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How It Works
To add two fractions, you first find a common denominator using the Least Common Multiple (LCM). Convert each fraction so both share that denominator, add the numerators, then simplify the result by dividing by the Greatest Common Divisor (GCD).
Example Problem
Add 1/4 + 1/3:
- LCM of 4 and 3 = 12.
- Convert: 1/4 = 3/12, 1/3 = 4/12.
- Add numerators: 3 + 4 = 7.
- Result: 7/12
Frequently Asked Questions
How to add fractions with different denominators?
Find the LCM of the two denominators, rewrite each fraction with that common denominator, then add the numerators. For 2/5 + 1/3, the LCM is 15, giving 6/15 + 5/15 = 11/15.
Do you always need to simplify after adding fractions?
It is standard practice to reduce the result to lowest terms. Divide both the numerator and denominator by their GCD. If the GCD is 1, the fraction is already simplified.
What is a mixed number result?
When the numerator is larger than the denominator, the fraction can be written as a mixed number. For example, 7/4 = 1 3/4. This calculator automatically shows the mixed form when applicable.
Related Calculators
- Fraction Subtraction Calculator — subtract fractions with step-by-step work.
- Fraction Multiplication Calculator — multiply fractions and simplify.
- Simplify Fraction Calculator — reduce a fraction to lowest terms.
- Fraction Division Calculator — divide fractions using the reciprocal method.
- LCM Calculator — find the least common multiple for unlike denominators.