Question
A whole number or it’s opposites in adding imtegers
Answers
GPT-4o mini
When you add integers, you're working with whole numbers which can be either positive, negative, or zero.
Here are some basic points about adding integers:
1. **Positive and Negative Integers**:
- If you add a positive integer to a positive integer, the result is positive. For example, \(3 + 2 = 5\).
- If you add a negative integer to a negative integer, the result is negative. For example, \(-3 + (-2) = -5\).
- If you add a positive integer to a negative integer, the result depends on the values of the integers:
- If the positive integer is larger, the result is positive. For example, \(5 + (-3) = 2\).
- If the negative integer is larger in absolute value, the result is negative. For example, \(3 + (-5) = -2\).
- If they are equal in absolute value, the result is zero. For example, \(5 + (-5) = 0\).
2. **Zero**:
- Adding zero to any integer does not change the integer. For example, \(7 + 0 = 7\) and \(-3 + 0 = -3\).
3. **Commutative Property**:
- The order in which you add integers does not affect the sum. For example, \(4 + (-6) = (-6) + 4\).
4. **Associative Property**:
- When adding multiple integers, the way you group them does not change the sum. For example, \((2 + 3) + (-5) = 2 + (3 + (-5))\).
By understanding these principles, you can effectively add whole numbers and their opposites in various combinations. If you have specific examples or problems you'd like to work through, feel free to share!
Here are some basic points about adding integers:
1. **Positive and Negative Integers**:
- If you add a positive integer to a positive integer, the result is positive. For example, \(3 + 2 = 5\).
- If you add a negative integer to a negative integer, the result is negative. For example, \(-3 + (-2) = -5\).
- If you add a positive integer to a negative integer, the result depends on the values of the integers:
- If the positive integer is larger, the result is positive. For example, \(5 + (-3) = 2\).
- If the negative integer is larger in absolute value, the result is negative. For example, \(3 + (-5) = -2\).
- If they are equal in absolute value, the result is zero. For example, \(5 + (-5) = 0\).
2. **Zero**:
- Adding zero to any integer does not change the integer. For example, \(7 + 0 = 7\) and \(-3 + 0 = -3\).
3. **Commutative Property**:
- The order in which you add integers does not affect the sum. For example, \(4 + (-6) = (-6) + 4\).
4. **Associative Property**:
- When adding multiple integers, the way you group them does not change the sum. For example, \((2 + 3) + (-5) = 2 + (3 + (-5))\).
By understanding these principles, you can effectively add whole numbers and their opposites in various combinations. If you have specific examples or problems you'd like to work through, feel free to share!