How does the addition or subtraction of negative numbers affect the sign of the sum or difference?
When you add or subtract negative numbers, you follow a set of rules to determine the sign of the sum or difference. Here are the rules:
1. Adding two negative numbers: When you add two negative numbers, the sum will always be negative. This is because, conceptually, adding a negative number means moving in the opposite direction on the number line. So, when you add two negative values, you are moving further away from zero in the negative direction.
Example: -3 + (-5) = -8
2. Subtracting a negative number: When you subtract a negative number, it is essentially the same as adding a positive number. This results in the sign of the number being changed.
Example: 7 - (-2) = 7 + 2 = 9
3. Adding a positive and a negative number: When you add a positive number to a negative number, you need to look at their magnitudes (absolute values). The sign of the sum will be the same as the number with the greater magnitude.
Example: -4 + 6 = 2 (Since 6 has a greater magnitude than -4, the sum is positive.)
4. Subtracting a positive and a negative number: When you subtract a negative number from a positive number, it is equivalent to adding a positive number. Therefore, the sign of the difference will be the same as the sign of the positive number.
Example: 8 - (-3) = 8 + 3 = 11
Remembering these rules will help you accurately determine the sign of the sum or difference when adding or subtracting negative numbers.