Add Fractions Calculator | Free Tool with Step-by-Step Solutions

How to Add Fractions

Adding fractions follows a simple pattern: make the denominators match, then add the numerators. Below is a quick overview — for a full walk-through with more examples, visit our How to Add Fractions guide.

Adding Fractions with the Same Denominator

When the denominators are already equal, keep the denominator and add the numerators. For instance, 2/7 + 3/7 = 5/7. That's it — no conversion needed.

Adding Fractions with Different Denominators

When denominators differ, you first need a common denominator. The most efficient choice is the Least Common Denominator (LCD) — the smallest number both denominators divide into evenly. Multiply each fraction's numerator and denominator so both fractions share the LCD, then add the numerators. Finally, simplify the result if the numerator and denominator share a common factor. Need help finding the LCD? Try our LCD Calculator.

Adding Mixed Numbers

A mixed number like 2 ¾ can be converted to an improper fraction first: multiply the whole number by the denominator, add the numerator, and place the result over the original denominator (2 ¾ → 11/4). Then proceed with the addition as usual. Convert back to a mixed number at the end if desired. Our Mixed Number Calculator handles these conversions automatically.

Looking for a deeper explanation with diagrams and more practice? Read the full How to Add Fractions tutorial.

Worked Examples

Example 1 — Same Denominator

3/8 + 1/8

Denominators are both 8, so add the numerators directly: 3 + 1 = 4. The result is 4/8. Simplify by dividing both by 4.

= 1/2

Example 2 — Different Denominators

2/3 + 1/4

LCD of 3 and 4 is 12. Convert: 2/3 = 8/12 and 1/4 = 3/12. Add numerators: 8 + 3 = 11. The result is already in simplest form.

= 11/12

Example 3 — Mixed Numbers

1 2/5 + 2 1/3

Convert to improper fractions: 1 2/5 = 7/5 and 2 1/3 = 7/3. LCD of 5 and 3 is 15. Convert: 7/5 = 21/15, 7/3 = 35/15. Add: 21 + 35 = 56. Result 56/15 → 3 11/15.

= 3 11/15

Example 4 — Result Needs Simplifying

5/6 + 1/6

Same denominator, add numerators: 5 + 1 = 6. Result is 6/6, which simplifies to a whole number.

= 1

Common Mistakes When Adding Fractions

✕ Adding the denominators. In 1/3 + 1/4, the answer is not 2/7. You must find a common denominator first, then add only the numerators.
✕ Forgetting to convert both fractions. When you find the LCD, every fraction must be converted — not just one of them.
✕ Skipping simplification. Always check if the numerator and denominator share a common factor. Divide both by their GCD to get the simplest form.
✕ Ignoring the whole-number part. With mixed numbers, convert to improper fractions before adding. Don't just add the whole numbers and fractions separately (though the shortcut works, it's error-prone if not careful).
✕ Using a common multiple that's too large. While any common multiple works, the LCD keeps numbers small and easier to simplify. Our LCD Calculator can help.

Practice Problems

Try these on paper first, then reveal the answer to check your work.

1/6 + 2/6 1/2

3/5 + 1/4 17/20

7/10 + 3/10 1

2 1/2 + 1 3/4 4 1/4

5/9 + 2/3 1 2/9

Frequently Asked Questions

How do you add fractions with different denominators?

Find the Least Common Denominator (LCD) of the two denominators. Convert each fraction so it has the LCD as its new denominator by multiplying the numerator and denominator by the same factor. Add the numerators and keep the LCD as the denominator. Simplify the result if possible.

Can I add mixed numbers with this calculator?

Yes. Enter the whole-number part in the first box alongside the numerator and denominator. The calculator converts mixed numbers to improper fractions behind the scenes, performs the addition, and converts the result back to a mixed number automatically.

What is the LCD and why do I need it?

The Least Common Denominator (LCD) is the smallest number that both denominators divide into evenly. You need it so that both fractions share a common denominator — only then can you add the numerators directly. You can always use a larger common multiple, but the LCD keeps numbers manageable.

Do I always need to simplify the answer?

While mathematically valid without simplifying, reducing to lowest terms gives you the cleanest form. The calculator does this automatically by dividing numerator and denominator by their Greatest Common Divisor (GCD). Teachers and textbooks almost always require simplified answers.

What if my fractions already have the same denominator?

Then it's even simpler — just add the numerators and keep the shared denominator. For example, 2/7 + 3/7 = 5/7. No LCD calculation is needed. Still remember to simplify the answer if the numerator and denominator share a common factor.

Related Calculators

Explore more fraction tools: Subtract Fractions Calculator, Multiply Fractions Calculator, Divide Fractions Calculator, Simplify Fractions Calculator, and the Master Fractions Calculator on our homepage.