Quick answer

Find LCD, scale both fractions, subtract numerators over LCD, then simplify. The LCD step matches addition exactly.

Formula

  • LCD = lcm(b, d)
  • a/b - c/d → (scaled a - scaled c) / LCD
  • Simplify final answer

Introduction

Subtraction requires the same denominator alignment as addition. Students often subtract denominators by mistake; only numerators change after scaling.

When the first fraction is smaller than the second, the result numerator may be negative before simplification rules are applied in later courses.

Mixed-number subtraction can require borrowing from the whole part. Still begin with LCD on the fractional denominators.

If addition is still new, study LCD for adding fractions first because the LCD portion is identical.

Denominator alignment

Never subtract denominators directly. Build equivalent fractions first, then subtract the top numbers.

Example: 7/8 - 1/4. LCD = 8. Work: 7/8 - 2/8 = 5/8.

Example with larger LCD: 5/6 - 1/4. LCD = 12 gives 10/12 - 3/12 = 7/12.

Write the subtraction step clearly: one line for LCD, one line for equivalents, one line for the difference.

More fraction pairs with the same structure appear in least common denominator examples if you want extra drills before a test.

Mixed number subtraction

  • Convert to improper if helpful
  • Find LCD of fractional denominators
  • Subtract numerators, simplify

For 3 1/4 - 1 1/2, denominators 4 and 2 give LCD 4. Improper forms 13/4 and 3/2 become 13/4 - 6/4 = 7/4 = 1 3/4.

Borrowing from a whole number is a whole-number skill layered on top of fraction subtraction. The LCD step still happens first on the fractional parts.

Always simplify the final answer if gcd greater than 1 divides numerator and denominator.

Subtraction procedure

  1. Find LCD Same methods as addition: multiples, primes, or gcd.
  2. Scale both fractions Record equivalents side by side for clarity.
  3. Subtract numerators Keep the LCD as denominator.
  4. Simplify Reduce and convert to mixed form when needed.

Example: 5/6 - 1/4

lcm(6, 4) = 12. Equivalents: 10/12 - 3/12 = 7/12.

Check denominators 6 and 4 at /#calculator before subtracting on paper.