Simplifying Expressions Review worksheet with math problems and multiple-choice questions.

Let’s solve each problem step by step, carefully checking our work.

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Problem 1: Simplify 8 ÷ 4 + 2 × 5

Order of operations (PEMDAS/BODMAS):
→ Do division and multiplication first (left to right), then addition and subtraction.

Step 1: 8 ÷ 4 = 2
Step 2: 2 × 5 = 10
Step 3: 2 + 10 = 12

✔ Final answer for this one: 12

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Problem 2: What is the first step in simplifying (5 - 3 + 1) × 6 - 2 + 7?

We must do what’s inside parentheses first. Inside: (5 - 3 + 1)

Inside parentheses, we go left to right:
First operation is 5 - 3, not 3 + 1 — because subtraction comes before addition when going left to right.

So first step: subtract 5 - 3

That matches option D

✔ Answer: D. subtract 5 - 3

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Problem 3: Simplify 64 - 9 + 2(7 × 3)

Step 1: Parentheses → 7 × 3 = 21
Now expression: 64 - 9 + 2(21) → which is 64 - 9 + 42

Step 2: Left to right for addition/subtraction:
64 - 9 = 55
55 + 42 = 97

Looking at choices: 13, 42, 55, 97 → correct is 97

✔ Answer: 97

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Problem 4: Simplify 5 × (81 ÷ 9) + 8 - 3

Step 1: Parentheses → 81 ÷ 9 = 9
Expression becomes: 5 × 9 + 8 - 3

Step 2: Multiplication → 5 × 9 = 45
Now: 45 + 8 - 3

Step 3: Left to right:
45 + 8 = 53
53 - 3 = 50

✔ Answer: 50

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Problem 5: Three students simplified 1 + (2 × 4 + 2) × 12

Student A: 132
Student B: 121
Student C: 145

Let’s compute correctly:

Step 1: Inside parentheses: 2 × 4 + 2
→ First multiply: 2 × 4 = 8
→ Then add: 8 + 2 = 10

Now expression: 1 + (10) × 12

Step 2: Multiply: 10 × 12 = 120
Step 3: Add: 1 + 120 = 121

So Student B is correct.

✔ Answer: Student B

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Problem 6: Look at 9 × 4 - 30 ÷ 10. What does it look like after the first step?

Order of operations: multiplication and division come before subtraction, and we do them left to right.

Leftmost operation: 9 × 4 = 36
Then next: 30 ÷ 10 = 3
But the question asks: “after the first step” — meaning only the very first operation done.

Since 9 × 4 is on the left, that’s the first step.

After doing 9 × 4, we get: 36 - 30 ÷ 10

The other choice, “9 × 4 - 3”, would be after BOTH multiplication AND division are done — that’s two steps.

So after *first* step: 36 - 30 ÷ 10

✔ Answer: 36 - 30 ÷ 10

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Final Answer:
1. 12
2. D
3. 97
4. 50
5. Student B
6. 36 - 30 ÷ 10