The Fraction Calculator helps you perform addition, subtraction, multiplication, and division of fractions easily.
Results are displayed in three forms: simplified fraction (reduced using GCF), mixed number, and decimal. Includes step-by-step solutions to help understand the calculation process.
Calculator information
📋 How to use this calculator
- Enter the first fraction by filling in the numerator (top) and denominator (bottom). Example: 2/3.
- Choose the operation: add (+), subtract (-), multiply (x), or divide (/).
- Enter the second fraction the same way. For mixed numbers, fill in the whole part and the fractional part.
- Click Compute to see the result in three formats: simplified proper fraction, mixed number, and decimal.
- Review the step-by-step solution shown to understand how denominators are unified or how the fraction is simplified.
- Make sure denominators are not zero (to avoid division errors) and that the divisor in a division operation is not zero.
🧮 Basic Fraction Operations
Add/Subtract: a/b +/- c/d = (a*d +/- c*b) / (b*d); Multiply: a/b x c/d = (a*c) / (b*d); Divide: a/b / c/d = (a*d) / (b*c); Simplify: numerator/GCD, denominator/GCD
- a, c = numerators
- b, d = denominators, b != 0 and d != 0
- GCD = Greatest Common Divisor
A mixed number p (q/r) is converted to an improper fraction (p*r + q)/r before performing operations.
💡 Worked example: Adding 2/3 + 3/4
Given:- Fraction 1 = 2/3
- Fraction 2 = 3/4
- Operation = addition
Steps:- Find a common denominator: LCM of 3 and 4 is 12
- Convert 2/3 = 8/12 (multiply by 4/4)
- Convert 3/4 = 9/12 (multiply by 3/3)
- Add numerators: 8/12 + 9/12 = 17/12
- Simplify: GCD(17,12) = 1, result stays 17/12
- Convert to a mixed number: 17 / 12 = 1 remainder 5, giving 1 5/12
- Decimal: 17 / 12 = 1.4167
Result: Result = 17/12 (improper fraction) = 1 5/12 (mixed) = 1.4167 (decimal). The result is greater than 1 because both fractions are close to 1.
❓ Frequently asked questions
What is the difference between proper, mixed, and decimal fractions?
Improper or proper fraction: numerator/denominator, e.g., 7/4. Mixed number: a whole number plus a fraction, e.g., 1 3/4 (equal to 7/4). Decimal fraction: expressed in base 10, e.g., 1.75. All three can be converted between one another. Mixed numbers are more intuitive for values greater than 1, while improper fractions are easier to use in calculations.
How do I simplify a fraction?
Find the Greatest Common Divisor (GCD) between the numerator and denominator, then divide both by it. Example 18/24: GCD(18,24) = 6, result is 18/6 over 24/6 = 3/4. The Euclidean algorithm can find the GCD: repeatedly divide and take the remainder until the remainder is zero. A fraction is in lowest terms when the GCD of numerator and denominator is 1.
How do I add fractions with different denominators?
Find the Least Common Multiple (LCM) of the two denominators. Convert both fractions to equivalent fractions with that LCM as the denominator. Add the numerators and keep the denominator. Simplify the result if needed. Example 1/4 + 1/6: LCM = 12, so 3/12 + 2/12 = 5/12.
Is dividing fractions the same as multiplying?
Yes. Dividing by a fraction is the same as multiplying by its reciprocal. a/b / c/d = a/b x d/c. Example 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6. This concept is often taught as 'keep, change, flip' in elementary school. Important: neither the second fraction's denominator nor its numerator can be zero.
What are equivalent fractions?
Equivalent fractions are different fractions that represent the same value, e.g., 1/2 = 2/4 = 3/6 = 50/100. They are created by multiplying or dividing both numerator and denominator by the same nonzero number. The concept is essential when finding common denominators for addition or subtraction. The simplest form is the standard representation where GCD(numerator, denominator) = 1.
📚 Sources & references
Last updated: May 11, 2026