Fraction Calculator
MathAdd, subtract, multiply, and divide fractions instantly. Get results as simplified fractions, mixed numbers, and decimals. Perfect for students and teachers.
1/2 + 1/3 = 0/1
Enter values above and choose an operation
Result
01
Decimal
0
Numerator
0
Denominator
1
What is a Fraction?
A Fraction Calculator performs the four arithmetic operations — addition, subtraction, multiplication, and division — on two fractions and returns the result as a simplified fraction, decimal, and mixed number. It shows full step-by-step working so you can follow and learn the method, not just get the answer.
Fractions are a core building block of school mathematics, appearing throughout the NCERT curriculum from Class 3 to Class 10 and featuring in CBSE, ICSE, and state board examinations, entrance tests like NTSE and JEE, and everyday applications from cooking measurements to percentage calculations.
This calculator handles:
- Proper fractions (e.g., 3/4), improper fractions (e.g., 7/3), and negative fractions
- All four operations: + − × ÷
- Automatic GCD-based simplification of results
- Mixed number representation (e.g., 7/3 = 2⅓)
See the Percentage Calculator for converting fractions to percentages, and the Ratio Calculator for ratio simplification.
How to use this Fraction calculator
- Enter Numerator 1 and Denominator 1 for the first fraction.
- Select the Operation: Add, Subtract, Multiply, or Divide.
- Enter Numerator 2 and Denominator 2 for the second fraction.
- Results appear instantly: the simplified Result Numerator and Denominator, the Decimal Result (highlighted), and the Mixed Number parts.
- Open the Steps panel to see full working — including the common denominator step, intermediate calculations, and the simplification step.
- For negative fractions, enter a negative numerator (e.g., −3 for −3/4).
Formula & Methodology
Addition: a/b + c/d = (a×d + c×b) / (b×d), then simplify by GCD
Subtraction: a/b − c/d = (a×d − c×b) / (b×d), then simplify by GCD
Multiplication: a/b × c/d = (a×c) / (b×d), then simplify by GCD
Division: a/b ÷ c/d = (a×d) / (b×c) (multiply by reciprocal), then simplify by GCD
Simplification uses the Euclidean GCD algorithm: repeatedly replace (a, b) with (b, a mod b) until b = 0; the GCD is a. Then divide both numerator and denominator by GCD.
Worked examples:
1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6 = 0.8333... 3/4 − 1/6 = (3×6 − 1×4) / (4×6) = (18 − 4) / 24 = 14/24 Simplify: GCD(14,24) = 2 → 7/12 = 0.5833... 2/3 × 3/5 = (2×3) / (3×5) = 6/15 Simplify: GCD(6,15) = 3 → 2/5 = 0.4 5/6 ÷ 2/3 = 5/6 × 3/2 = (5×3) / (6×2) = 15/12 Simplify: GCD(15,12) = 3 → 5/4 = 1.25 = 1¼Frequently Asked Questions
How do you add fractions with different denominators?
To add fractions with different denominators, first find a common denominator (the LCM of both denominators), convert each fraction, then add the numerators. For example: 1/3 + 1/4 = (4/12) + (3/12) = 7/12. The calculator does this automatically, using the product of both denominators as the working denominator and then simplifying the result.
How do you multiply fractions?
To multiply fractions, multiply the numerators together and the denominators together, then simplify. For example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. Unlike addition and subtraction, multiplication does not require a common denominator. It is the simplest of the four fraction operations.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flip) of the second. For example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2⅔. The phrase 'keep, change, flip' (KCF) is a common mnemonic: keep the first fraction, change division to multiplication, flip the second fraction. The calculator shows each step in the steps panel.
What is a simplified fraction?
A simplified (or reduced) fraction is one where the numerator and denominator share no common factors other than 1 — the GCD (Greatest Common Divisor) of numerator and denominator is 1. For example, 6/8 simplifies to 3/4 (dividing both by 2). The calculator automatically simplifies all results using the Euclidean algorithm for GCD.
What is a mixed number and how is it read?
A mixed number combines a whole number and a proper fraction: for example, 7/3 = 2⅓ (two and one-third). The 'Mixed Number (Integer)' output shows the whole number part, and the 'Mixed Number (Fraction Numerator)' shows the remaining numerator (with the result denominator unchanged). So if the result is 2/1 whole + 1/3 fraction, the outputs will be Integer: 2, Fraction Numerator: 1, Denominator: 3, reading as 2 and 1/3.
Why does the calculator show the result numerator and denominator separately?
The calculator outputs the numerator and denominator of the simplified fraction as separate numbers because the platform displays each output individually. Together they form your fraction result: Result = Numerator / Denominator. The Decimal Result shows the same value as a decimal. For example, if Result Numerator = 5 and Result Denominator = 6, the fraction is 5/6 = 0.8333...
Can the calculator handle negative fractions?
Yes. Enter a negative numerator for a negative fraction. For example, −1/2 is entered as Numerator 1: −1, Denominator 1: 2. The calculator handles all combinations of positive and negative fractions correctly. By convention, the calculator keeps the negative sign in the numerator — for example, −3/4 rather than 3/−4.
How do fractions appear in the Indian school curriculum?
Fractions are introduced in Class 3–4 under the NCERT mathematics curriculum and remain central through Class 6–8, where operations on fractions (addition, subtraction, multiplication, division) are core topics. The CBSE and state board examinations regularly include fraction problems in Classes 5–10. This calculator is useful for checking homework, understanding step-by-step solutions, and verifying competitive exam answers (NTSE, Olympiads) where fraction arithmetic is common.
How do I use the Fraction Calculator?
Enter the first fraction's Numerator 1 and Denominator 1. Select the operation (Add, Subtract, Multiply, or Divide). Enter the second fraction's Numerator 2 and Denominator 2. The result appears instantly showing the simplified fraction (numerator + denominator), the decimal equivalent, and the mixed number form. The Steps panel shows the full working so you can learn or verify the method.
What is the difference between proper and improper fractions?
A proper fraction has a numerator smaller than its denominator (e.g., 3/4, 2/7) — its decimal value is between 0 and 1. An improper fraction has a numerator equal to or larger than the denominator (e.g., 7/4, 5/5) — its decimal value is ≥ 1. Improper fractions can be converted to mixed numbers: 7/4 = 1¾. In Indian school maths, students are typically asked to give answers as mixed numbers or simplified proper fractions.
What is the LCD (Least Common Denominator) method?
The LCD method for adding/subtracting fractions uses the smallest common denominator (LCM of the denominators) rather than the product of denominators. For example, adding 1/4 + 1/6: LCD = 12 (not 24 = 4×6). This gives 3/12 + 2/12 = 5/12 — a smaller intermediate number that needs less simplification. This calculator uses the product method (always uses d1×d2) and then simplifies — the final answer is always the same, though the working numbers are larger.
Can I use this for comparing fractions?
Yes — subtract the fractions: if the result is positive, the first fraction is larger; if negative, the second is larger; if zero, they are equal. For example, to compare 3/5 vs 2/3: calculate 3/5 − 2/3 = 9/15 − 10/15 = −1/15, which is negative, so 3/5 < 2/3. Alternatively, convert both to decimals using the calculator: 3/5 = 0.6, 2/3 ≈ 0.667 — the decimal form makes comparison immediate.