In mathematics the difference is the result of subtracting one number from another, and represents the operation of removing objects from a collection. Mathematicians use the term "difference," because it shows by how much the two numbers in the subtraction problem differ.
A basic subtraction problem is made up of three parts: the minuend, the subtrahend and the difference. The minuend is the number which appears first in the problem. This is the number which is being subtracted from. The subtrahend appears second, and is the amount being subtracted from the minuend. The difference appears last, after the equals sign, and is the amount of space between the minuend and subtrahend.
If the minuend is greater than the subtrahend, then the difference is always positive. If the minuend is less than the subtrahend, then the difference is always negative. In the order of operations, differences are the last things calculated, along with sums. Therefore, parentheses are necessary to calculate a difference before an exponent, product or quotient.
For subtracting large numbers by hand, use partial differences. These rely on the subtraction of digits in certain positions, rather than the whole number. For example, a partial difference of 753 - 491 is 700 - 400.