Order of Operations worksheet with problems and step-by-step guidance for solving math expressions.

Let's solve each problem step by step using the Order of Operations, which is often remembered by the acronym PEMDAS:

- Parentheses
- Exponents
- Multiply and Divide (from left to right)
- Add and Subtract (from left to right)

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Problem 1:

1. (9 + 3) ÷ 2 = ?

Step 1: Solve inside parentheses:
9 + 3 = 12

Step 2: Divide:
12 ÷ 2 = 6

✔ Answer: 6

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Problem 2:

2. 6 ÷ 1 + 4 = ?

Step 1: Division first:
6 ÷ 1 = 6

Step 2: Add:
6 + 4 = 10

✔ Answer: 10

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Problem 3:

3. (2 × 5) - 4 = ?

Step 1: Parentheses:
2 × 5 = 10

Step 2: Subtract:
10 - 4 = 6

✔ Answer: 6

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Problem 4:

4. 36 ÷ [4 + (8 ÷ 4)] = ?

Step 1: Innermost parentheses:
8 ÷ 4 = 2

Now the expression becomes:
36 ÷ [4 + 2]

Step 2: Inside brackets:
4 + 2 = 6

Step 3: Divide:
36 ÷ 6 = 6

✔ Answer: 6

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Problem 5:

5. 50 - 5 × (27 ÷ 3) = ?

Step 1: Parentheses:
27 ÷ 3 = 9

Now:
50 - 5 × 9

Step 2: Multiply:
5 × 9 = 45

Step 3: Subtract:
50 - 45 = 5

✔ Answer: 5

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Problem 6:

6. 15 + 24 ÷ (9 - 2) = ?

Step 1: Parentheses:
9 - 2 = 7

Now:
15 + 24 ÷ 7

Step 2: Division:
24 ÷ 7 ≈ 3.428...
But let's keep it as a fraction or decimal depending on preference.

However, since this is likely for whole numbers, we'll calculate exactly:

24 ÷ 7 = 3 with remainder 3 → but in decimal: ≈ 3.4286

So:
15 + 3.4286 ≈ 18.4286

But if we are to express as a mixed number:
24 ÷ 7 = 3⅓
So: 15 + 3⅓ = 18⅓

✔ Answer: 18⅓ or 18.4286 (approx)

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Problem 7:

Do (12 + 4) ÷ 2 and 12 + 4 ÷ 2 have the same answer? Explain why.

Let’s evaluate both:

#### First expression: (12 + 4) ÷ 2
- Parentheses: 12 + 4 = 16
- Then divide: 16 ÷ 2 = 8

#### Second expression: 12 + 4 ÷ 2
- Division first: 4 ÷ 2 = 2
- Then add: 12 + 2 = 14

So:
- (12 + 4) ÷ 2 = 8
- 12 + 4 ÷ 2 = 14

✘ They do not have the same answer.

Why? Because parentheses change the order of operations. In the first expression, addition happens before division. In the second, division happens before addition due to PEMDAS rules.

✔ Answer: No, they do not have the same answer. The parentheses in the first expression force addition to happen before division, while in the second, division happens first.

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✔ Final Answers:

1. 6
2. 10
3. 6
4. 6
5. 5
6. 18⅓ or 18.4286
7. No, because parentheses change the order of operations — in (12+4)÷2, you add first; in 12+4÷2, you divide first.

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