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Fraction Calculator

Add, subtract, multiply, or divide any two fractions. Results automatically simplified to lowest terms with decimal equivalent. Free fraction calculator.

Reviewed for accuracy by Marcus Webb and the Blueprint Dynamics editorial team (last updated July 2026). Our calculators use primary-source formulas and are cross-checked against IRS publications, Fannie Mae guidelines, and Federal Reserve data. Learn more about our methodology.

Fraction Calculator

1/2 + 1/3 =

5
6
= 0.83333333

Fraction operations — how the math works

A fraction represents a part of a whole: numerator / denominator. The numerator is how many parts you have; the denominator is how many equal parts the whole is divided into. Addition and subtraction require a common denominator — you cannot add thirds and quarters directly because the units differ. Find the least common denominator (LCD), convert both fractions to equivalent fractions with that denominator, then add or subtract the numerators. Multiplication is simpler: multiply numerators together and denominators together. Division: multiply the first fraction by the reciprocal (flip) of the second.

Finding the least common denominator

The LCD is the smallest number that both denominators divide into evenly. Method 1 — List multiples: for 3 and 4, list multiples of each (3: 3,6,9,12,15... 4: 4,8,12,16...) and find the first match = 12. Method 2 — Use LCM formula: LCD = (a × b) / GCD(a,b). GCD of 3 and 4 = 1 (no common factors), so LCD = (3 × 4) / 1 = 12. Converting: 1/3 = 4/12, 1/4 = 3/12. Now you can add: 4/12 + 3/12 = 7/12.

Simplifying fractions

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD). GCD of 18 and 24: factors of 18 are 1,2,3,6,9,18; factors of 24 are 1,2,3,4,6,8,12,24. Greatest common factor = 6. So 18/24 = (18÷6)/(24÷6) = 3/4. A quick check: if the numerator and denominator are both even, divide both by 2. Repeat until you can no longer simplify.

Mixed numbers and improper fractions

An improper fraction has a numerator larger than the denominator (e.g., 7/3). A mixed number expresses this as a whole number plus a proper fraction (2 1/3). Converting improper to mixed: divide numerator by denominator. 7 ÷ 3 = 2 remainder 1, so 7/3 = 2 1/3. Converting mixed to improper: multiply the whole number by the denominator, add the numerator. 2 1/3 = (2 × 3 + 1) / 3 = 7/3. When performing arithmetic operations with mixed numbers, it's usually easiest to convert to improper fractions first, calculate, then convert back.

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© 2026 Blueprint Dynamics. Front Desk is for informational purposes only — not financial advice. Calculations are estimates and may not reflect your actual loan terms. Always consult a qualified professional before making major financial decisions.