Fraction Calculator
Add, subtract, multiply, and divide proper, improper, and mixed fractions with step-by-step reduction.
Parameters & Inputs
Summary & Breakdown
Step-by-Step Solution
(3*3)/12 + (2*4)/12 = 9/12 + 8/12 = 17/12.
About the Fraction Calculator
Fractions represent rational numbers as exact ratios of two integers, avoiding the rounding errors inherent in decimal notation.
This calculator executes addition, subtraction, multiplication, and division across proper, improper, and mixed fractions.
It provides step-by-step simplification, lowest common denominator (LCD) derivation, greatest common divisor (GCD) factoring, and decimal approximations.
How the Calculations Work
Converts mixed numbers to improper fractions, finds LCD for addition/subtraction, multiplies reciprocals for division, and simplifies via the Euclidean greatest common divisor algorithm.
a/b + c/d = (ad + bc) / bd | (a/b) ÷ (c/d) = (a*d) / (b*c)
Variables & Definitions
- Numerator: The top integer indicating how many fractional parts are taken
- Denominator: The bottom integer indicating total equal parts in the whole
- GCD: Greatest Common Divisor used to simplify the resulting fraction to lowest terms
Adding 3/4 + 2/3: Common denominator is 12. 3/4 = 9/12, and 2/3 = 8/12. 9/12 + 8/12 = 17/12, which converts to the mixed number 1 5/12 or decimal 1.4167.
Key Terms Explained
Proper Fraction
A fraction where the numerator is strictly smaller than the denominator (e.g., 3/4).
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator (e.g., 17/12).
Mixed Number
A whole integer combined with a proper fraction (e.g., 1 5/12).
Reciprocal
The fraction inverted upside down; multiplying a number by its reciprocal yields 1.
Practical Tips & Pitfalls to Avoid
Never divide by zero
A fraction denominator can never equal zero, as division by zero is mathematically undefined.
Convert mixed numbers first
Multiplying or dividing mixed numbers is simplest when converted to improper fractions first.
Reduce early to keep numbers small
Cross-canceling common factors before multiplying fractions saves tedious reduction later.
Check if improper or mixed is preferred
Higher mathematics and algebra prefer improper fractions; carpentry and cooking prefer mixed numbers.
Frequently Asked Questions
Find the Least Common Multiple (LCM) of the denominators, rewrite each fraction with that common denominator, and then add only the numerators.
Dividing by a fraction is equivalent to multiplying by its inverse reciprocal, because dividing by 1/2 is the same as asking how many halves fit into a number (multiplying by 2).
The largest integer that divides evenly into both numerator and denominator without remainder, used to simplify fractions.
Yes, but a negative divided by a negative is positive (-3 / -4 = 3/4). If only one is negative, the whole fraction is negative.
Divide the numerator by the denominator using simple division (e.g., 3 ÷ 4 = 0.75).