# How do I write an improper fraction?

Converts an improper fraction to a mixed number, or a mixed number to an improper fraction, with the division or multiplication shown step by step and the result in lowest terms.

- Page: https://www.acalculator.org/math/improper-fraction-calculator
- JSON spec: https://www.acalculator.org/math/improper-fraction-calculator.json
- Version: cb2be5011f06

## Default answer

Example with the default inputs (Convert Improper fraction to mixed number, Numerator 11, Denominator 6): 11/6 = 1 5/6

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| mode | Convert | Which way to convert: an improper fraction to a mixed number, or a mixed number to a fraction. |
| w | Whole number | The whole-number part of the mixed number. A minus sign makes the whole mixed number negative. |
| n | Numerator | The top number of the fraction. |
| d | Denominator | The bottom number of the fraction: how many equal parts make one whole. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| typed | You typed | The fraction or mixed number you typed. |
| result | Answer | The mixed number (for an improper fraction) or the improper fraction (for a mixed number), with the fraction as typed. |
| simplest | In lowest terms | The same answer with the fraction part reduced by the greatest common factor. |
| mixed | Mixed number | The number as a whole number and a proper fraction, in lowest terms. |
| improper | Improper fraction | The number as one fraction, in lowest terms. |
| decimal | Decimal | The value of the number as a decimal. |
| steps | Steps | The division (or multiplication and addition) that gives the answer. |

## Method

Improper to mixed: a ÷ b = q remainder r, so a/b = q r/b. Mixed to improper: w n/d = (w × d + n)/d. Both are then reduced by the greatest common factor.

## Assumptions

- Numbers are whole numbers up to 10¹² in size; the arithmetic is exact.
- A minus sign applies to the whole number: −2 1/3 means −(2 + 1/3) = −7/3. In a mixed number, type the minus sign on the whole number.
- In a mixed number the fraction part must be less than 1 (when there is a whole part).
- The answer keeps the fraction as typed; "In lowest terms" reduces it.

## Worked examples

1. mode = improper, n = 11, d = 6 gives result = 1 5/6, mixed = 1 5/6, improper = 11/6, decimal = 1.833333. Source: OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 11/6 = 1 5/6.
2. mode = improper, n = 33, d = 8 gives result = 4 1/8, decimal = 4.125. Source: OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 33/8 = 4 1/8.
3. mode = mixed, w = 4, n = 2, d = 3 gives result = 14/3, improper = 14/3, mixed = 4 2/3. Source: OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 4 2/3 = 14/3.
4. mode = improper, n = 10, d = 4 gives result = 2 2/4, simplest = 2 1/2, improper = 5/2, decimal = 2.5.
5. mode = mixed, w = -2, n = 1, d = 3 gives result = −7/3, mixed = −2 1/3, decimal = -2.333333.

## FAQ

### What is an improper fraction?

A fraction whose numerator is equal to or greater than its denominator, such as 11/6 or 4/4. Its value is 1 or more. A proper fraction, such as 3/4, has a numerator smaller than its denominator and is less than 1.

### How do I turn an improper fraction into a mixed number?

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. 11 ÷ 6 = 1 remainder 5, so 11/6 = 1 5/6.

### How do I turn a mixed number into an improper fraction?

Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 4 2/3: 4 × 3 = 12, 12 + 2 = 14, so 4 2/3 = 14/3.

### Do I need to simplify the answer?

The fraction part can often be reduced. 10/4 is 2 2/4, and 2/4 reduces to 1/2, so the answer in lowest terms is 2 1/2. The calculator shows both.

### How do negative mixed numbers work?

The minus sign applies to the whole mixed number: −2 1/3 means −(2 + 1/3), which is −7/3, not −2 + 1/3. Type the minus sign on the whole number.

### What if the numerator divides evenly?

Then there is no fraction part and the answer is a whole number. 12/4 = 3 exactly, with remainder 0.

## Sources

- OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (improper fractions and mixed numbers; convert an improper fraction to a mixed number by dividing, and a mixed number to an improper fraction by multiplying and adding). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions (retrieved 2026-10-02)