Fraction Calculator
Add, subtract, multiply, and divide fractions. Simplify fractions and convert to decimals.
About Fraction Calculator
A fraction calculator performs arithmetic operations (add, subtract, multiply, divide) on fractions and mixed numbers. Working with fractions is one of the most challenging topics in elementary mathematics, and errors are common when finding common denominators, cross-multiplying, or simplifying results. This tool handles all fraction operations with proper mathematical precision, automatically simplifying results to their lowest terms.
How to Use
Enter your fractions as numerator/denominator (e.g., 3/4) or as mixed numbers (e.g., 1 3/4). Select the operation (add, subtract, multiply, or divide). The calculator shows the result as both an improper fraction and a mixed number, plus the decimal equivalent. It also shows the step-by-step process including how the common denominator was found and how the result was simplified.
Formula / Key Equations
Addition: a/b + c/d = (ad + bc) / bd. Subtraction: a/b - c/d = (ad - bc) / bd. Multiplication: a/b × c/d = ac / bd. Division: a/b ÷ c/d = a/b × d/c = ad / bc. Simplification: divide numerator and denominator by their Greatest Common Divisor (GCD).
Common Use Cases
Solving math homework problems involving fractions. Calculating recipe measurements that need to be doubled, halved, or adjusted. Working with measurements in carpentry and sewing that use fractional inches. Comparing fraction sizes by converting to decimals. Learning and practicing fraction arithmetic.
Limitations
The calculator works with positive and negative fractions, proper and improper fractions, and mixed numbers. Very large numerators or denominators may encounter display limitations. It does not handle complex fractions (fractions within fractions), algebraic fractions, or partial fractions. Results are mathematically exact until converted to decimal form.
Frequently Asked Questions
How do I enter a mixed number?
Enter mixed numbers using the format: whole number, space, numerator/denominator. For example, enter '2 3/4' for two and three-quarters. The calculator will convert it to an improper fraction (11/4) for computation and show both the fraction and mixed number results.
How does the calculator simplify fractions?
The calculator finds the Greatest Common Divisor (GCD) of the numerator and denominator, then divides both by the GCD. For example, 8/12: GCD(8,12) = 4, so the simplified fraction is (8/4)/(12/4) = 2/3.
Why do I need a common denominator to add fractions?
Adding fractions is like adding apples and oranges — you need the same unit. The common denominator makes both fractions use the same 'sized pieces' so they can be combined. For example, 1/4 + 2/3 becomes 3/12 + 8/12 = 11/12.
Can I divide by a fraction?
Yes. Dividing by a fraction is the same as multiplying by its reciprocal (flipped). So 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. The calculator handles this automatically.
Does the calculator show the steps?
Yes. The calculator displays the step-by-step process including finding the least common denominator, converting fractions, performing the operation, and simplifying the result. This is helpful for students learning fraction arithmetic.
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