Add 2/3 + 1/4
Input
2/3 + 1/4Output
11/12 · Decimal: 0.9167 · LCD: 12 · Working: 8/12 + 3/12 = 11/12The LCD of 3 and 4 is 12. Convert: 2/3 = 8/12, 1/4 = 3/12. Sum: 11/12 (already in lowest terms since GCD(11,12) = 1).
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A fraction calculator applies standard fraction rules and simplifies the result, so you can solve +, −, ×, and ÷ operations with clear working.
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A fraction calculator adds, subtracts, multiplies, and divides fractions, returning simplified fractions (and often mixed numbers and decimals).
Fraction arithmetic often requires finding a common denominator (for addition/subtraction) and simplifying results by dividing numerator and denominator by their greatest common divisor (GCD). This calculator performs the operations and returns the simplified result so you can verify homework, measurements, or recipe scaling quickly.
We apply standard fraction rules for each operation, then simplify by dividing numerator and denominator by their greatest common divisor (GCD).
Formula
Add/Subtract: a/b ± c/d = (ad ± bc) / bd (after finding a common denominator)
Multiply: (a/b) × (c/d) = (ac) / (bd)
Divide: (a/b) ÷ (c/d) = (a/b) × (d/c)
Simplify: divide numerator and denominator by GCD(numerator, denominator)Type the numerator and denominator separately (e.g. 3 and 4 for 3/4). For mixed numbers, enter the whole number separately (e.g. 1 and 3/4 for 1¾).
Choose: + (addition), − (subtraction), × (multiplication), ÷ (division).
Type the second numerator and denominator.
The result appears as a simplified fraction, a mixed number (if improper), and a decimal. The step-by-step working shows the LCD for addition/subtraction or the cross-multiplication for division.
Input
2/3 + 1/4Output
11/12 · Decimal: 0.9167 · LCD: 12 · Working: 8/12 + 3/12 = 11/12The LCD of 3 and 4 is 12. Convert: 2/3 = 8/12, 1/4 = 3/12. Sum: 11/12 (already in lowest terms since GCD(11,12) = 1).
Input
5/6 ÷ 2/3Output
5/4 = 1¼ · Decimal: 1.25Division by a fraction = multiplication by its reciprocal: 5/6 × 3/2 = 15/12. Simplify: GCD(15,12) = 3 → 5/4 = 1 remainder 1 → 1¼.
Common real-world scenarios where this tool saves time.
Students learning fraction arithmetic
Verify fraction homework answers and see the complete working to understand where you went wrong or confirm your process was correct.
Bakers and cooks scaling recipes
Scale a recipe that calls for 3/4 cup by 1/3 (making a smaller batch): 3/4 × 1/3 = 3/12 = 1/4 cup. Fraction arithmetic for cooking is error-prone mentally — use the calculator for precision.
Carpenters and DIY builders
Woodworking uses fractional measurements (1 5/8 inch, 7/16 inch). Adding and subtracting these fractions for cut lists and gap calculations requires finding common denominators.
How to perform each arithmetic operation with fractions — the rules the calculator follows.
| Operation | Rule | Example | Result |
|---|---|---|---|
| Addition | Find LCD, convert, add numerators | 1/3 + 1/4 | 4/12 + 3/12 = 7/12 |
| Subtraction | Find LCD, convert, subtract numerators | 3/4 − 1/3 | 9/12 − 4/12 = 5/12 |
| Multiplication | Multiply numerators × numerators, denominators × denominators | 2/3 × 3/4 | 6/12 = 1/2 |
| Division | Multiply by the reciprocal of the divisor | 2/3 ÷ 4/5 | 2/3 × 5/4 = 10/12 = 5/6 |
| Simplification | Divide numerator and denominator by their GCD | 6/9 | GCD=3 → 2/3 |
Always simplify fractions after computing. An improper fraction can be written as a mixed number — both forms can be correct.
Only numerators combine after converting to a common denominator.
Reduce by GCD to get the fraction in lowest terms.
For a/b ÷ c/d, multiply a/b by d/c before simplifying.
Keep negatives consistent (prefer sign on numerator) before simplification.
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Find the Least Common Denominator (LCD) — the smallest multiple shared by both denominators. Convert each fraction to have the LCD as the denominator, then add the numerators. Example: 1/4 + 1/6. LCD(4,6)=12. 1/4=3/12, 1/6=2/12. 3/12+2/12=5/12.
Multiply the first fraction by the reciprocal (flip) of the second fraction: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Then simplify.
Divide both numerator and denominator by their Greatest Common Divisor (GCD). GCD(12,18)=6: 12/18 = 2/3. To find GCD, use the Euclidean algorithm: repeatedly divide the larger by the smaller and take the remainder until reaching 0; the last non-zero remainder is the GCD.
For addition/subtraction, rewrite each fraction with the same denominator (LCD), combine numerators, then simplify.
Yes. After simplification, improper fractions can be expressed as mixed numbers and decimals for easier interpretation.
A denominator of zero is undefined. Enter non-zero denominators only.
Fraction Calculator keeps typical inputs on your device—nothing is uploaded to EverydayTools servers for core calculations.
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Reviewed by EverydayTools Editorial Team on 2026-05-28.
Enter numerator and denominator
Enter numerator and denominator
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