multiplicative inverses. The subtraction of a real number (the subtrahend) from another (the minuend) can then be defined as the addition of the minuend and the additive inverse of the subtrahend. For example, . Alternatively, instead of requiring these unary operations, the binary operations of subtraction and division can be taken as basic. Properties Anti-commutativity Subtraction is anti-commutative, meaning that if one reverses the terms in a difference left-to-right, the result is the negative of the original result. Symbolically, if a and b are any two numbers, then a − b = −(b − a). Non-associativity Subtraction is non-associative, which comes up when one tries to define repeated subtraction. In general, the expression "a − b − c" can be defined to mean either (a − b) − c or a − (b − c), but these two possibilities lead to different answers. To resolve this issue, one must establish an order of operations, with different orders yielding different results. Predecessor In the context of integers, subtraction of one also plays a special role: for any integer a, the integer is the largest integer less than a, also known as the predecessor of a. Units of measurement When subtracting two numbers with units of measurement such as kilograms or pounds, they must have the same unit. In most cases, the difference will have the same unit as the original numbers. Percentages Changes in percentages can be reported in at least two forms, percentage change and percentage point change. Percentage change represents the relative change between the two quantities as a percentage, while percentage point change is simply the number obtained by subtracting the two percentages. As an example, suppose that 30% of widgets made in a factory are defective. Six months later, 20% of widgets are defective. The percentage change is = − = %, while the percentage point change is −10 percentage points. In computing The method of complements is a technique used to subtract one number from another using only the addition of positive numbers. This method was commonly used in mechanical calculators, and is still used in modern computers. To subtract a binary number y (the subtrahend) from another number x (the minuend), the ones' complement of y is added to x and one is added to the sum. The leading digit "1" of the result is then discarded. The method of complements is especially useful in