Cancelling out

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Cancelling out is a mathematical process used for removing subexpressions from a mathematical expression, when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects.^[1] For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.^[2] As another example, if a×b=a×c, then the multiplicative term a can be canceled out if a≠0, resulting in the equivalent expression b=c; this is equivalent to dividing through by a.