Worksheet with answers for integer arithmetic problems.

Problem Description:

The task involves solving a series of arithmetic operations involving integers. The operations include addition, subtraction, multiplication, and division. Each problem is already solved in the image, but I will explain the reasoning behind each type of operation to ensure clarity.

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Key Rules for Integer Operations:

1. Addition:
- Adding two positive integers: Add their absolute values, and the result is positive.
- Adding two negative integers: Add their absolute values, and the result is negative.
- Adding a positive and a negative integer: Subtract the smaller absolute value from the larger one, and the sign of the result matches the number with the larger absolute value.

2. Subtraction:
- Subtracting a positive integer is the same as adding its opposite.
- Subtracting a negative integer is the same as adding its positive counterpart.

3. Multiplication:
- Positive × Positive = Positive
- Negative × Negative = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative

4. Division:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative

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Detailed Explanation of Selected Problems:

#### 1. Addition
- Problem: $(-6) + (-13)$
- Both numbers are negative. Add their absolute values: $6 + 13 = 19$.
- The result is negative: $-19$.
- Answer: $-19$

- Problem: $(+5) + (+9)$
- Both numbers are positive. Add their absolute values: $5 + 9 = 14$.
- The result is positive: $14$.
- Answer: $14$

#### 2. Subtraction
- Problem: $(-6) - (-13)$
- Subtracting a negative is the same as adding its positive counterpart: $-6 + 13$.
- Add the numbers: $13 - 6 = 7$.
- The result is positive: $7$.
- Answer: $7$

- Problem: $(-12) - (+7)$
- Subtracting a positive is the same as adding its negative counterpart: $-12 - 7$.
- Add the numbers: $-12 - 7 = -19$.
- The result is negative: $-19$.
- Answer: $-19$

#### 3. Multiplication
- Problem: $(+13) \times (-4)$
- A positive number multiplied by a negative number results in a negative product.
- Multiply the absolute values: $13 \times 4 = 52$.
- The result is negative: $-52$.
- Answer: $-52$

- Problem: $(+5) \times (+13)$
- A positive number multiplied by a positive number results in a positive product.
- Multiply the absolute values: $5 \times 13 = 65$.
- The result is positive: $65$.
- Answer: $65$

#### 4. Division
- Problem: $(+90) \div (-10)$
- A positive number divided by a negative number results in a negative quotient.
- Divide the absolute values: $90 \div 10 = 9$.
- The result is negative: $-9$.
- Answer: $-9$

- Problem: $(-84) \div (+6)$
- A negative number divided by a positive number results in a negative quotient.
- Divide the absolute values: $84 \div 6 = 14$.
- The result is negative: $-14$.
- Answer: $-14$

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Verification of All Problems:

The solutions provided in the image are correct based on the rules of integer arithmetic. Each operation follows the guidelines for addition, subtraction, multiplication, and division of integers.

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Final Answer:

All problems are correctly solved in the image. The solutions are consistent with the rules of integer operations.

$$
\boxed{\text{All answers are correct.}}
$$