How to Add Fractions
Adding fractions is the one arithmetic skill that looks harder than it is. The rule is simple: you can only add fractions that share a denominator, so the whole job is finding a common one. Once the denominators match, you add the numerators and keep the denominator — then simplify. The fraction calculator above does all of it and shows the working, and this page teaches the method with examples you can follow by hand.
The default example in the calculator is 3/4 + 1/2. The denominators are 4 and 2, so the common denominator is 4: 1/2 becomes 2/4, and 3/4 + 2/4 = 5/4, which is 1 1/4 as a mixed number and 1.25 as a decimal. That is the whole method in one sum — the rest of this page is variations on it.
Whole (optional), then numerator / denominator
Whole (optional), then numerator / denominator
Adding Fractions with the Same Denominator
When the denominators already match, adding fractions is as easy as adding whole numbers: add the numerators and keep the denominator. 1/4 + 1/4 = 2/4, which simplifies to 1/2. 2/5 + 1/5 = 3/5. 5/6 + 1/6 = 6/6 = 1. The denominator is the size of the pieces — quarters, fifths, sixths — and adding the numerators counts how many pieces you have. You never add the denominators: 1/4 + 1/4 is not 2/8, because the pieces are still quarters, not eighths.
The only step left is simplifying. 2/4 becomes 1/2 because numerator and denominator share the factor 2. 6/6 becomes 1 because the numerator equals the denominator. A fraction is finished when the numerator and denominator share no common factor except 1 — and the calculator above shows the greatest common divisor it divided by, so you can see the simplification happening.
Adding Fractions with Different Denominators
When the denominators differ, you cannot add yet — the pieces are different sizes. First find a common denominator, usually the lowest common multiple (LCM) of the two denominators, then rewrite each fraction with it.
Step 1 — Find the common denominator. For 3/4 + 1/2, the denominators are 4 and 2. The LCM is 4.
Step 2 — Rewrite each fraction. 3/4 stays 3/4. 1/2 becomes 2/4, because 2 × 2 = 4 on the bottom and 1 × 2 = 2 on the top. Whatever you multiply the denominator by, multiply the numerator by the same number.
Step 3 — Add the numerators. 3/4 + 2/4 = 5/4.
Step 4 — Simplify and convert. 5/4 is already in lowest terms. As a mixed number it is 1 1/4, and as a decimal it is 1.25.
When the LCM Is Not Obvious
For 1/3 + 1/6, the LCM of 3 and 6 is 6: 1/3 becomes 2/6, and 2/6 + 1/6 = 3/6 = 1/2. For 1/2 + 1/3, the LCM of 2 and 3 is 6: 1/2 becomes 3/6, 1/3 becomes 2/6, and the sum is 5/6. When the denominators share no factors, the LCM is simply their product — for 2/3 + 1/5, use 15: 10/15 + 3/15 = 13/15. The calculator shows the LCM it used in the working, so you can check each step.
Worked Examples
The table below works through the additions people meet most often, with the common denominator and the simplified answer for each.
| Addition | Common denominator | Rewritten | Answer |
|---|---|---|---|
| 1/4 + 1/4 | 4 | 1/4 + 1/4 | 2/4 = 1/2 |
| 3/4 + 1/2 | 4 | 3/4 + 2/4 | 5/4 = 1 1/4 |
| 1/2 + 1/3 | 6 | 3/6 + 2/6 | 5/6 |
| 1/3 + 1/6 | 6 | 2/6 + 1/6 | 3/6 = 1/2 |
| 3/8 + 1/4 | 8 | 3/8 + 2/8 | 5/8 |
| 2/3 + 1/5 | 15 | 10/15 + 3/15 | 13/15 |
| 5/6 + 1/6 | 6 | 5/6 + 1/6 | 6/6 = 1 |
| 2/5 + 1/5 | 5 | 2/5 + 1/5 | 3/5 |
The 1/2 + 1/3 row is the classic case: two fractions that look simple but need the LCM before they can be added. The Khan Academy — Fractions has free practice problems for exactly this skill, with visual models that show why the common denominator works.
Adding Mixed Numbers
Mixed numbers — a whole number with a fraction, like 1 1/2 — are added in two parts or by converting first. The reliable method is conversion: turn each mixed number into an improper fraction, add as usual, then convert back. For 1 1/2 + 2 3/4: 1 1/2 is 3/2, and 2 3/4 is 11/4. The LCM of 2 and 4 is 4, so 3/2 becomes 6/4, and 6/4 + 11/4 = 17/4, which is 4 1/4. The calculator takes mixed numbers directly — enter the whole part, numerator, and denominator for each — and shows the conversion in the working.
The shortcut method works too when the fractions are friendly: add the whole numbers (1 + 2 = 3), add the fractions (1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4), then combine (3 + 1 1/4 = 4 1/4). Both methods give the same answer; conversion is safer when the fractions are awkward, because it removes the chance of forgetting to carry the extra whole.
