Subtracting Fractions – Step-by-Step
Subtracting fractions follows the same denominator rule as addition. Get a common denominator first, then subtract the numerators.
Subtracting mixed numbers introduces a wrinkle that pure fraction subtraction does not: borrowing. When the fraction part of the number you are subtracting is larger than the fraction part you are subtracting from (like 5¼ − 2¾), you must “borrow” one whole unit from the first whole number and rewrite it as an extra fraction — the exact same idea as borrowing/regrouping when subtracting multi-digit whole numbers like 502 − 138. Carpenters and tailors use this constantly: cutting a 5¼ metre plank down by 2¾ metres requires exactly this kind of borrowing to work out the length of the remaining piece.
Case 1 - Like Fractions
(7-4)/9 = 3/9 = 1/3
Case 2 - Unlike Fractions
LCM(4,5) = 20. 3/4 = 15/20. 2/5 = 8/20. 15/20 - 8/20 = 7/20. Answer: 7/20.
LCM(6,8) = 24. 5/6 = 20/24. 3/8 = 9/24. 20/24 - 9/24 = 11/24. Answer: 11/24.
Case 3 - Mixed Numbers (No Borrowing)
Wholes: 4-2=2. Fractions: 3/4 - 1/2. LCM=4: 3/4 - 2/4 = 1/4. Answer: 2 and 1/4.
Case 4 - Mixed Numbers (Borrowing Needed)
Convert to improper fractions to avoid errors.
16/3 - 11/4. LCM=12: 64/12 - 33/12 = 31/12 = 2 and 7/12.
Subtracting from a Whole Number
Key Takeaways
- Find the LCD before subtracting unlike fractions.
- Subtract numerators; keep the denominator.
- Convert mixed numbers to improper fractions to avoid borrowing errors.
- Always simplify the answer.