Mixed Number Calculator
Convert between mixed numbers and improper fractions. Shows both the fraction and decimal representation along with step-by-step work.
Mixed Number → Improper Fraction
Improper Fraction → Mixed Number
About this Calculator
Convert between mixed numbers and improper fractions. Shows both the fraction and decimal representation along with step-by-step work.
Formula & Calculations
Formula
Mixed → Improper: (whole × denominator + numerator) / denominator. Improper → Mixed: quotient = floor(num/den), remainder = num mod den.Where:
- Whole=The integer part of a mixed number
- Numerator=The top number of the fractional part
- Denominator=The bottom number of the fractional part (must be positive)
Assumptions
- The denominator must be positive and non-zero.
- The fractional part of a mixed number should have a numerator smaller than the denominator (proper fraction).
- Negative mixed numbers are handled by keeping the sign on the whole number part.
Calculation Examples
Example 1
Inputs:Mixed: 3 1/4 → Improper
Result:13/4 = 3.25
3 × 4 + 1 = 13 over 4. Decimal: 13 ÷ 4 = 3.25.
Example 2
Inputs:Improper: 25/4 → Mixed
Result:6 1/4
25 ÷ 4 = 6 remainder 1. Mixed number: 6 1/4.
Frequently Asked Questions
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 3 1/2. It represents the sum of the whole number and the fraction: 3 + 1/2 = 3.5.
When would I use a mixed number vs. an improper fraction?
Mixed numbers are easier to read and compare (e.g., knowing 3 1/2 is between 3 and 4). Improper fractions are easier to use in calculations (addition, multiplication). Cooking, construction, and everyday measurements often use mixed numbers.