Subtracting fractions

Subtracting fractions means finding the difference between two or more fractions — how much is left once one part is taken away from another. The key rule is that fractions can only be subtracted directly when they share the same denominator; in that case you simply subtract the numerators and keep the common denominator. When the denominators differ, the fractions must first be rewritten over a common denominator, usually the least common multiple, so that the parts being compared are the same size. After subtracting, the result is normally simplified to its lowest terms, and an improper fraction can be expressed as a mixed number. Unlike addition, order matters here, because subtraction is not commutative — swapping the fractions changes the sign of the answer. This operation appears constantly in everyday life, from adjusting recipes and measuring materials to tracking time, money, and portions. It also lays the groundwork for algebra, where subtracting rational expressions relies on exactly the same reasoning.