Positive and Negative Integers Division | Integer Worksheets - Free Printable

Problem Description:

The task involves solving division problems involving positive and negative integers. The goal is to compute the quotient for each division problem and determine whether the result is positive or negative.

Key Rules for Division of Integers:

1. Same Signs: When dividing two integers with the same sign (both positive or both negative), the result is positive.
- Example: \( 6 \div 3 = 2 \) (both positive)
- Example: \( -6 \div -3 = 2 \) (both negative)

2. Different Signs: When dividing two integers with different signs (one positive and one negative), the result is negative.
- Example: \( 6 \div -3 = -2 \) (positive divided by negative)
- Example: \( -6 \div 3 = -2 \) (negative divided by positive)

Step-by-Step Solution:

#### 1. \( -4 \div 2 = \)
- Dividend: \(-4\) (negative)
- Divisor: \(2\) (positive)
- Different signs → Result is negative
- Calculation: \( -4 \div 2 = -2 \)
- Answer: \(-2\) (negative)

#### 2. \( 45 \div 5 = \)
- Dividend: \(45\) (positive)
- Divisor: \(5\) (positive)
- Same signs → Result is positive
- Calculation: \( 45 \div 5 = 9 \)
- Answer: \(9\) (positive)

#### 3. \( -32 \div (-4) = \)
- Dividend: \(-32\) (negative)
- Divisor: \(-4\) (negative)
- Same signs → Result is positive
- Calculation: \( -32 \div (-4) = 8 \)
- Answer: \(8\) (positive)

#### 4. \( 65 \div (-9) = \)
- Dividend: \(65\) (positive)
- Divisor: \(-9\) (negative)
- Different signs → Result is negative
- Calculation: \( 65 \div (-9) = -\frac{65}{9} \approx -7.22 \)
- Answer: \(-\frac{65}{9}\) or \(-7.22\) (negative)

#### 5. \( -55 \div 11 = \)
- Dividend: \(-55\) (negative)
- Divisor: \(11\) (positive)
- Different signs → Result is negative
- Calculation: \( -55 \div 11 = -5 \)
- Answer: \(-5\) (negative)

#### 6. \( -88 \div (-4) = \)
- Dividend: \(-88\) (negative)
- Divisor: \(-4\) (negative)
- Same signs → Result is positive
- Calculation: \( -88 \div (-4) = 22 \)
- Answer: \(22\) (positive)

#### 7. \( 132 \div 11 = \)
- Dividend: \(132\) (positive)
- Divisor: \(11\) (positive)
- Same signs → Result is positive
- Calculation: \( 132 \div 11 = 12 \)
- Answer: \(12\) (positive)

#### 8. \( 98 \div (-7) = \)
- Dividend: \(98\) (positive)
- Divisor: \(-7\) (negative)
- Different signs → Result is negative
- Calculation: \( 98 \div (-7) = -14 \)
- Answer: \(-14\) (negative)

#### 9. \( -272 \div 16 = \)
- Dividend: \(-272\) (negative)
- Divisor: \(16\) (positive)
- Different signs → Result is negative
- Calculation: \( -272 \div 16 = -17 \)
- Answer: \(-17\) (negative)

#### 10. \( -418 \div (-22) = \)
- Dividend: \(-418\) (negative)
- Divisor: \(-22\) (negative)
- Same signs → Result is positive
- Calculation: \( -418 \div (-22) = 19 \)
- Answer: \(19\) (positive)

Final Answers:

1. \( -4 \div 2 = -2 \) (negative)
2. \( 45 \div 5 = 9 \) (positive)
3. \( -32 \div (-4) = 8 \) (positive)
4. \( 65 \div (-9) = -\frac{65}{9} \) (negative)
5. \( -55 \div 11 = -5 \) (negative)
6. \( -88 \div (-4) = 22 \) (positive)
7. \( 132 \div 11 = 12 \) (positive)
8. \( 98 \div (-7) = -14 \) (negative)
9. \( -272 \div 16 = -17 \) (negative)
10. \( -418 \div (-22) = 19 \) (positive)

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \ -2 \ (\text{negative}) \\
2. & \ 9 \ (\text{positive}) \\
3. & \ 8 \ (\text{positive}) \\
4. & \ -\frac{65}{9} \ (\text{negative}) \\
5. & \ -5 \ (\text{negative}) \\
6. & \ 22 \ (\text{positive}) \\
7. & \ 12 \ (\text{positive}) \\
8. & \ -14 \ (\text{negative}) \\
9. & \ -17 \ (\text{negative}) \\
10. & \ 19 \ (\text{positive})
\end{aligned}
}
\]