Adding integers involves different steps depending on whether the integers have the same sign or different signs. Here's a breakdown:
Adding Integers with the Same Sign
When adding integers with the same sign (both positive or both negative), simply add their absolute values and keep the common sign.
- Example 1: 3 + 5 = 8 (Both positive, so the answer is positive)
- Example 2: -2 + (-4) = -6 (Both negative, so the answer is negative)
Adding Integers with Different Signs
When adding integers with different signs (one positive and one negative), follow these steps (based on the reference):
Step 1: Find the Absolute Values. Take the absolute value of each number. The absolute value of a number is its distance from zero, always a non-negative value.
Step 2: Subtract. Subtract the smaller absolute value from the larger absolute value.
Step 3: Determine the Sign. Copy the sign of the number that has the larger absolute value. This will be the sign of your answer.
Here's a table summarizing the steps with examples:
| Step | Description | Example 1: -7 + 4 | Example 2: 10 + (-3) |
|---|---|---|---|
| 1. Absolute Values | Find the absolute value of each integer. | -7 | |
| 2. Subtract | Subtract the smaller absolute value from the larger. | 7 - 4 = 3 | 10 - 3 = 7 |
| 3. Determine the Sign | The result takes the sign of the number with the larger absolute value. | -7 has a larger absolute value than 4, so the result is negative. | 10 has a larger absolute value than -3, so the result is positive. |
| Final Answer | -3 | 7 |
In summary, the key difference is that when the signs are the same, you add the absolute values. When the signs are different, you subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.
