F6 · Subtracting Fractions: Take Away Parts of the Same Size
“I can subtract two fractions by first rewriting them with a common denominator, then subtracting the numerators — including simple mixed numbers — and I never subtract the denominators.”
7/8 − 1/4. Step 1: The parts are different sizes — quarters must be renamed as eighths first. Step 2: 8 is a multiple of 4. Relating factor: 1/4 = 2/8. Step 3: Now both fractions name eighths. Subtract the numerators, keep the denominator: 7/8 − 2/8 = 5/8. Model: a bar in eighths with 2 eighths crossed out from 7, beside a 0–2 number line in eighths: start at 7/8 and jump back 2/8 to land on 5/8. Subtraction counts how many parts are left — the size of the parts never changes, so the denominator never changes.
Why must 1/4 become 2/8 before we subtract?
5/6 − 1/3 → 1/3 = 2/6, so 5/6 − 2/6 = 3/6 = 1/2
“9/10 − 3/5: 3/5 = 6/10, so 9/10 − 6/10 = ___” → 3/10
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.