Arithmetic Operations
Fraction Subtraction
Subtracting fractions follows the same rules as adding them: you must have the same denominator before you can combine the numerators.
Same Denominator
Subtract the numerators; keep the denominator unchanged.
5/7 − 2/7 = 3/7 (5−2=3, denominator stays 7)
Different Denominators
Find the lowest common denominator (LCD), convert both fractions, then subtract.
Example: 3/4 − 1/3
- LCD of 4 and 3 = 12.
- Convert: 3/4 = 9/12 and 1/3 = 4/12.
- Subtract: 9/12 − 4/12 = 5/12.
3/4 − 1/3 = 9/12 − 4/12 = 5/12
Example: 2/3 − 1/4
LCD=12: 8/12 − 3/12 = 5/12
Simplifying
4/8 − 2/8 = 2/8 → simplify by 2 → 1/4
Key Takeaways
- Same denominator: subtract numerators, keep denominator.
- Different denominators: find LCD, convert, then subtract.
- Always simplify the result.
- If the result is negative, check whether the question asked for a signed answer.
Practice: Subtract These Fractions
Two fractions are shown below. Give your answer as a fraction (e.g. 5/12), simplified where possible. If you get it wrong (or leave it blank), we'll find the LCD together.
Calculate the difference.