Making Sense of Inverse Operations - Free Printable

Problem: Solving the given arithmetic problems and understanding inverse operations

The task involves solving each problem step by step and identifying any patterns or observations related to inverse operations. Let's solve each problem systematically.

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#### Problem 1: \( 8 + 4 - 4 = \)
1. Start with \( 8 \).
2. Add \( 4 \): \( 8 + 4 = 12 \).
3. Subtract \( 4 \): \( 12 - 4 = 8 \).

Answer: \( 8 \)

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#### Problem 2: \( 10 \times 2 \div 2 = \)
1. Start with \( 10 \).
2. Multiply by \( 2 \): \( 10 \times 2 = 20 \).
3. Divide by \( 2 \): \( 20 \div 2 = 10 \).

Answer: \( 10 \)

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#### Problem 3: \( 7 - 2 + 2 = \)
1. Start with \( 7 \).
2. Subtract \( 2 \): \( 7 - 2 = 5 \).
3. Add \( 2 \): \( 5 + 2 = 7 \).

Answer: \( 7 \)

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#### Problem 4: \( 30 \div 3 \times 3 = \)
1. Start with \( 30 \).
2. Divide by \( 3 \): \( 30 \div 3 = 10 \).
3. Multiply by \( 3 \): \( 10 \times 3 = 30 \).

Answer: \( 30 \)

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#### Problem 5: \( 15 + 10 - 10 = \)
1. Start with \( 15 \).
2. Add \( 10 \): \( 15 + 10 = 25 \).
3. Subtract \( 10 \): \( 25 - 10 = 15 \).

Answer: \( 15 \)

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#### Problem 6: \( 42 - 11 + 11 = \)
1. Start with \( 42 \).
2. Subtract \( 11 \): \( 42 - 11 = 31 \).
3. Add \( 11 \): \( 31 + 11 = 42 \).

Answer: \( 42 \)

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Observations:

- In each problem, the first number is the same as the final answer.
- This happens because the operations in each problem are inverse pairs:
- Addition and subtraction are inverses.
- Multiplication and division are inverses.
- When an operation is followed by its inverse (e.g., adding a number and then subtracting the same number), the original value remains unchanged.

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Final Answers:

1. \( 8 \)
2. \( 10 \)
3. \( 7 \)
4. \( 30 \)
5. \( 15 \)
6. \( 42 \)

Highlighted Pattern:

The first number of each problem is the same as the answer because the operations involve inverse pairs that cancel each other out.

Final Answer Boxed:
\[
\boxed{8, 10, 7, 30, 15, 42}
\]