How to Subtract Fractions
Subtracting fractions requires a common denominator. Once both fractions share the same denominator, you subtract the numerators and keep the denominator unchanged, then simplify if possible.
The Process
Step 1: Find the LCD
The Least Common Denominator is the smallest number that both denominators divide into evenly.
LCD(6, 4) = 12
Step 2: Convert
Multiply each fraction's numerator and denominator so both have the LCD.
5/6 = 10/12, 1/4 = 3/12
Step 3: Subtract & Simplify
Subtract the numerators, keep the denominator, and reduce using the GCD.
10/12 - 3/12 = 7/12
Special Cases
- Same denominators: Simply subtract the numerators. Example: 5/8 - 3/8 = 2/8 = 1/4.
- Whole numbers: Write whole numbers as fractions over 1. Example: 3 - 1/4 = 12/4 - 1/4 = 11/4.
- Negative results: If the first fraction is smaller, the result is negative.
- Mixed numbers: Convert to improper fractions first, then subtract.
Formula
For fractions a/b and c/d: a/b - c/d = (a*d - c*b) / (b*d), then simplify by dividing by the GCD.