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Fraction Calculator

Math

Add, subtract, multiply, and divide fractions instantly. Get results as simplified fractions, mixed numbers, and decimals. Perfect for students and teachers.

Reviewed by the thecalcu.com team · Last updated June 30, 2026

1/2 + 1/3 = 0/1

Enter values above and choose an operation

Result

0
1

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.

Why Use a Fraction Calculator?

Fraction arithmetic is error-prone: the common denominator for addition and subtraction, the reciprocal for division, and simplification steps all provide opportunities for mistakes. For students checking homework or learning from errors, step-by-step working is more valuable than just the answer.

For teachers, tutors, and parents across India helping children with maths homework, especially for Classes 5–8 where fraction operations are most intensively tested, having an instant verifier with visible steps saves time and enables targeted correction.

Who Should Use This Calculator?

School students (Classes 4–10) working through NCERT fraction chapters, checking homework, or preparing for board examinations and competitive tests.

JEE and NTSE aspirants where fraction manipulation appears within algebra, number theory, and quantitative aptitude sections.

Teachers and tutors who want to quickly demonstrate fraction operations with full working visible on screen.

Adults in professional contexts who need fraction calculations for measurements, recipes, engineering ratios, or financial calculations involving partial quantities.

How to use this Fraction calculator

  1. Enter Numerator 1 and Denominator 1 for the first fraction.
  2. Select the Operation: Add, Subtract, Multiply, or Divide.
  3. Enter Numerator 2 and Denominator 2 for the second fraction.
  4. Results appear instantly: the simplified Result Numerator and Denominator, the Decimal Result (highlighted), and the Mixed Number parts.
  5. Open the Steps panel to see full working, including the common denominator step, intermediate calculations, and the simplification step.
  6. 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 = 1¼

Frequently Asked Questions

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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
Also known as
fraction additionfraction divisionfraction multiplicationfractions calculatoradd fractions