Deriving the Addition and Subtraction Rules for Fractions from First Principles
Fractions | Algebra | First Principles The familiar rules for adding and subtracting fractions can be derived directly from the properties of real numbers. The key idea is that multiplying a number by 1 does not change its value. By writing 1 in a suitable fractional form, both fractions can be expressed with the same denominator. Assumptions Let a, b, c, d ∈ ℝ, with b ≠ 0 and d ≠ 0. Addition of Two Fractions Begin with two fractions whose denominators are not necessarily equal: a b + c d = a b · 1 + c d · 1 = a b ...