Improper Fraction Calculator
Improper to mixed, and mixed back to improper.
Blank: converts improper → mixed. Filled: converts mixed → improper.
The three kinds of fraction
- Proper — numerator smaller than denominator, so the value is less than 1. Example 2/3.
- Improper — numerator greater than or equal to the denominator, so the value is 1 or more. Example 7/3.
- Mixed — a whole number beside a proper fraction. Example 2 1/3.
“Improper” is a historical label, not a criticism. Improper fractions are usually the easier form to compute with, which is why algebra tends to convert mixed numbers into them rather than the reverse.
Improper to mixed
Divide and keep the remainder. 7 ÷ 3 is 2 remainder 1, so 7/3 is 2 1/3. The quotient becomes the whole number, the remainder stays over the same denominator.
Mixed to improper
Multiply the whole number by the denominator and add the numerator. For 2 1/3: (2 × 3) + 1 = 7, over 3, giving 7/3. The denominator never changes.
Negative mixed numbers
The sign applies to the whole quantity, not just the integer part. −2 1/3 means −(2 + 1/3) = −7/3, not −2 + 1/3. This is a reliable source of sign errors in algebra.