Adding and Subtracting Fractions

Pre-Algebra · Axiom Academy

LESSON Adding and Subtracting Fractions Why fractions only combine when their pieces are the same size — and the exact algorithm for getting there with the least common denominator. 1. Why Pieces Must Be the Same Size A fraction is a count of equal pieces: means two of the pieces you get by cutting a whole into 5 . When two fractions are cut the same way — like denominators — adding is just counting the shaded pieces together. When they are cut differently — unlike denominators — the pieces are different sizes, so a raw count is meaningless. Like denominators — just add the numerators Unlike denominators — the pieces don't match yet 2. Finding the LCD: List Multiples The least common denominator (LCD) is the smallest number both denominators divide into evenly. The most direct way to find it: write out the multiples of each denominator and stop at the first one they share. Step the two ladders of multiples forward together until a number lands in both rows. 3. Finding the LCD: Prime Factorization For larger numbers, break each denominator into its prime factors , then build the LCD from the highest power of every prime that appears. Nothing gets double-counted, and nothing essential is missed. Factor each number, then take each prime to the largest exponent it reaches in either factorization. 4. Adding: Re-Slice, Then Count

This is the written version of the interactive lesson above. See the full Pre-Algebra course.