Remainder in subtraction

The remainder in a subtraction sentence is the result of subtracting one number from another. It is the solution to the problem and is more precisely referred to as the difference. The term "remainder" or "the rest" is most commonly used in elementary textbooks, but "difference" is preferable since remainder can also be confused with a remainder in division. The figure below depicts the components that make up a subtraction sentence, including the remainder.

The above problem can also be depicted using a number line. In the figure below, the magnitude of each term is represented by a colored line. The minuend, 7, is shown in blue and the subtrahend is shown in red. Both are represented by solid lines of the same color. The remainder, or the solution to the subtraction problem, is shown in green. It is represented by a dotted green line.

As can be seen from the figure, the minuend is comprised of the subtrahend and the remainder, which also demonstrates the relationship between addition and subtraction. In both cases there are smaller parts that make up a whole. Addition sentences can easily be converted into subtraction sentences by rearranging terms. This will become even more apparent in algebra, where understanding of the components of a number sentence, or more precisely, an equation, enables us to solve a variety of algebraic equations.


Find the remainder to complete each of the following subtraction sentences.

1. 12 - 9 = ?

12 - 9 = 3

2. 100 - 80 = ?

100 - 80 = 20

3. 9 - 12 = ?

9 - 12 = -3