Convert between improper fractions and mixed numbers in both directions.
A mixed number combines a whole part with a proper fraction (e.g. 3 2/5). An improper fraction has a numerator larger than its denominator (e.g. 17/5). To convert improper→mixed, divide; to convert mixed→improper, multiply the whole by the denominator and add the numerator.
Improper to Mixed
whole = numerator ÷ denominator (integer part); remainder = numerator mod denominator
Mixed to Improper
Improper numerator = whole × denominator + numerator
When the absolute value of the numerator is greater than or equal to the denominator. For example, 7/4, 13/5, and 9/9 are all improper.
Yes — 3 2/5 and 17/5 are the same quantity, just written differently. Mixed form is more intuitive for everyday use; improper form is easier for arithmetic.