Fraction Calculator
Add, subtract, multiply, and divide fractions with our easy-to-use fraction calculator.
Understanding Fractions
A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents how many parts we have, while the denominator represents the total number of equal parts that make up the whole.
Types of Fractions
- Proper Fractions: The numerator is less than the denominator (e.g., 3/4).
- Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 5/3).
- Mixed Numbers: A whole number and a proper fraction combined (e.g., 1 1/2).
Fraction Operations
Our calculator supports the four basic operations with fractions:
1. Addition
To add fractions with the same denominator, add the numerators and keep the denominator the same. For fractions with different denominators, find a common denominator first.
Formula: a/b + c/d = (ad + bc)/bd
2. Subtraction
To subtract fractions with the same denominator, subtract the numerators and keep the denominator the same. For fractions with different denominators, find a common denominator first.
Formula: a/b - c/d = (ad - bc)/bd
3. Multiplication
To multiply fractions, multiply the numerators together and multiply the denominators together.
Formula: a/b × c/d = (a×c)/(b×d)
4. Division
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Formula: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)
Simplifying Fractions
A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
For example, to simplify 8/12:
1. Find the GCD of 8 and 12, which is 4.
2. Divide both numbers by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
3. The simplified fraction is 2/3.
Common Applications of Fractions
Cooking and Recipes
Recipes often use fractions for measurements, such as 3/4 cup of flour or 1/2 teaspoon of salt. Sometimes you might need to halve or double a recipe, which requires fraction operations.
Construction and Carpentry
Measurements in construction often involve fractions of inches or feet. Carpenters need to add, subtract, and convert between fractions regularly.
Finance
Fractions are used in finance for interest rates, discounts, and proportional calculations.
Time Management
We often express time in fractions, such as quarter-hour (1/4 hour = 15 minutes) or half-hour (1/2 hour = 30 minutes).