What are the Order of Operations? (Video & Practice) - Free Printable

Let's solve each of these Order of Operations (Advanced) problems step by step using the PEMDAS rule:

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

---

#1

$$
[(15 + 5) + (26 - 6)^2] + 3^2
$$

Step 1: Simplify inside parentheses
- $15 + 5 = 20$
- $26 - 6 = 20$

So now:
$$
[20 + (20)^2] + 3^2
$$

Step 2: Exponents
- $20^2 = 400$
- $3^2 = 9$

Now:
$$
[20 + 400] + 9 = 420 + 9 = \boxed{429}
$$

✔ Answer: 429

---

#2

$$
6(2 + 18 - 9) + (3 × 4)^2
$$

Step 1: Parentheses
- $2 + 18 - 9 = 20 - 9 = 11$

So:
$$
6(11) + (3 × 4)^2
$$

Step 2: Multiplication inside parentheses
- $3 × 4 = 12$, so $(12)^2 = 144$

Now:
$$
6 × 11 = 66
\quad \text{and} \quad 66 + 144 = \boxed{210}
$$

✔ Answer: 210

---

#3

$$
[(3 + 2)^2 + (10 + 1)] + 2^3
$$

Step 1: Parentheses
- $3 + 2 = 5$ → $5^2 = 25$
- $10 + 1 = 11$

Now:
$$
[25 + 11] + 2^3 = 36 + 8 = \boxed{44}
$$

✔ Answer: 44

---

#4

$$
[-12 ÷ (-4)] × [144 ÷ (15 - 3)]
$$

Step 1: Parentheses
- $15 - 3 = 12$

Now:
$$
[-12 ÷ (-4)] × [144 ÷ 12]
$$

Step 2: Division
- $-12 ÷ (-4) = 3$
- $144 ÷ 12 = 12$

Now:
$$
3 × 12 = \boxed{36}
$$

✔ Answer: 36

---

#5

$$
(6 × 7) + 26 + 1^2 - 5
$$

Step 1: Parentheses and exponents
- $6 × 7 = 42$
- $1^2 = 1$

Now:
$$
42 + 26 + 1 - 5
$$

Step 2: Left to right
- $42 + 26 = 68$
- $68 + 1 = 69$
- $69 - 5 = \boxed{64}$

✔ Answer: 64

---

#6

$$
5 + [3 × (35 + 7)]
$$

Step 1: Parentheses
- $35 + 7 = 42$

Now:
$$
5 + [3 × 42] = 5 + 126 = \boxed{131}
$$

✔ Answer: 131

---

#7

$$
15 ÷ 5 + (36 + 12)^2 - 4
$$

Step 1: Parentheses
- $36 + 12 = 48$ → $48^2 = 2304$

Now:
$$
15 ÷ 5 + 2304 - 4
$$

Step 2: Division
- $15 ÷ 5 = 3$

Now:
$$
3 + 2304 - 4 = 2307 - 4 = \boxed{2303}
$$

✔ Answer: 2303

---

#8

$$
8(5 + 15) - (7 + 13)
$$

Step 1: Parentheses
- $5 + 15 = 20$
- $7 + 13 = 20$

Now:
$$
8 × 20 - 20 = 160 - 20 = \boxed{140}
$$

✔ Answer: 140

---

#9

$$
[(9 × 4) ÷ 12] + 5 - 4^2
$$

Step 1: Parentheses
- $9 × 4 = 36$

Now:
$$
[36 ÷ 12] + 5 - 4^2 = 3 + 5 - 16
$$

Step 2: Exponent
- $4^2 = 16$

Now:
$$
3 + 5 = 8, \quad 8 - 16 = \boxed{-8}
$$

✔ Answer: -8

---

#10

$$
3[(9 + 14) - (81 ÷ 9)]
$$

Step 1: Parentheses
- $9 + 14 = 23$
- $81 ÷ 9 = 9$

Now:
$$
3[23 - 9] = 3[14] = \boxed{42}
$$

✔ Answer: 42

---

✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | 429 |
| 2 | 210 |
| 3 | 44 |
| 4 | 36 |
| 5 | 64 |
| 6 | 131 |
| 7 | 2303 |
| 8 | 140 |
| 9 | -8 |
|10 | 42 |

Let me know if you'd like this formatted as a printable answer sheet!