Fraction Calculator
Six fraction tools on one page: a fraction calculator, a mixed numbers calculator, a simplify fractions calculator, decimal-to-fraction and fraction-to-decimal converters, and a big number fraction calculator for very large integers. Every answer is simplified automatically and shown with its calculation steps. In each fraction field, the box above the black line is the numerator and the box below it is the denominator.
Fraction Calculator
Mixed Numbers Calculator
Enter each value as a mixed number (like -2 3/4), a fraction (like 3/4), or a whole number.
Simplify Fractions Calculator
Decimal to Fraction Calculator
Fraction to Decimal Calculator
Big Number Fraction Calculator
Use this calculator if the numerators or denominators are very big integers. Results are exact — no rounding.
What is a fraction?
A fraction is a number that represents part of a whole. It is written with two numbers separated by a line: the numerator (top) counts how many equal parts you have, and the denominator (bottom) says how many equal parts the whole was divided into. In the fraction 38, the numerator is 3 and the denominator is 8. Picture a pie cut into 8 equal slices: eating 3 slices means you ate 38 of the pie, and 58 remains — the shaded pie alongside shows exactly that. A denominator can never be 0, because dividing a whole into zero parts is meaningless and the fraction would be undefined.
Addition
Unlike whole numbers, fractions can only be added directly when they share a denominator. One reliable method is to multiply each fraction's numerator and denominator by the other fraction's denominator, which guarantees a common denominator:
ab + cd = a×db×d + c×bd×b = ad + bcbd
A tidier method uses the least common multiple (LCM) of the denominators as the common denominator — it keeps the numbers smaller and the answer closer to simplified form. For 34 + 16, the LCM of 4 and 6 is 12: multiply the first fraction by 3 and the second by 2 to get 912 + 212 = 1112. The calculator above uses the LCM method in its steps.
Subtraction
Subtraction works exactly like addition — reach a common denominator first, then subtract the numerators:
ab − cd = ad − bcbd · EX: 34 − 16 = 712
Multiplication
Multiplying is the simplest operation: no common denominator is needed. Multiply the numerators together and the denominators together, then simplify if possible:
ab × cd = acbd · EX: 34 × 16 = 324 = 18
Division
To divide by a fraction, multiply by its reciprocal — the fraction flipped upside down. The reciprocal of 34 is 43, so division turns into the multiplication you already know:
ab ÷ cd = ab × dc = adbc · EX: 34 ÷ 16 = 184 = 92 = 4 12
Simplification
A fraction is simplified when its numerator and denominator share no common factor larger than 1. To simplify, divide both by their greatest common factor (GCF): 220440 is far easier to work with as 12. Results on this page are always returned in lowest terms, in both improper-fraction form (like 92) and mixed-number form (4 12).
Converting between fractions and decimals
Each place to the right of a decimal point is a power of ten: tenths are 101, hundredths 102, thousandths 103, and so on. So a decimal becomes a fraction by writing its digits over that power of ten and simplifying — 0.1234 extends to the fourth decimal place, giving 123410000, which simplifies to 6175000. Going the other way, a fraction becomes a decimal by dividing the numerator by the denominator: 27 = 0.28571428571429… The two converter tools above handle both directions.
Frequently Asked Questions
How do you add fractions with different denominators?
Find a common denominator — the least common multiple (LCM) of the two denominators is the most efficient choice. Multiply each numerator and denominator by whatever makes the denominators equal, then add the numerators and keep the common denominator. Simplify the result by dividing the numerator and denominator by their greatest common factor. The calculator above shows every one of these steps.
How do you multiply and divide fractions?
To multiply fractions, multiply the numerators together and the denominators together, then simplify. To divide fractions, multiply the first fraction by the reciprocal of the second — flip the second fraction's numerator and denominator — and then multiply as usual.
How do you convert a decimal to a fraction?
Write the decimal over the power of ten matching its last decimal place (for example, 1.375 = 1375/1000), then divide the numerator and denominator by their greatest common factor to simplify (1375/1000 = 11/8 = 1 3/8).
Can this calculator handle very big fractions?
Yes. The Big Number Fraction Calculator at the bottom of the page uses exact integer arithmetic, so numerators and denominators with dozens of digits are computed exactly, with no rounding.