How to Add and Subtract Fractions: A Simple Step-by-Step Guide
Learn why fractions confuse people, the one rule that makes fraction addition easy, and how to add or subtract any two fractions step by step.
Why Fractions Confuse People
Fractions feel confusing because the rules for adding them are different from the rules for adding whole numbers. With whole numbers, you just add the digits. With fractions, you cannot add the numerators (the top numbers) unless the denominators (the bottom numbers) are the same first. This extra step is where most people get stuck.
The confusion deepens because multiplying fractions is actually simpler than adding them. To multiply fractions, you just multiply the tops together and multiply the bottoms together. But many people try to apply that same logic to addition, which produces wrong answers.
Once you understand the single rule that governs fraction addition — denominators must match — everything else follows logically. The math is not difficult. It just requires one extra step that whole number addition does not.
The One Rule That Makes It Easy (Common Denominator)
You can only add or subtract fractions when their denominators are the same. A denominator tells you what size pieces you are working with. You cannot add halves and thirds directly any more than you can add apples and oranges without converting them to a common unit.
When denominators already match, addition is trivial: add the numerators and keep the denominator. Two thirds plus one third equals three thirds, which simplifies to one whole. Easy.
When denominators do not match, you need to convert both fractions to equivalent fractions that share a common denominator. This is the core skill in fraction addition, and it is the one step most people need to practice until it becomes routine.
Adding Fractions With Different Denominators
To add one half plus one third, you first need a common denominator. Find the least common multiple (LCM) of 2 and 3. The multiples of 2 are 2, 4, 6, 8. The multiples of 3 are 3, 6, 9. The smallest number that appears in both lists is 6. So 6 is your common denominator.
Convert each fraction to an equivalent fraction with denominator 6. For one half: multiply both numerator and denominator by 3 to get three sixths. For one third: multiply both by 2 to get two sixths. Now you have three sixths plus two sixths, which equals five sixths.
Always simplify the result if possible. Five sixths has no common factor between 5 and 6 other than 1, so it is already in its simplest form. If the result were four sixths, you would simplify by dividing both by 2 to get two thirds.
Subtracting Fractions the Same Way
Subtracting fractions follows the exact same process as adding them. Find the common denominator, convert both fractions, then subtract the numerators instead of adding them. The denominator stays the same.
For example, three quarters minus one third: the LCM of 4 and 3 is 12. Three quarters becomes nine twelfths (multiply by 3). One third becomes four twelfths (multiply by 4). Nine twelfths minus four twelfths equals five twelfths.
When subtracting mixed numbers (numbers with a whole number part and a fraction part), it sometimes helps to convert them to improper fractions first, then apply the standard subtraction process, and then convert the result back to a mixed number if needed.