Cancellation is a method of shortening mathematical problems by striking out terms or factors. To multiply the fractions 3/10 and 4/3, a person would get 12, or 4 times 3, for the numerator, and 30, or 10 times 3, for the denominator. The fraction 12/30 may be reduced by dividing the 12 and 30 by the common factors of 3 and 2. But it is easier to do the divisions before multiplying, rather than after. This is done by cancellation, or by striking out the old terms and replacing them with new ones. The 3’s can be divided by 3, and 10 and 4 can be divided by 2.
To calculate the value of the expression 26 + 7 + 4 – 7, you can cancel the 7’s to avoid the work of adding and then subtracting them. In an equation, you can cancel factors or divisors common to both sides, or equal terms that are added to or subtracted from both sides. For example, in the equation x-squared + y-squared + x – 2 = x-squared + y-squared + 4, you could cancel the x-squared and y-squared terms by subtracting them from each side of the equation.
