Mixed Number Calculator

Convert mixed numbers to improper fractions, improper fractions back to mixed numbers, and simplify any mixed value to its lowest terms. Every conversion shows the working so you can trace exactly how the result was obtained.

Choose a conversion

For a proper fraction, leave the Whole field at 0.

Choose a conversion mode, enter values, and press Convert.

Mixed numbers and improper fractions

A mixed number combines a whole number with a proper fraction: 2 ½ means "2 plus one-half". An improper fraction has a numerator larger than or equal to its denominator: 5/2 is the improper form of 2 ½.

Both forms describe the same quantity. Improper fractions are more convenient for arithmetic because the whole rule "multiply numerator and denominator separately" applies directly. Mixed numbers are more intuitive for everyday use ("two and a half cups of flour").

Mixed → improper

a b/c → (a × c + b) / c

Multiply the whole part by the denominator, add the numerator, and put the result over the original denominator.

Improper → mixed

Divide the numerator by the denominator. The quotient is the whole part; the remainder is the new numerator; the denominator stays the same.

17 / 4 → 4 remainder 1 → 4 ¼

Worked examples

Example 1 — Mixed to improper

Convert 3 ⅔ to an improper fraction.

(3 × 3 + 2) / 3 = (9 + 2) / 3 = 11/3.

3 ⅔ = 11/3

Example 2 — Improper to mixed

Convert 11/3 to a mixed number.

11 ÷ 3 = 3 remainder 2 → 3 ⅔.

11/3 = 3 ⅔

Example 3 — Negative mixed number

Convert −2 ¼ to an improper fraction.

The sign applies to the whole value. (−2 × 4 − 1) / 4 = −9/4.

−2 ¼ = −9/4

Example 4 — Fraction that is already proper

Convert 3/4 to improper form.

3/4 is already proper, so no change is required. The whole part is 0 and the numerator is 3.

3/4 = 3/4 (already proper)

Common mistakes

  • Forgetting to multiply the whole part by the denominator. 2 ¾ is not (2 + 3)/4 = 5/4. It is (2 × 4 + 3)/4 = 11/4.
  • Swapping numerator and denominator in the conversion. Mixed → improper keeps the denominator unchanged. The whole part is multiplied by the denominator, then the numerator is added.
  • Sign handling with negative mixed numbers. −2 ½ means the entire value is negative, not just the whole part. Convert to −5/2, not −3/2.
  • Assuming a whole part is always required. Proper fractions like 3/4 have a whole part of 0. Enter 0 (or leave the whole field empty) for these.

Fraction Calculator

Add, subtract, multiply and divide fractions.

Decimal to Fraction Converter

Convert any decimal into a simplified fraction.

Fraction to Decimal Converter

Convert a fraction into its decimal equivalent.

Greatest Common Factor Calculator

Simplify fractions using the GCD.

Frequently asked questions

A mixed number combines a whole number with a proper fraction, such as 3 ½. It represents the sum of the two: 3 + ½ = 3.5.

Multiply the whole part by the denominator, add the numerator, and put the result over the original denominator. For 2 ¾: (2 × 4 + 3) / 4 = 11/4.

Divide the numerator by the denominator. The integer quotient becomes the whole part, the remainder becomes the new numerator, and the denominator stays the same. For 17/4: 17 ÷ 4 = 4 remainder 1, so 4 ¼.

Yes. Put the minus sign in the Whole field to indicate a negative mixed number. For example, −2 ¼ converts to −9/4.

Improper fractions are easier to use in arithmetic because the standard fraction rules (multiply numerators, multiply denominators) apply directly. Mixed numbers are easier to read and understand at a glance. Both forms are correct — use whichever is more convenient for your task.