Fractions are one of the first abstract mathematical concepts we learn, representing parts of a whole. While fundamental, performing arithmetic with fractions—especially addition and subtraction—can be tricky because it requires finding a common denominator. Our Fraction Calculator is a powerful tool designed to handle all the basic arithmetic operations: addition, subtraction, multiplication, and division. It simplifies the entire process, from finding common denominators to reducing the final answer to its simplest form, making it an invaluable tool for students checking their homework and anyone needing a quick, accurate fraction calculation.
How to Use the Fraction Calculator
Performing fraction arithmetic is a simple, three-step process:
- Enter the First Fraction: Input the numerator and denominator for your first fraction.
- Select the Operation: Choose whether you want to add (+), subtract (-), multiply (×), or divide (÷).
- Enter the Second Fraction: Input the numerator and denominator for your second fraction.
- Calculate: Click the "Calculate" button to see the result, which will be displayed as a simplified fraction and its decimal equivalent.
The Rules of Fraction Arithmetic
Each arithmetic operation has its own specific set of rules when working with fractions.
Addition and Subtraction: The Common Denominator
This is the most complex operation. You cannot add or subtract fractions unless they have the same denominator. If they don't, you must first find a "common denominator." The least common denominator (LCD) is the smallest number that both original denominators can divide into evenly.
Once you have a common denominator, you convert each fraction into an equivalent fraction with that new denominator. Then, you simply add or subtract the numerators, keeping the denominator the same.
Example: 1/2 + 1/3
- The LCD of 2 and 3 is 6.
- Convert the fractions: 1/2 becomes 3/6, and 1/3 becomes 2/6.
- Add the numerators: 3 + 2 = 5.
- The result is 5/6.
Multiplication: The Simplest Operation
Multiplying fractions is the most straightforward operation. You simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
(a/b) × (c/d) = (a × c) / (b × d)
Example: (2/3) × (4/5) = (2 × 4) / (3 × 5) = 8/15.
Division: Invert and Multiply
To divide one fraction by another, you use a simple rule: "invert and multiply." This means you flip the second fraction upside down (finding its reciprocal) and then multiply it by the first fraction.
(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)
Example: (1/2) ÷ (3/4) becomes (1/2) × (4/3) = (1 × 4) / (2 × 3) = 4/6. This final fraction can then be simplified.
Simplifying Fractions
After performing any operation, the final step is to simplify, or "reduce," the resulting fraction to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator and the denominator, and then dividing both by that number. For our division example above, the fraction was 4/6. The GCD of 4 and 6 is 2. Dividing both by 2 gives us the simplified answer, 2/3. Our calculator performs this simplification for you automatically.
Frequently Asked Questions
What is an improper fraction?
An improper fraction is a fraction where the numerator is larger than or equal to the denominator (e.g., 7/4). It represents a value of 1 or greater. This calculator handles improper fractions correctly in all its operations.
What is a mixed number?
A mixed number is a way of writing an improper fraction by combining a whole number and a proper fraction (e.g., 1 ¾). To convert a mixed number to an improper fraction, you multiply the whole number by the denominator, add the numerator, and put the result over the original denominator (1 ¾ = (1×4+3)/4 = 7/4). Our calculator works with standard fractions, not mixed numbers.
What if the denominator is zero?
Division by zero is undefined in mathematics. A fraction cannot have a denominator of zero. The calculator will show an error if you attempt to enter a zero in the denominator field.