What Is a Fraction Calculator?
A fraction calculator performs arithmetic operations on fractions and mixed numbers, including addition, subtraction, multiplication, and division. It automatically simplifies results to their lowest terms, saving time on manual reduction and ensuring accurate answers for math homework, cooking recipes, and engineering calculations.
How to Use This Fraction Calculator
- Enter the numerator and denominator of the first fraction (Fraction A).
- Enter the numerator and denominator of the second fraction (Fraction B).
- Click Calculate to see all four operations (addition, subtraction, multiplication, and division) at once, each shown in simplified form with its decimal equivalent.
Key Concepts
Adding or subtracting fractions requires a common denominator: a⁄b ± c⁄d = (ad ± bc)⁄bd. Multiplication is straightforward: a⁄b × c⁄d = ac⁄bd. Division inverts the second fraction: a⁄b ÷ c⁄d = ad⁄bc. Results are simplified by dividing both numerator and denominator by their greatest common divisor (GCD). A proper fraction has a numerator smaller than the denominator; an improper fraction can be converted to a mixed number.
a/b + c/d = (a × d + b × c) ÷ (b × d)
Frequently Asked Questions
How do I add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction, then add the numerators. For example, 1⁄3 + 1⁄4 = 4⁄12 + 3⁄12 = 7⁄12.
Why is dividing by a fraction the same as multiplying by its reciprocal?
Division asks “how many times does the divisor fit into the dividend?” Inverting the divisor and multiplying answers this question because multiplication and division are inverse operations.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2¾. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator: 2¾ = 11⁄4.