Dividing integers involves a simple three-step process, focusing on absolute values and then determining the sign of the result.
Steps for Dividing Integers
Here's a step-by-step guide on how to divide integers, incorporating the information from the provided reference:
| Step | Description | Example: (-12) ÷ (3) |
|---|---|---|
| Step 1: Divide Absolute Values | Begin by dividing the absolute values of the integers. The absolute value of a number is its distance from zero, always a positive number. | Absolute value of -12 is 12. Absolute value of 3 is 3. So, 12 ÷ 3 = 4. |
| Step 2: Determine the Sign | Next, determine the sign of the quotient (the result of the division). - If both integers have the same sign (both positive or both negative), the result is positive. - If the integers have different signs (one positive, one negative), the result is negative. | Since -12 is negative and 3 is positive, the result will be negative. |
| Step 3: Combine for Final Answer | Combine the result from Step 1 with the sign from Step 2. This will give you the final quotient. | The result from step 1 was 4, and the sign from step 2 was negative. So, the final answer is -4. |
Practical Insights
- Understanding Absolute Value: The absolute value is crucial because it simplifies the initial division process. Think of it as making all numbers positive to perform the arithmetic and then dealing with the sign.
- Sign Rules: Remember the basic rules for signs:
- Positive ÷ Positive = Positive
- Negative ÷ Negative = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative
- Zero Division: Division by zero is undefined.
- Fractions: Integer division can lead to fractions or decimals in certain cases. This process focuses on obtaining integer quotients.
Examples
- Example 1: 15 ÷ 3 = 5 (Both positive, so positive result)
- Example 2: -20 ÷ -5 = 4 (Both negative, so positive result)
- Example 3: 24 ÷ -6 = -4 (One positive, one negative, so negative result)
