Fraction Calculator
Add, subtract, multiply and divide fractions with results simplified to lowest terms, shown as mixed numbers and decimals. Includes a fraction simplifier.
About the Fraction Calculator
This fraction calculator adds, subtracts, multiplies and divides any two fractions and always reduces the answer to lowest terms. Every result is shown three ways: as a simplified fraction, as a mixed number, and as a decimal — covering whatever format your homework or recipe needs.
The calculator applies the textbook rules: cross-multiplication over a common denominator for addition and subtraction (a/b + c/d = (ad + cb)/bd), straight multiplication of numerators and denominators, and multiplying by the reciprocal for division. It then divides by the greatest common divisor to simplify.
A second section simplifies any single fraction — type 24/36 and get 2/3 instantly, with its decimal and mixed-number forms. Students, parents helping with math homework, carpenters working in fractional inches and cooks scaling recipes all get exact answers without decimal rounding errors.
How to Use the Fraction Calculator
- 1Enter the numerator and denominator of both fractions.
- 2Choose the operation: add, subtract, multiply or divide.
- 3Read the simplified result, mixed-number form and decimal value.
- 4To reduce a single fraction, use the simplify section below.
Frequently Asked Questions
How do you add fractions with different denominators?
Convert both fractions to a common denominator, then add the numerators. The general rule is a/b + c/d = (a×d + c×b) ÷ (b×d). For 1/2 + 3/4: (1×4 + 3×2) ÷ 8 = 10/8, which simplifies to 5/4 or the mixed number 1 1/4. This calculator performs the conversion and simplification automatically.
How do you divide fractions?
Multiply by the reciprocal — flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c = ad/bc. So 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3. The phrase "keep, change, flip" is the classroom mnemonic: keep the first fraction, change ÷ to ×, flip the second. Division by a fraction with numerator 0 is undefined.
How does the calculator simplify fractions to lowest terms?
It finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both by it. For 24/36 the GCD is 12, giving 2/3. A fraction is in lowest terms when the GCD is 1. Negative signs are normalised to the numerator, so 3/−4 is displayed as −3/4.
What is a mixed number and when is it shown?
A mixed number combines a whole part and a proper fraction, like 1 3/4 instead of the improper fraction 7/4. The calculator shows the mixed form whenever the absolute value of the result exceeds 1 and it is not a whole number. Improper fractions are preferred mid-calculation; mixed numbers are clearer for final answers and measurements.
Can I enter negative numbers or decimals?
Negative whole numbers work fine in any numerator or denominator — the sign is handled and normalised in the result. Decimals are not accepted, because fraction arithmetic is exact while decimals introduce rounding. To use 2.5, express it as the fraction 5/2 instead, and the calculator will keep every step exact.