A good starting objective is the definition of subtraction. Subtraction is the opposite process of addition. Whereas addition is the sum of two separate numbers, subtraction is the remainder of two separate numbers. This process is identified by the use of a minus symbol. This symbol defines which number is to be taken from which number. Understanding which number is subtracted from which number is a key point that must be understood before the actual subtraction process can take place.
The subtraction process removes one number from another, to create a final remainder (3 - 2 = 1). The first number, called the minuend, is the starting number and is subtracted by the second number, called the subtrahend, to produce a final number, called the difference. The minuend will always remain to the left of the minus symbol and the subtrahend will remain to the right of the minus symbol.
The horizontal subtraction process (3 - 2 = 1) is useful to illustrate single-digit number subtraction, but for double-digit numbers and higher the vertical method helps illustrate the process better. This process is done by placing the minuend over the subtrahend, making sure to line up each place value in both. From this point it becomes possible to subtract a single number from the subtrahend with the corresponding number in the minuend, and placing the final difference in the correct place value.
When a number in the subtrahend place value is greater than the number in the same minuend place value (21 - 12), it becomes necessary to use borrowing. Borrowing is the subtraction method in which a single numerical value from a higher place value is taken and placed on the previous value, allowing positive subtraction of the subtrahend number from the minuend number. For example, in 21-12, you would convert the 2 in 21 to a 1, and the 1 to an 11, changing the one's place value subtraction from 1 - 2, to 11 - 2.