Fraction Calculator
Add, subtract, multiply, and divide fractions easily. Results are automatically simplified.
Fractions are the building blocks of precise measurement, yet operating with them can often be confusing. Our Fraction Calculator simplifies the process of adding, subtracting, multiplying, and dividing fractions. It automatically handles common denominators and reduces the final result to its simplest form, making it perfect for students, chefs resizing recipes, and DIY enthusiasts measuring materials.
Math Input
Reduced Fraction
--Frequently Asked Questions
Why Fractions Matter
Fractions represent parts of a whole, but adding or subtracting them can be a headache when denominators (the bottom numbers) don't match. This calculator handles the heavy lifting of finding standard common denominators and reducing results to their simplest form, saving you from tedious manual math.
1. A History of Parts: The Eye of Horus
Fractions have been around almost as long as civilization. Ancient Egyptians (c. 1800 BC) were obsessed with them but had a peculiar rule: they primarily used "Unit Fractions" (fractions with a 1 on top, like 1/2, 1/4, 1/7).
Legend says the "Eye of Horus" hieroglyph represented fractional parts. Each line of the eye corresponded to a specific fraction (1/2, 1/4, 1/8, etc.), which, when added together, nearly equaled 1—representing the wholeness of the god.
2. Precision vs. Approximation
In a digital world of decimals, fractions might seem old-fashioned, but they are often more precise. `1/3` is exact, while `0.333...` is always an approximation. This precision is critical in:
- Cooking & Baking: Recipes are the most common place we see fractions. Doubling a recipe that calls for "3/4 cup" of sugar requires adding fractions (3/4 + 3/4 = 6/4 = 1 1/2 cups). Precision here makes the difference between a delicious cake and a dry disaster.
- Construction & DIY: Tape measures in the US are marked in fractions (1/16, 1/8, 1/4 inch). "Measure twice, cut once" relies on your ability to add and subtract these fractions accurately.
- Music: Time signatures (4/4, 3/4) and note lengths (whole, half, quarter, eighth notes) are purely fractional. Understanding rhythm is essentially understanding how to add fractions to equal a whole measure.
3. Operations Guide
- Multiplying: Multiply straight across (top × top, bottom × bottom).
- Dividing: Flip the second fraction upside down (reciprocal) and then multiply.
- Adding/Subtracting: You MUST find a Common Denominator first. For example, to add 1/2 + 1/3, you convert both to /6 (3/6 + 2/6 = 5/6).
4. Frequently Asked Questions (FAQ)
Q: What is a "Mixed Number"?
A mixed number combines a whole number and a fraction (e.g., 1 1/2). It is often easier to visualize than an "improper fraction" (3/2), though improper fractions are easier to calculate with.
Q: Why simplify fractions?
Simplifying makes numbers easier to understand. "50/100" is correct, but "1/2" is instantly recognizable.