Mixed Fraction Calculator
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator: 2⅔ = (2×3+2)/3 = 8/3. Reverse the process (divide) to go back.
Convert both ways, mixed number to improper fraction, or improper fraction to mixed number, with steps.
How to use this calculator
Choose the direction, fill in the parts, and press Calculate. Mixed → improper: enter the whole part, numerator, and denominator (e.g. whole = 1, numerator = 1, denominator = 2 for 1½). Improper → mixed: enter just the numerator and denominator (e.g. 7 and 3 for 7/3), the whole-part field is ignored.
Both directions simplify the result to lowest terms automatically.
Whether checking homework, scaling a recipe, or converting project measurements, the steps panel shows each transformation transparently.
How it works
Mixed → improper: multiply the whole part by the denominator and add the numerator: a b/c = (a·c + b)/c. So 1½ = (1·2 + 1)/2 = 3/2. The logic: each whole contains c copies of 1/c.
Improper → mixed: divide the numerator by the denominator. The quotient is the whole part; the remainder stays over the denominator: 7/3 = 2 remainder 1 = 2⅓. Then simplify the fractional remainder if possible (the calculator divides by the GCD).
Pro tips
For adding mixed numbers: convert to improper first, add, convert back, it beats juggling whole and fraction parts separately. For multiplying: always use improper form; (2½)(3⅓) = (5/2)(10/3) = 50/6 = 25/3 = 8⅓. Estimating: round the fraction part to the nearest half for quick mental checks.
Worked example
Example: 2⅔ → improper, then back
Forward: (2 × 3 + 2)/3 = 8/3.
Backward: 8 ÷ 3 = 2 remainder 2 → 2⅔. GCD(2,3) = 1, already simplest.
Check: 8/3 = 2.666… and 2⅔ = 2.666…. ✓
More examples: 3½ → 7/2; 11/5 → 2⅕; −2⅓ → −7/3.
Common mistakes
- Adding instead of multiplying: 2⅔ is not (2+2)/3, it is (2×3+2)/3. The whole part contributes c copies of 1/c each.
- Forgetting to simplify the remainder: 10/4 → 2 remainder 2 → 2²/₄ must be reduced to 2½.
- Sign errors with negatives: −1½ = −3/2, not −1/2. The negative applies to the whole value.
- Numerator ≥ denominator in a “mixed” input: 1 5/2 is not a proper mixed number, simplify to 3½ first.
When to use it
Recipes (2½ cups), woodworking (3⅜ inches), and any homework that says “write as an improper fraction” or “write as a mixed number.” Improper fractions are easier to multiply and divide; mixed numbers are easier to picture. For the decimal equivalents, see the fraction to decimal calculator.
Full walkthrough: scaling a recipe
Double 2 1/3 cups: convert to (2×3+2)/3 = 8/3; double: 16/3; back: 16 div 3 = 5 remainder 1 = 5 1/3 cups. Improper form avoids the classic error of doubling to “4 2/3”.
Key takeaway: improper fractions for computing, mixed numbers for understanding. Convert, compute, convert back. With negative mixed numbers, keep the sign on the whole value: -2 1/3 = -7/3, never -5/3. When the whole part is zero, you have a plain proper fraction, no conversion needed. Double-check by converting back: the round trip must return your starting value every single time without exception.
Frequently asked questions
Multiply the whole number by the denominator, add the numerator, and put the result over the same denominator: 2⅔ = (2×3+2)/3 = 8/3.
Divide the numerator by the denominator. The quotient is the whole part and the remainder goes over the denominator: 8/3 = 2 remainder 2 = 2⅔.
3/2. (1 × 2 + 1)/2 = 3/2. It is already in lowest terms since GCD(3, 2) = 1.
Yes, always reduce to lowest terms. This calculator divides by the GCD automatically in both directions.
11/4. (2 × 4 + 3)/4 = 11/4. GCD(11, 4) = 1, so it is already in lowest terms.
2 1/4. 9 ÷ 4 = 2 remainder 1, so 2 1/4. The remainder fraction 1/4 is already simplified.
Convert both to improper fractions first, add them, then convert back. For 1 1/2 + 2 1/3: 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6. The calculator handles each conversion step.