Quick Answer: How to Add and Subtract Fractions
To add or subtract two fractions with different denominators: 1. Find the Least Common Multiple (LCM) of the denominators to create a Common Denominator. 2. Convert both numerators to equivalent fractions. 3. Add or subtract the numerators while keeping the common denominator unchanged. 4. Simplify the final fraction by dividing both numerator and denominator by their Highest Common Factor (HCF). For example, to add 3/4 and 2/5: Common denominator is 20. 3/4 = 15/20 and 2/5 = 8/20. Sum = (15 + 8) / 20 = 23/20. As a mixed number, this equals 1 3/20 (decimal 1.15). Solve any fraction problem with full working on our [Fraction Calculator](/fraction-calculator).
Step-by-Step Rules for All 4 Operations
• Addition: (a/b) + (c/d) = (ad + bc) / bd • Subtraction: (a/b) - (c/d) = (ad - bc) / bd • Multiplication: (a/b) × (c/d) = (a × c) / (b × d) (Multiply numerators directly; multiply denominators directly; no common denominator needed!) • Division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc) (Invert the second fraction and multiply).
How to Handle Mixed Numbers
A mixed number consists of an integer whole part and a proper fraction (for example, 2 3/4): Step 1: Convert to an Improper Fraction Multiply the whole number by the denominator and add the numerator: 2 3/4 = (2 × 4 + 3) / 4 = 11/4. Step 2: Perform the arithmetic operation using improper fractions. Step 3: Convert the result back to a mixed number if the numerator exceeds the denominator: Divide 11 by 4 = 2 with remainder 3 -> 2 3/4.
Worked Example: Subtraction with Different Denominators
Evaluate: 5/6 - 3/8 1. Find LCM of denominators 6 and 8: Multiples of 6: 6, 12, 18, 24, 30... Multiples of 8: 8, 16, 24, 32... Least Common Denominator = 24. 2. Scale numerators: 5/6 = (5 × 4) / (6 × 4) = 20/24 3/8 = (3 × 3) / (8 × 3) = 9/24 3. Subtract numerators: (20 - 9) / 24 = 11/24. 4. Check simplification: Since 11 is prime and does not divide 24, 11/24 is already in simplest form (decimal ≈ 0.4583).
Handling Division by Zero
In mathematics, dividing by zero is undefined. In fraction arithmetic, this occurs whenever a denominator is zero, or when dividing by a fraction whose numerator is zero (e.g. dividing by 0/5). Our calculator detects zero denominators immediately and returns a friendly error before computation.