Add, subtract, multiply, and divide fractions with automatic simplification and step-by-step working. Also simplifies mixed numbers and converts to decimals — free fraction calculator.
With automatic simplification and step-by-step working
This fraction calculator handles all four operations — addition, subtraction, multiplication, and division — with automatic simplification to the lowest terms and step-by-step working shown below the result. Fractions are one of the most commonly tested math concepts in US middle and high school curricula, and errors in fraction arithmetic cascade into wrong answers on algebra, chemistry, and cooking conversion problems. Whether you're simplifying 18/24 (which reduces to 3/4) or adding 3/4 + 2/3 (which requires finding the common denominator of 12), this calculator shows every step clearly.
Mixed numbers — like 2 3/4 or 5 1/8 — are also handled. The calculator converts them to improper fractions for computation, then converts the result back to a mixed number for the final answer. This is the same approach taught in US Common Core math standards and used on the SAT and ACT. The result also displays as a decimal (3/4 = 0.75) and percentage (75%), making it useful for anyone converting between fractions and other number formats in real-world contexts like recipe scaling, measurements, or financial ratios.
To add fractions, find the least common denominator (LCD), convert both fractions, then add numerators. Example: 1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12. This calculator finds the LCD and shows every step automatically.
Multiply fractions by multiplying numerators together and denominators together, then simplify. Example: 3/4 × 2/3 = 6/12 = 1/2. Cross-canceling before multiplying keeps the numbers smaller and the steps cleaner.
To divide fractions, flip the second fraction (the reciprocal) and multiply. "Keep, Change, Flip." Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. Division always becomes multiplication in the final step.
A fraction is simplified when the GCF of numerator and denominator equals 1. To simplify 18/24: GCF is 6, so divide both by 6 → 3/4. The calculator does this automatically using the Euclidean algorithm.
Fractions cannot be added until they describe parts of the same whole, which is what a common denominator provides. Multiplication and division need no such preparation — you multiply across, or invert and multiply — which is why those operations feel easier despite being conceptually harder. The efficient common denominator is the least common multiple rather than the product of the two denominators; using the product always works but produces larger numbers that then need reducing. Simplifying at the end means dividing both parts by their greatest common divisor.
a/b + c/d = (a·d + c·b) / (b·d), then simplifyUsing the LCM: convert both to /LCM(b,d) and add numeratorsa/b × c/d = ac/bda/b ÷ c/d = a/b × d/c = ad/bcwhere:
Assumptions: Exact rational arithmetic — no rounding at any stage, which is the advantage of keeping values as fractions rather than converting to decimals early.
Add two fractions using the least common multiple rather than the product of denominators.
Result3/8 + 5/12 = 19/24
Using the product 8 × 12 = 96 instead would have given 36/96 + 40/96 = 76/96, requiring a reduction by 4 to reach the same 19/24. Both are correct; the LCM route avoids the extra step. As a decimal 19/24 is 0.7916̅, a repeating value the fraction represents exactly.