Cancel refers to an operation used in term mathematics to remove terms from an expression leaving it in a simpler form. For example, in the fraction 6/8, the factor 2 can be removed from both the numerator and the denominator leaving the irreducible fraction 3/4. In this instance the 2 is said to be canceled out of the expression. Canceling is particularly useful for solving algebraic equations. The solution to the equation x - 7 = 4 is obtained by adding 7 to each side of the equation resulting in x = 11. When we add 7 to the left side of the equation, we cancel the -7 and put the equation in a simpler form. Typically, canceling is performed by using inverse operations. These are operations such as multiplication and division or addition and subtraction which "undo" one another.
Bittinger, Marvin L., and Davic Ellenbogen. Intermediate Algebra: Concepts and Applications. 6th ed. Reading, MA: Addison-Wesley Publishing, 2001.
Blitzer, Robert. Algebra and Trigonometry. 2nd ed. Englewood Cliffs, NJ: Prentice Hall, 2003.