Final answer:
Subtracting a negative integer is equivalent to adding its positive counterpart. This applies to scalar numbers and vectors, with vector subtraction involving the addition of a negative vector (which is a vector in the opposite direction). The order of addition and subtraction doesn't affect the result due to the associative property.
Step-by-step explanation:
Subtracting a negative integer from a number or another integer can be understood as adding the positive form of that integer. For instance, if you have the operation 5 - (+3), you would perform the subtraction normally: 5 - 3 equalling 2. If instead, the operation is subtracting a negative, such as subtracting -6 from 2 (2 - (-6)), it becomes an addition: 2 + 6 resulting in 8 because the minus sign of the negative number is changed to a plus sign.
Vector subtraction follows a similar logic. When subtracting vector B from vector A (A - B), it's equivalent to adding the negative of B (A + (-B)) to A. The negative vector is simply the vector with the same magnitude but pointing in the opposite direction. This method is also used in graphical subtraction of vectors.
The rules of subtraction can be generalised:
- When subtracting, change the sign of the number being subtracted and add.
- When two positive numbers are added, the result is positive (e.g., 3+2 = 5).
- When two negative numbers are added, the result is negative (e.g., -4 + (-2) = -6).
- If the numbers have opposite signs, subtract the smaller number from the larger and take the sign of the larger number (e.g., -5 + 3 = -2).
The order in which subtraction or addition is performed does not affect the result due to the associative property of addition.