Fraction Calculator
Add, subtract, multiply and divide fractions.
Comprehensive Guide to Fractions
While decimals are common in modern finance and science, fractions remain an essential part of everyday math, particularly in cooking, construction, woodworking, and algebra. Our Fraction Calculator helps you add, subtract, multiply, and divide fractions effortlessly, returning the answer in its simplest form.
Understanding the Anatomy of a Fraction
A fraction represents a part of a whole. It consists of two numbers separated by a horizontal or diagonal line:
- Numerator (Top Number): Indicates how many parts you have.
- Denominator (Bottom Number): Indicates how many parts make up the complete whole.
For example, in the fraction 3/4, you have 3 parts out of a total 4 parts needed to make a whole.
Rules for Calculating with Fractions
- Adding & Subtracting: To add or subtract fractions, they must have the same denominator (a common denominator). Once the denominators match, you simply add or subtract the numerators while keeping the denominator the same.
- Multiplying: This is much simpler. You do not need a common denominator. Simply multiply the top numbers together to get the new numerator, and multiply the bottom numbers together to get the new denominator.
- Dividing: The rule for division is "keep, change, flip." Keep the first fraction the same, change the division sign to a multiplication sign, and flip the second fraction upside down (creating its reciprocal). Then, multiply normally.
Simplifying (Reducing) Fractions
Our calculator automatically reduces the final answer to its simplest form. A fraction is in its simplest form when the top and bottom numbers can no longer be divided evenly by the same whole number (other than 1).
Example: If your calculation results in 10/20, both numbers can be divided by 10. The simplified fraction is 1/2.
Proper, Improper, and Mixed Fractions
- Proper Fraction: The numerator is smaller than the denominator (e.g., 3/4).
- Improper Fraction: The numerator is larger than or equal to the denominator (e.g., 5/4). This means the value is 1 or greater.
- Mixed Number: A whole number combined with a proper fraction (e.g., 1 ¼). Our calculator can easily convert between improper fractions and mixed numbers.