A mixed number combines a whole number and a proper fraction, such as 2 3/4. Arithmetic with mixed numbers requires converting them to improper fractions, performing the operation, then simplifying back to lowest terms. Enter two values in any combination of mixed numbers, fractions, or integers, select an operator, and get the simplified result with its decimal equivalent.
How Mixed Number Arithmetic Works
- Convert each mixed number to an improper fraction: 2 3/4 becomes (2x4+3)/4 = 11/4.
- For addition and subtraction, find a common denominator, then add or subtract the numerators.
- For multiplication, multiply numerators together and denominators together: 3/4 x 2/3 = 6/12.
- For division, multiply the first fraction by the reciprocal of the second: 3/4 / 2/3 = 3/4 x 3/2 = 9/8.
- Simplify the result by dividing numerator and denominator by their GCD, then convert back to a mixed number if applicable.
Greatest Common Divisor and Simplification
Every fraction result is reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD is found via the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. For example, GCD(12, 8) proceeds as 12 mod 8 = 4, then 8 mod 4 = 0, giving GCD = 4, so 8/12 simplifies to 2/3.
Input Format Reference
- Mixed number: type the whole part, a space, then the fraction (e.g., 1 1/2).
- Proper fraction: numerator/denominator (e.g., 3/4).
- Improper fraction: numerator/denominator where numerator >= denominator (e.g., 7/4).
- Whole number: just the integer (e.g., 5, treated as 5/1).
FAQ
Q: How do I enter a mixed number?
A: Type the whole number, a space, and the fraction. For example, 2 3/4 means two and three-quarters. The calculator converts it to the improper fraction 11/4 internally.
Q: Why does the calculator simplify fractions automatically?
A: Simplified (lowest-terms) fractions are easier to read and compare. The calculator divides both numerator and denominator by their greatest common divisor so 6/8 becomes 3/4 and 14/4 becomes 3 1/2.
Q: What happens if I divide by zero?
A: Division by zero is undefined. If the second fraction evaluates to zero (e.g., 0/5 or just 0), the calculator displays an error instead of a result.