Understanding BODMAS with Fractions
Solving fractions with multiple operators can be tricky. The BODMAS rule guarantees precise and consistent results. The order of operations for fractions is identical to regular numbers, but you must find common denominators for addition/subtraction and flip divisors for division.
Fraction BODMAS Example
✓ Step-by-Step
1/2 + 3/4 × 2/3
1. Multiply: 3/4 × 2/3 = 6/12 = 1/2
2. Add: 1/2 + 1/2 = 1
= 1 ✓
Step-by-Step Rules for Fraction Operations
Each fraction operation requires a specific technique before you can apply BODMAS priority.
Fraction Operations Guide
Addition
Find LCD, convert numerators, then add: a/b + c/d = (ad+bc)/bd
Subtraction
Find LCD, convert numerators, then subtract: a/b - c/d = (ad-bc)/bd
Multiplication
Multiply straight across: a/b × c/d = ac/bd
Division
Flip divisor and multiply: a/b ÷ c/d = a/b × d/c
Common Mistakes to Avoid
These errors frequently occur when combining fractions with order of operations:
Common Mistakes — Click to Reveal
Adding Before MultiplyingClick to see
1/3 + 1/3 × 3 → 2/3 × 3 = 2 ✗
1/3 + 1/3 × 3 → 1/3 + 1 = 4/3 ✓
Multiply first per BODMAS
Reciprocal ErrorClick to see
(1/2) ÷ (3/4) → 1×3 / 2×4 = 3/8 ✗
(1/2) ÷ (3/4) → 1/2 × 4/3 = 2/3 ✓
Flip the divisor first