Common Mistakes
Most wrong fraction answers come from the same short list of errors. Check yours against it before trusting the result.
- Adding numerators and denominators. 1/2 + 1/3 is 5/6, not 2/5 — find a common denominator first.
- Forgetting to simplify. 6/12 is 1/2; an unsimplified answer is correct but unfinished.
- Multiplying by the wrong reciprocal. Dividing by 2/5 means multiplying by 5/2, not by 2/5.
- Mixing whole numbers and fractions. Convert mixed numbers to improper fractions before adding or multiplying.
- Dividing by zero. A denominator of zero has no meaning — check both denominators before calculating.
- Rounding a repeating decimal too early. 1/3 is 0.333…, not 0.33 — round only at the end, and say that it repeats.
Related Tools
Related tools on this site: the main fraction calculator for any fraction sum, the ratio calculator for the ratio behind a fraction, the percentage calculator to turn a fraction into a percent, and the basic calculator for decimal arithmetic.
Key Takeaways
If you remember nothing else from this page, remember these five points.
- 3/4 + 1/2 = 5/4 = 1 1/4: find a common denominator, add the numerators, simplify.
- 12/18 simplifies to 2/3 — divide numerator and denominator by their GCD, which is 6.
- 3/4 as a decimal is 0.75: divide the numerator by the denominator.
- 1 1/2 is 3/2 as an improper fraction: 1 × 2 + 1 = 3, over 2.
- Dividing by a fraction means multiplying by its reciprocal: 3/4 ÷ 2/5 = 15/8.
Try It Yourself
- Enter the two fractions in the calculator above, whole parts included.
- Pick the operation and read the answer with the step-by-step working.
- Check the GCD shown to see how the answer was simplified.
- Convert the answer to a decimal or a mixed number as needed.
Quick Reminders
- Never add denominators — only numerators, and only after they match.
- Convert mixed numbers to improper fractions before multiplying or dividing.
- A denominator of zero has no meaning — check both denominators.
- 1/3 is 0.333…, repeating — round only at the end.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/3 | 0.333… | 33.33% |
Keep the fraction as a fraction for exact work and use the decimal only for measuring, money, or comparison — a rounded decimal is an approximation, and the fraction is the exact value.
Adding Mixed Numbers, Step by Step
Mixed numbers add the same way as fractions: convert the whole part, find a common denominator, add, and simplify. The table works four examples all the way through.
| Addition | Common denominator | Working | Answer |
|---|---|---|---|
| 1 1/2 + 2 1/4 | 4 | 1 2/4 + 2 1/4 | 3 3/4 |
| 2 1/3 + 1 1/6 | 6 | 2 2/6 + 1 1/6 | 3 1/2 |
| 1 2/5 + 3/10 | 10 | 1 4/10 + 3/10 | 1 7/10 |
| 2 3/4 + 1 1/2 | 4 | 2 3/4 + 1 2/4 | 4 1/4 |
Watch the last row: 2 3/4 + 1 2/4 makes 3 5/4, and 5/4 is 1 1/4, so the whole part grows by one — forgetting that regrouping step is the most common mistake with mixed numbers.
Frequently Asked Questions
How do you add fractions step by step?
Find a common denominator, rewrite each fraction with it, add the numerators, keep the denominator, then simplify. For 3/4 + 1/2: the common denominator is 4, 1/2 becomes 2/4, 3/4 + 2/4 = 5/4, which is 1 1/4.
How do you add fractions with different denominators?
Find the lowest common multiple of the denominators and rewrite each fraction with it. For 1/2 + 1/3, the LCM is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. Whatever you multiply the denominator by, multiply the numerator by the same number.
What is 3/4 + 1/2?
5/4, which is 1 1/4 as a mixed number and 1.25 as a decimal. The common denominator is 4: 1/2 becomes 2/4, and 3/4 + 2/4 = 5/4.
Can you add fractions by adding the numerators and denominators?
No. 1/2 + 1/3 is 5/6, not 2/5. Adding the denominators changes the size of the pieces, which is meaningless. Only the numerators are added, and only after the denominators match.
How do you add mixed numbers?
Convert each mixed number to an improper fraction first, then add as usual. 1 1/2 + 2 3/4 becomes 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4. The calculator takes mixed numbers directly and shows the conversion.
What is 1/2 + 1/3 as a fraction?
5/6. The common denominator is 6: 1/2 is 3/6 and 1/3 is 2/6, so 3/6 + 2/6 = 5/6. As a decimal that is about 0.833.
What is 1/4 + 3/4?
1. The denominators already match, so add the numerators: 1 + 3 = 4, over 4, which is 4/4 = 1.
How do you add three fractions?
The same way: find a common denominator for all three, rewrite each one, add the numerators, and simplify. For 1/2 + 1/3 + 1/6, the common denominator is 6: 3/6 + 2/6 + 1/6 = 6/6 = 1.
Disclaimer: This calculator is for general information and education. Fractions are exact arithmetic, but measurements and quantities you enter should be checked against the original source.