Fraction Addition Calculator
Adding fractions is the one arithmetic operation where the easy instinct is wrong. You cannot add the tops and add the bottoms: 1/2 + 1/3 is not 2/5. The denominators are the units, halves and thirds, and units must match before anything adds, exactly as meters must match feet. This calculator adds two fractions or mixed numbers and shows every step the way a teacher would: the least common denominator, the equivalent fractions, the addition, and the simplification to lowest terms, plus the mixed-number and decimal forms.
Enter each fraction as an optional whole number plus numerator and denominator. The calculator returns the simplified sum with the full working, so you can check homework, verify a recipe scaling, or finally settle the argument about 2/3 + 3/4.
Quick Answer
2/3 + 3/4 = 17/12, which is 1 5/12 as a mixed number and about 1.4167 as a decimal. The least common denominator of 3 and 4 is 12, so the fractions become 8/12 and 9/12, the numerators add to 17, and 17/12 is already in lowest terms.
Key takeaways
- Never add denominators. Convert to a common denominator first, then add only the numerators.
- The least common denominator keeps numbers small: for 3 and 4 it is 12, while multiplying denominators also gives 12 here but blows up on pairs like 6 and 8 (48 vs 24).
- Always simplify at the end by dividing top and bottom by their greatest common divisor.
- Convert mixed numbers to improper fractions before you start; add the whole parts separately only if you enjoy extra bookkeeping.
Why denominators must match first
A fraction’s denominator names the unit: thirds, quarters, eighths. Adding 2/3 + 3/4 directly would be adding thirds to quarters, which is as meaningless as adding 2 meters to 3 feet and calling it 5 of something. The common denominator is the shared unit that makes addition possible. The least common denominator is simply the smallest shared unit, which keeps the arithmetic tidy.
Better with the LCD: convert both to twelfths (or whatever the LCD is), add numerators, keep the denominator, simplify
The two routes always agree, but the LCD route needs less simplifying afterward. For 3/4 + 5/6, multiplying denominators gives 18/24 + 20/24 = 38/24, which then reduces by 2; the LCD route goes straight to 9/12 + 10/12 = 19/12. Same answer, half the cleanup.
Adding fractions in four steps
Walked through for the worked example: 2/3 and 3/4 are already proper, so step 1 is trivial. The LCD of 3 and 4 is 12. Converting gives 8/12 and 9/12. Adding numerators gives 17/12. The GCD of 17 and 12 is 1, so the fraction is already simplified, and as a mixed number it is 1 5/12.
The three cases, side by side
| Case | Example | What you do | Result |
|---|---|---|---|
| Same denominator | 3/8 + 2/8 | Add numerators only: (3+2)/8 | 5/8 |
| Different denominators | 1/4 + 1/6 | LCD of 4 and 6 is 12: 3/12 + 2/12 | 5/12 |
| Mixed numbers | 2 1/3 + 1 1/6 | Improper: 7/3 + 7/6 = 14/6 + 7/6 | 21/6 = 7/2 = 3 1/2 |
The mixed-number case is where most homework errors happen: students add the whole parts and the fractions separately and forget that the fraction sum can itself exceed one. Converting to improper fractions first removes that trap entirely. Try 2 1/3 + 1 1/6 in the calculator above and watch the steps handle it.
Finding the LCD without the guesswork
For small denominators you can spot the least common denominator by listing multiples: 4, 8, 12 and 6, 12, so 12 it is. For larger or awkward pairs like 18 and 24, prime factorization is the reliable method. Break each denominator into primes: 18 = 2 x 3 x 3, and 24 = 2 x 2 x 2 x 3. The LCD takes each prime the maximum number of times it appears in either denominator: three 2s and two 3s, giving 2 x 2 x 2 x 3 x 3 = 72. Check: 72/18 = 4 and 72/24 = 3, both whole, and no smaller number works for both. The calculator runs this same logic internally, which is why it can handle denominators well beyond what you would want to factor by hand.
One more habit worth building: reduce each fraction before finding the LCD. Adding 4/10 + 6/15 looks like an LCD of 30, but reducing first to 2/5 + 2/5 gives an LCD of 5 and the answer 4/5 with almost no arithmetic. Simplification is not just the last step; used early, it is a shortcut.
What competing calculators miss
The fraction tools ranking today mostly compute correctly but teach nothing. WpCalc’s adding-fractions tool is the strongest of the bunch, with mixed-number support and automatic recalculation, but it never explains why the LCD beats multiplying denominators, so users copy the answer without the method. HackMath is an expression solver that happens to accept fractions; it shows steps for whole expressions, not the fraction-addition method itself. Calculator-im, CalculatorOnline, and CalcMate all cover the four operations with steps, yet none let you enter mixed numbers directly in a dedicated addition flow, and none discuss the same-denominator shortcut or the simplify-at-the-end discipline. This calculator’s winning moves are the mixed-number inputs with proper sign handling, the explicit LCD choice with the reasoning beside it, and results in all four useful forms at once: simplified fraction, mixed number, decimal, and the full teacher-style working.
Frequently asked questions
Because the denominator is the unit. 1/2 + 1/3 would give 2/5 by that method, but 2/5 (0.4) is smaller than 1/2 (0.5) alone, which is absurd: adding a positive amount cannot shrink the total. Convert to common denominators first so the units match.
The smallest number both denominators divide into evenly. Multiplying the denominators always works as a common denominator, but it often produces larger numbers that need more simplifying. The LCD gives the same answer with less cleanup.
Convert each to an improper fraction first: multiply the whole number by the denominator and add the numerator. Then add as usual and convert back. For 2 1/3: (2 x 3 + 1)/3 = 7/3.
In school and in any formal answer, yes: divide numerator and denominator by their greatest common divisor until the fraction is in lowest terms. 21/6 must become 7/2. The calculator does this automatically and shows the GCD.
Then just add the numerators and keep the denominator: 3/8 + 2/8 = 5/8. No conversion needed. The calculator detects this and the LCD step is trivial.
The same method extends: find one common denominator for all of them (the LCM of all denominators), convert each, and add all the numerators. Add them pairwise with this calculator if you prefer: compute the first two, then add the third to the result.
Because most real-world uses, from recipe scaling to measurements, end in decimal. 17/12 = 1.4167 is the form you would actually type into a scale or a spreadsheet.
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References
- OpenStax. “Prealgebra: Add and Subtract Fractions with Different Denominators.” OpenStax Prealgebra: Fractions with Different Denominators Accessed October 19, 2026.
- Khan Academy. “Adding Fractions with Unlike Denominators.” Khan Academy: Adding Fractions with Unlike Denominators Accessed October 19, 2026.
- Purplemath. “Adding and Subtracting Fractions.” Purplemath: Adding and Subtracting Fractions Accessed October 19, 2026.
- Math is Fun. “Adding Fractions.” Math is Fun: Adding Fractions Accessed October 19, 2026.
- National Council of Teachers of Mathematics. “Principles and Standards for School Mathematics: Number and Operations.” NCTM Standards for School Mathematics Accessed October 19, 2026.