Fraction Calculator
Perform operations with fractions, simplify, convert between formats, work with mixed numbers, decimals, and big number fractions
Fraction Calculator
Perform basic arithmetic operations on fractions: addition, subtraction, multiplication, and division.
Fraction Operation Formulas
Addition:
a/b + c/d = (a×d + b×c) / (b×d)
Example: 1/2 + 1/4 = (1×4 + 2×1) / (2×4) = 6/8 = 3/4
Subtraction:
a/b - c/d = (a×d - b×c) / (b×d)
Example: 1/2 - 1/4 = (1×4 - 2×1) / (2×4) = 2/8 = 1/4
Multiplication:
a/b × c/d = (a×c) / (b×d)
Example: 1/2 × 1/4 = (1×1) / (2×4) = 1/8
Division:
a/b ÷ c/d = (a×d) / (b×c)
Example: 1/2 ÷ 1/4 = (1×4) / (2×1) = 4/2 = 2
Results
To convert an improper fraction to a mixed number:
1. Divide the numerator (17) by the denominator (5).
2. The quotient (3) is the whole number part.
3. The remainder (2) becomes the new numerator.
4. The original denominator (5) remains the same.
Common Fractions
Fractions are useful for precise calculations and representing parts of a whole. They're especially important in cooking, construction, and mathematical applications.
Key Features
Basic Operations
Perform addition, subtraction, multiplication, and division of fractions with step-by-step explanations.
Simplification
Reduce fractions to their simplest terms using greatest common divisor (GCD) to find equivalent fractions.
Format Conversion
Convert between improper fractions, mixed numbers, and decimals for flexible representation of fractional values.
Mixed Numbers
Convert between improper fractions and mixed numbers with precision and ease.
Decimal Conversions
Convert between fractions and decimals with customizable precision levels.
Understanding Fractions
Learn how fractions work and their mathematical properties
What are Fractions?
A fraction represents a part of a whole or a division of two integers. It consists of a numerator (top number) and a denominator (bottom number). The numerator represents how many parts we have, while the denominator represents the total number of equal parts that make up a whole.
Types of Fractions
Proper Fractions:
Numerator < Denominator (e.g., 3/4, 1/2)
Improper Fractions:
Numerator ≥ Denominator (e.g., 5/3, 7/4)
Mixed Numbers:
Whole number + proper fraction (e.g., 2 1/3, 1 3/4)
Working with Fractions
Equivalent Fractions
Fractions that represent the same value but have different numerators and denominators.
Create equivalent fractions by multiplying or dividing both numerator and denominator by the same number:
1/2 = 2/4 = 3/6 = 4/8 = ...
Finding equivalent fractions is essential for adding and subtracting fractions with different denominators.
Simplifying Fractions
Reducing fractions to their simplest form where numerator and denominator have no common factors except 1.
Steps to simplify a fraction:
- Find the GCD of the numerator and denominator
- Divide both numerator and denominator by the GCD
8/12 = (8÷4)/(12÷4) = 2/3
Adding and Subtracting
To add or subtract fractions, you need a common denominator.
Steps:
- Find the least common multiple (LCM) of the denominators
- Convert each fraction to an equivalent fraction with the LCM as denominator
- Add or subtract the numerators, keeping the denominator the same
- Simplify the result if possible
Multiplying and Dividing
Multiplication and division of fractions are straightforward operations.
To multiply:
a/b × c/d = (a×c)/(b×d)
To divide:
a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)
Remember: To divide by a fraction, multiply by its reciprocal.
Did You Know?
The word "fraction" comes from the Latin "fractus," meaning "broken." Ancient Egyptians used fractions with only unit numerators (like 1/2, 1/3, 1/4), and they had special symbols for common fractions. The modern notation for fractions with a horizontal line didn't become standardized until the 16th century, though the concept has been used in mathematics for thousands of years across many civilizations.
Frequently Asked Questions
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