What Are Fractions and Why Do We Use Them?
A fraction represents a part of a whole or, more generally, any number of equal parts. When written in standard formatting, a fraction consists of a **numerator** (on top) and a non-zero **denominator** (on bottom). Fractions extend our standard counting system, allowing us to specify rational locations between whole numbers seamlessly.
Check Out Our Permutations & Combinations CalculatorUnderstanding the Types of Fractions
- Proper Fractions: The numerator is strictly less than the denominator (e.g., $3/4$). Its absolute value is less than 1.
- Improper Fractions: The numerator is greater than or equal to the denominator (e.g., $5/4$). Its value is greater than or equal to 1.
- Mixed Numbers: A combination of a whole number and a proper fraction (e.g., $1\ \frac{1}{4}$).
Fractions Arithmetic Made Simple
Our calculator evaluates standard algebraic steps to solve fractions with complete, un-rounded accuracy:
- Addition & Subtraction: Converts both fractions to a Least Common Denominator (LCD), performs operations on the numerators, and simplifies.
- Multiplication: Multiplies numerators together and denominators together directly: $(n_1 \times n_2) / (d_1 \times d_2)$.
- Division: Multiplies the first fraction by the reciprocal (inverse) of the second fraction: $(n_1 \times d_2) / (d_1 \times n_2)$.