How to Add Fractions (Same & Different Denominators)

By ZeroFee Tools · October 15, 2026 · 8 min read

Adding fractions is one of those skills that feels mysterious until the method clicks, and then it feels obvious forever. The entire subject reduces to one rule: you can only add pieces that are the same size. When the denominators match, you just add the tops. When they do not, you resize the pieces first. Our fraction calculator guide walks through the tool that checks this work, and the free Fraction Calculator adds, subtracts, and simplifies any fractions instantly.

This guide covers same denominators, the least common denominator method for different ones, mixed numbers, and a quick subtraction refresher, each with worked examples you can verify by hand.

Adding fractions with the same denominator

When denominators match, keep the denominator and add the numerators: 1/4 + 2/4 = 3/4. Then simplify if possible, as with 2/6 + 3/6 = 5/6.

This is the easy case, and it is worth mastering first because the harder case reduces to it. Keep the bottom number exactly as it is and add the top numbers. 1/4 + 2/4: the pieces are quarters in both, so you have one quarter plus two quarters, which is three quarters, 3/4.

Try 3/8 + 4/8. Denominators match at 8, so add the numerators: 3 + 4 = 7, giving 7/8. Can it simplify? 7 and 8 share no common factor, so 7/8 is final. Now 2/10 + 3/10 = 5/10, which simplifies: divide top and bottom by 5 to get 1/2. The simplification step is easy to forget and easy to check.

Watch for answers bigger than one whole. 5/6 + 4/6 = 9/6, and 9/6 simplifies to 3/2, which is the mixed number 1 1/2. An answer like 9/6 is not wrong, but the simplified or mixed form is the expected finish. The Fraction Calculator shows both forms automatically.

Different denominators: the LCD method

Find the least common denominator (the smallest number both denominators divide into), rewrite each fraction with it, then add as usual. For 1/3 + 1/6, the LCD is 6: 2/6 + 1/6 = 3/6 = 1/2.

Quick vocabulary: the denominator (bottom number) names the size of the pieces, and the numerator (top number) counts how many you have. In 3/4 the pieces are quarters and you have three of them. You can only add pieces of the same size, which is why different denominators must be converted first, and you should always simplify the final answer.

The least common denominator is the smallest number that both denominators divide into evenly. For 1/3 + 1/6, list multiples: 3 goes 3, 6, 9... and 6 goes 6, 12... The smallest shared multiple is 6. Rewrite 1/3 as 2/6 (multiply top and bottom by 2), keep 1/6 as is, and add: 2/6 + 1/6 = 3/6, which simplifies to 1/2.

A meatier example: 2/3 + 3/4. Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. The LCD is 12. Convert: 2/3 becomes 8/12 (multiply by 4), 3/4 becomes 9/12 (multiply by 3). Add: 8/12 + 9/12 = 17/12, which is 1 5/12. Whatever you multiply the bottom by, multiply the top by the same number; that keeps the fraction equivalent.

One more: 3/8 + 1/6. Multiples of 8: 8, 16, 24. Multiples of 6: 6, 12, 18, 24. LCD is 24. Convert: 3/8 = 9/24, 1/6 = 4/24. Add: 13/24. It does not simplify, so 13/24 is the answer. If finding the LCD feels slow, any common denominator works in a pinch (here 48 would too), but the LCD keeps numbers small and simplification easy.

Adding mixed numbers

Add the whole-number parts and the fraction parts separately, then combine and simplify. For 1 1/2 + 2 3/4: wholes give 3, fractions give 1/2 + 3/4 = 5/4 = 1 1/4, so the total is 4 1/4.

A mixed number like 2 3/4 is just a whole number plus a fraction, so handle the two parts separately. Take 1 1/2 + 2 3/4. First the wholes: 1 + 2 = 3. Then the fractions: 1/2 + 3/4. The LCD is 4, so 1/2 becomes 2/4, and 2/4 + 3/4 = 5/4, which is 1 1/4. Combine: 3 + 1 1/4 = 4 1/4.

Watch for the case where the fraction sum reaches or passes a whole. In 2 2/3 + 1 2/3: wholes give 3, fractions give 4/3, which is 1 1/3. Combine: 3 + 1 1/3 = 4 1/3. Forgetting to carry the extra whole is the classic mixed-number error; always check whether your fraction sum is an improper fraction.

The alternative method is converting everything to improper fractions first: 1 1/2 becomes 3/2, 2 3/4 becomes 11/4, then add with LCD 4: 6/4 + 11/4 = 17/4 = 4 1/4. Same answer. Use whichever method you find cleaner; the separate-parts method usually involves smaller numbers.

Subtracting fractions: the quick version

Subtraction follows the exact same rules as addition: match the denominators with the LCD, then subtract the numerators. For 5/6 - 1/3: convert 1/3 to 2/6, then 5/6 - 2/6 = 3/6 = 1/2.

Everything you just learned applies to subtraction with one change: subtract the tops instead of adding them. 5/6 - 1/3: the LCD is 6, so 1/3 becomes 2/6, and 5/6 - 2/6 = 3/6 = 1/2. Same-denominator subtraction is just as direct: 7/8 - 3/8 = 4/8 = 1/2.

With mixed numbers, subtract wholes and fractions separately, but borrow if the fraction part would go negative. In 3 1/4 - 1 3/4: the fraction 1/4 - 3/4 cannot be done directly, so borrow 1 from the 3, making it 2 5/4, then subtract: 2 5/4 - 1 3/4 = 1 2/4 = 1 1/2. Borrowing works exactly like borrowing in ordinary subtraction.

As always, simplify the final answer. Our fraction calculator guide shows how the tool handles the borrowing and simplifying steps visibly, which is useful when you are learning.

Step-by-step: add any two fractions

Check the denominators, find the LCD if they differ, rewrite both fractions, add the numerators, and simplify. Five steps, and the same pattern works every time.

1. Look at the denominators. If they match, skip to step 4. If not, you need the LCD. Example: 2/3 + 3/4.
2. Find the least common denominator. List multiples of each denominator until you find the smallest shared one. For 3 and 4, the LCD is 12.
3. Rewrite both fractions with the LCD. Multiply top and bottom of each by whatever makes the bottom equal the LCD: 2/3 = 8/12, 3/4 = 9/12.
4. Add the numerators, keep the denominator. 8/12 + 9/12 = 17/12. The bottom number never changes during the addition itself.
5. Simplify and convert if needed. 17/12 = 1 5/12. Divide top and bottom by any common factor, and write improper results as mixed numbers.
6. Verify with the calculator. Enter the original fractions in the free Fraction Calculator to confirm your answer.

6 tips for fraction confidence

Draw the pieces when stuck, never add denominators, keep numbers small with the LCD, and always simplify at the end.

• Never add the denominators. 1/2 + 1/2 is 2/2 = 1, not 2/4. Adding bottoms is the single most common fraction error.
• Draw it when stuck. Sketch two bars or circles, shade the fractions, and the answer often becomes visible before the arithmetic finishes.
• Use the LCD, not just any common denominator. Any shared multiple works, but the LCD keeps numbers small and usually skips the simplification step.
• Multiply top and bottom by the same number. That is what keeps a rewritten fraction equivalent. Change one without the other and the value changes.
• Simplify last, not first. You can simplify inputs too, but always simplify the final answer; it is the expected form.
• Estimate to catch nonsense. 1/3 + 1/6 must be less than 1. If your answer is 2/9 or 5, something went wrong before you finished.

Frequently asked questions