Add the numerators together and keep the denominator exactly as it is. Do not add the denominators. The denominator describes the size of the pieces, and that size does not change just because you are combining more of them.
● Free · Real-Time Calculator
Adding Fractions Calculator
Add two, three, four, or five fractions at once, even with completely unlike denominators. Every keystroke instantly updates the least common denominator, the equivalent fractions, and the simplified sum, so you can see exactly how the answer is built instead of just what it is.
- ✓Works with 2 to 5 fractions in one calculation
- ✓Supports whole numbers and mixed numbers
- ✓Shows the LCD, the conversion, and the sum inline
- ✓Automatically simplifies and converts to a mixed number
3Steps shown live
5Fractions at once
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Fraction Addition Live
Enter 2 to 5 fractions. Switch to Mixed to add whole-number parts.
Enter fractions above to see the LCD, the conversion, and the sum.
01 · METHOD
How to Add Fractions with Unlike Denominators
Fractions can only be added once they are measured in the same-size pieces. When two fractions have different denominators, you cannot add the numerators directly. A slice that is one-fourth of a pizza is not the same size as a slice that is one-sixth of a pizza. The fix is a three-step process that rewrites every fraction using a shared denominator before anything gets added.
1
Find the LCD
Find the least common denominator of every denominator in the problem. It is the smallest number each denominator divides into evenly.
2
Convert to equivalent fractions
Multiply each fraction's numerator and denominator by the factor that turns its denominator into the LCD.
3
Add the numerators
Add the new numerators over the shared denominator, then simplify and convert to a mixed number if needed.
a/b + c/d = (a × (LCD÷b) + c × (LCD÷d)) / LCD
For example, to add 1/4 and 1/6, the LCD of 4 and 6 is 12. Multiplying 1/4 by 3/3 gives 3/12, and multiplying 1/6 by 2/2 gives 2/12. Adding those numerators gives 3/12 + 2/12 = 5/12, which is already in lowest terms.
02 · SAME DENOMINATOR
Adding Fractions with Matching Denominators
When every fraction in the problem already shares the same denominator, the LCD step disappears entirely. The denominator is already common, so there is nothing left to convert.
3/8 + 2/8 = (3 + 2)/8 = 5/8. The denominator stays 8 throughout; only the numerators combine. If the result can be simplified, such as 4/8 + 2/8 = 6/8, reduce it afterward to 3/4.
03 · MIXED NUMBERS
Adding Mixed Numbers
A mixed number such as 1 1/2 combines a whole number and a fraction. To add mixed numbers correctly, convert each one into an improper fraction first, so the whole-number part cannot get lost or mishandled during the addition.
- Convert each mixed number to an improper fraction: multiply the whole number by the denominator and add the numerator, keeping the same denominator.
- Add the improper fractions using the standard LCD method: find the LCD, convert to equivalent fractions, then add the numerators.
- If the sum is an improper fraction, convert it back to a mixed number by dividing the numerator by the denominator; the quotient is the new whole number and the remainder sits over the original denominator.
1 1/2 + 2 3/4 = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4
Notice that the whole-number parts (1 and 2) are folded into the improper fractions before any addition happens. Adding the whole numbers and fraction parts separately can work for simple cases, but it breaks down the moment a "carry" is needed, for example when the fraction parts add up to more than one whole. Converting to improper fractions first avoids that pitfall entirely.
04 · EXAMPLES
Six Worked Examples of Adding Fractions
Each example below shows the same three steps used by the calculator above: find the LCD, convert to equivalent fractions, then add the numerators and simplify.
Example 1 LCD method
14 + 16
14 + 16
- LCD(4, 6) = 12
- 1/4 → 3/12 and 1/6 → 2/12
- 3/12 + 2/12 = 5/12
LCD 12
312 + 212 = 512
Example 2 LCD method
23 + 38
23 + 38
- LCD(3, 8) = 24
- 2/3 → 16/24 and 3/8 → 9/24
- 16/24 + 9/24 = 25/24
LCD 24
1624 + 924 = 2524
= 1 1/24
Example 3 LCD method
12 + 13 + 16
12 + 13 + 16
- LCD(2, 3, 6) = 6
- 1/2 → 3/6, 1/3 → 2/6, 1/6 stays 1/6
- 3/6 + 2/6 + 1/6 = 6/6 = 1
LCD 6
36 + 26 + 16 = 1
Example 4 Mixed numbers
1 1/2 + 2 3/4
32 + 114
- 1 1/2 → 3/2 and 2 3/4 → 11/4
- LCD(2, 4) = 4, so 3/2 → 6/4
- 6/4 + 11/4 = 17/4
LCD 4
64 + 114 = 174
= 4 1/4
Example 5 LCD method
35 + 27
35 + 27
- LCD(5, 7) = 35
- 3/5 → 21/35 and 2/7 → 10/35
- 21/35 + 10/35 = 31/35
LCD 35
2135 + 1035 = 3135
Example 6 LCD method
56 + 14
56 + 14
- LCD(6, 4) = 12
- 5/6 → 10/12 and 1/4 → 3/12
- 10/12 + 3/12 = 13/12
LCD 12
1012 + 312 = 1312
= 1 1/12
05 · COMMON MISTAKES
4 Common Mistakes When Adding Fractions
Most addition errors trace back to one of these four habits. Watching for them is often enough to catch a wrong answer before it happens.
Adding denominators instead of finding the LCD
1/4 + 1/6 is not 2/10. Denominators describe the size of the pieces, not a quantity to be summed. You must find a common denominator, ideally the LCD, before the numerators can be combined.
Forgetting to simplify the result
An answer like 6/8 is correct but incomplete. It should be reduced to 3/4. Always divide the numerator and denominator by their greatest common factor as a final step.
Not converting mixed numbers first
Adding whole numbers and fraction parts separately can silently produce the wrong total whenever the fractions add up to more than one. Convert every mixed number to an improper fraction before adding.
Adding across the fraction bar instead of across numerators
1/2 + 1/2 is 1, not 2/4. Once the denominators match, only the numerators are added; the shared denominator is written once, underneath the new numerator.
06 · FAQ
Frequently Asked Questions About Adding Fractions
How do you add fractions with different denominators?
Find the least common denominator (LCD) of all the fractions, convert each fraction into an equivalent fraction that uses the LCD, then add the numerators while keeping the shared denominator. Finish by simplifying the result to lowest terms. For example, adding 1/4 and 1/6 first requires converting both to twelfths.
What is 1/4 + 1/6?
The LCD of 4 and 6 is 12. Converting gives 3/12 + 2/12, which adds to 5/12. That fraction is already in lowest terms, so 1/4 + 1/6 = 5/12. Twelve works because it's the smallest number both 4 and 6 divide into evenly, avoiding larger denominators like 24.
How do you add mixed numbers?
Convert each mixed number into an improper fraction first (multiply the whole number by the denominator and add the numerator). Add the improper fractions using the LCD method, then convert the sum back into a mixed number if it is greater than one.
Do you need the LCD to add fractions?
You need a common denominator to add fractions, and the LCD is simply the smallest one. Any common denominator works, including the product of the two denominators, but the LCD keeps the numbers smaller and means the answer is more likely to already be in lowest terms.
What is 2/3 + 3/8?
The LCD of 3 and 8 is 24. Converting gives 16/24 + 9/24, which adds to 25/24. Since the numerator is larger than the denominator, this simplifies to the mixed number 1 1/24. Since 25 and 24 share no common factors besides 1, no further simplification is possible.