Fraction Calculator
Add, subtract, multiply and divide fractions with step-by-step working. Results are automatically simplified to lowest terms. Decimal equivalent shown.
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How Fraction Addition Works
To add or subtract fractions you first need a common denominator — a number both denominators divide into evenly. The most efficient common denominator is the LCM (lowest common multiple) of the two denominators. Convert both fractions to this denominator, then add or subtract the numerators. Finally, simplify by dividing both parts by their GCD.
Multiplying and Dividing Fractions
Multiplication is the simplest operation: multiply the numerators together and the denominators together. Division is just multiplication with the second fraction flipped (the reciprocal): a/b ÷ c/d = a/b × d/c.
Frequently Asked Questions
Find the LCM (lowest common multiple) of both denominators. Convert each fraction to an equivalent fraction with the LCM as the denominator by multiplying numerator and denominator by the appropriate factor. Then add the numerators. Example: 1/4 + 1/6. LCM of 4 and 6 is 12. 1/4 = 3/12, 1/6 = 2/12. Sum = 5/12.
Find the GCD (greatest common divisor) of the numerator and denominator, then divide both by it. Example: 12/18. GCD(12,18) = 6. 12/6 = 2, 18/6 = 3. Simplified: 2/3. If the GCD is 1, the fraction is already in its simplest form (it is irreducible).
An improper fraction has a numerator larger than or equal to its denominator — for example 7/4. It can be converted to a mixed number: 7/4 = 1 and 3/4 (one whole plus three quarters). This calculator displays results as mixed numbers when the result is improper.
Multiply the first fraction by the reciprocal (flipped version) of the second. a/b ÷ c/d = a/b × d/c. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 and 7/8.
GCD (greatest common divisor, also called HCF) is the largest number that divides both values exactly. LCM (lowest common multiple) is the smallest number both values divide into exactly. They are related: GCD(a,b) × LCM(a,b) = a × b. GCD is used to simplify fractions; LCM is used to find a common denominator.