involving the order of operations, especially with nested parentheses. Remember PEMDAS:
Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right).

Let’s solve each one step by step.

---

1) $ 6^2 - (32 - 29)^2 $

- Inside parentheses: $32 - 29 = 3$
- Exponents: $6^2 = 36$, and $3^2 = 9$
- Then: $36 - 9 = 27$

✔ Answer: 27

---

2) $ [(21 - 17) \times (14 - 9)]^2 $

- Inner parentheses: $21 - 17 = 4$, $14 - 9 = 5$
- Multiply: $4 \times 5 = 20$
- Square: $20^2 = 400$

✔ Answer: 400

---

3) $ 11^2 - 3 \times 8 - 5^2 - 19 $

- Exponents first: $11^2 = 121$, $5^2 = 25$
- Multiplication: $3 \times 8 = 24$
- Now: $121 - 24 - 25 - 19$
- Left to right:
- $121 - 24 = 97$
- $97 - 25 = 72$
- $72 - 19 = 53$

✔ Answer: 53

---

4) $ 11^2 - \{3 \times [8 - (5^2 - 19)]\} $

- Innermost: $5^2 = 25$, so $25 - 19 = 6$
- Next: $8 - 6 = 2$
- Then: $3 \times 2 = 6$
- $11^2 = 121$
- Finally: $121 - 6 = 115$

✔ Answer: 115

---

5) $ 11^2 - [3 \times (8 - 5)^2] - 19 $

- Inside parentheses: $8 - 5 = 3$
- Square it: $3^2 = 9$
- Multiply: $3 \times 9 = 27$
- $11^2 = 121$
- So: $121 - 27 - 19$
- $121 - 27 = 94$
- $94 - 19 = 75$

✔ Answer: 75

---

6) $ 12 \times (3 + 11 + 6) - 2^3 $

- Parentheses: $3 + 11 + 6 = 20$
- Multiply: $12 \times 20 = 240$
- Exponent: $2^3 = 8$
- Subtract: $240 - 8 = 232$

✔ Answer: 232

---

7) $ 4^2 + 2^2 \times [40 + (31 - 29)^2] $

- Innermost: $31 - 29 = 2$, then $2^2 = 4$
- Inside brackets: $40 + 4 = 44$
- Exponents: $4^2 = 16$, $2^2 = 4$
- Multiply: $4 \times 44 = 176$
- Add: $16 + 176 = 192$

✔ Answer: 192

---

8) $ 1^3 \times \{9 + [(9 - 21 + 7) - (2^2 - 5)]\} $

- First, $1^3 = 1$, so we can ignore multiplying by 1 until the end.
- Inside innermost:
- $9 - 21 + 7 = (9 + 7) - 21 = 16 - 21 = -5$
- $2^2 = 4$, so $4 - 5 = -1$
- Now: $(-5) - (-1) = -5 + 1 = -4$
- Then: $9 + (-4) = 5$
- Finally: $1 \times 5 = 5$

✔ Answer: 5

---

9) $ 10^2 \times 9 - (4^2 - 4 \times 10) $

- $10^2 = 100$, so $100 \times 9 = 900$
- Inside parentheses:
- $4^2 = 16$
- $4 \times 10 = 40$
- So: $16 - 40 = -24$
- Now: $900 - (-24) = 900 + 24 = 924$

✔ Answer: 924

---

10) $ 4^2 + 3^2 - [2 \times (11 + 9 - 13)] $

- Exponents: $4^2 = 16$, $3^2 = 9$ → sum so far: $16 + 9 = 25$
- Inside parentheses: $11 + 9 = 20$, $20 - 13 = 7$
- Multiply: $2 \times 7 = 14$
- Subtract: $25 - 14 = 11$

✔ Answer: 11

Now double-check all answers quickly:

1) 27
2) 400
3) 53
4) 115
5) 75
6) 232
7) 192
8) 5
9) 924
10) 11

All look correct.

Final Answer:
27, 400, 53, 115, 75, 232, 192, 5, 924, 11