Order of Operations worksheet for practicing identifying and solving mathematical expressions.

Let's solve each expression 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)

We will:
1. Highlight the operation that should be done first.
2. Then evaluate the expression.

---

1. $ 16 ÷ (1 + 7) = $

- First: Evaluate inside the parentheses: $1 + 7$
- So, highlight: (1 + 7)

Now evaluate:
$$
16 ÷ (1 + 7) = 16 ÷ 8 = 2
$$

✔ Answer: 2

---

2. $ 8 + 6 × 3 = $

- First: Multiplication comes before addition: $6 × 3$
- So, highlight: 6 × 3

Now evaluate:
$$
8 + 6 × 3 = 8 + 18 = 26
$$

✔ Answer: 26

---

3. $ 7 + 3 × 9 ÷ 3 = $

- First: Multiplication and division go left to right. First is $3 × 9$
- So, highlight: 3 × 9

Now evaluate:
$$
7 + 3 × 9 ÷ 3 = 7 + 27 ÷ 3 = 7 + 9 = 16
$$

✔ Answer: 16

---

4. $ 10 ÷ (4 + 1) × 2 = $

- First: Parentheses: $4 + 1$
- So, highlight: (4 + 1)

Now evaluate:
$$
10 ÷ (4 + 1) × 2 = 10 ÷ 5 × 2 = 2 × 2 = 4
$$

✔ Answer: 4

---

5. $ 7 + 12 ÷ 2 × 5 = $

- First: Division and multiplication from left to right: $12 ÷ 2$
- So, highlight: 12 ÷ 2

Now evaluate:
$$
7 + 12 ÷ 2 × 5 = 7 + 6 × 5 = 7 + 30 = 37
$$

✔ Answer: 37

---

6. $ 4 + 9 - 6 + 2 × 3 = $

- First: Multiplication: $2 × 3$
- So, highlight: 2 × 3

Now evaluate:
$$
4 + 9 - 6 + 2 × 3 = 4 + 9 - 6 + 6 = (4 + 9) - 6 + 6 = 13 - 6 + 6 = 7 + 6 = 13
$$

✔ Answer: 13

---

7. $ (19 - 4) × 2 + 7 = $

- First: Parentheses: $19 - 4$
- So, highlight: (19 - 4)

Now evaluate:
$$
(19 - 4) × 2 + 7 = 15 × 2 + 7 = 30 + 7 = 37
$$

✔ Answer: 37

---

8. $ 17 - (4 × 2) + 6 = $

- First: Parentheses: $4 × 2$
- So, highlight: (4 × 2)

Now evaluate:
$$
17 - (4 × 2) + 6 = 17 - 8 + 6 = 9 + 6 = 15
$$

✔ Answer: 15

---

✔ Final Answers Summary:

| Expression | First Operation Highlighted | Value |
|----------|-----------------------------|-------|
| $16 ÷ (1 + 7)$ | $(1 + 7)$ | 2 |
| $8 + 6 × 3$ | $6 × 3$ | 26 |
| $7 + 3 × 9 ÷ 3$ | $3 × 9$ | 16 |
| $10 ÷ (4 + 1) × 2$ | $(4 + 1)$ | 4 |
| $7 + 12 ÷ 2 × 5$ | $12 ÷ 2$ | 37 |
| $4 + 9 - 6 + 2 × 3$ | $2 × 3$ | 13 |
| $(19 - 4) × 2 + 7$ | $(19 - 4)$ | 37 |
| $17 - (4 × 2) + 6$ | $(4 × 2)$ | 15 |

---

Let me know if you'd like this formatted as a printable worksheet or with visual highlights!