Mixed Numbers and Improper Fractions

Written byOleh Soloninupdated 5 October 2026

Direction

Whole part

For a negative number, put the minus on the whole part.

Numerator

Denominator

Result

Improper fraction17/5
Decimal3.4
How it was worked out3 2/5 = (3 × 5 + 2)/5 = 17/5

Both directions, with the working

Converts a mixed number to an improper fraction and an improper fraction to a mixed number, shows the working on one line, simplifies the result and gives the decimal.

To write a mixed number as an improper fraction, multiply the whole part by the denominator and add the numerator; that is the new numerator over the same denominator: 3 2/5 = (3 × 5 + 2)/5 = 17/5.

To write an improper fraction as a mixed number, divide the numerator by the denominator with a remainder: the quotient is the whole part and the remainder the numerator, over the same denominator: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.

How to use

Choose the direction: mixed number to improper fraction, or improper fraction to mixed number.
Enter the whole part, numerator and denominator, or just the numerator and denominator of the improper fraction. For a negative number, put the minus on the whole part.
Read the answer, the working, the simplified form and the decimal to check it.

Mixed number to improper fraction

1. Multiply the whole part by the denominator. 2. Add the numerator. 3. Put the sum over the original denominator. 4. Simplify if the numerator and denominator share a factor.

With simplifying: 2 2/4 = (2 × 4 + 2)/4 = 10/4 = 5/2. You can also simplify first: 2 2/4 = 2 1/2 = 5/2, with the same answer.

Worked out with this calculator.
Mixed number	Working	Improper fraction
1 1/2	(1 × 2 + 1)/2	3/2
2 3/4	(2 × 4 + 3)/4	11/4
3 2/5	(3 × 5 + 2)/5	17/5
4 1/3	(4 × 3 + 1)/3	13/3
5 5/6	(5 × 6 + 5)/6	35/6
−2 3/4	−(2 × 4 + 3)/4	−11/4

Improper fraction to mixed number

Divide the numerator by the denominator with a remainder. The quotient is the whole part, the remainder is the numerator of the fraction part, and the denominator stays. With no remainder the fraction is a whole number: 20/4 = 5.

With a positive denominator, a fraction is improper when its numerator is at least as large as the denominator in absolute value, so it has a whole part: −11/4 is −2 3/4. A proper fraction such as 3/7 has a whole part of zero.

Worked out with this calculator.
Improper fraction	Division	Mixed number
7/2	7 ÷ 2 = 3 remainder 1	3 1/2
11/4	11 ÷ 4 = 2 remainder 3	2 3/4
17/5	17 ÷ 5 = 3 remainder 2	3 2/5
23/6	23 ÷ 6 = 3 remainder 5	3 5/6
20/4	20 ÷ 4 = 5 remainder 0	5

What this calculator shows

The improper fraction or the mixed number, whichever way you convert
The working on one line: multiply and add, or divide with a remainder
The simplified form when the numerator and denominator share a factor
The whole part, remainder and decimal to check against

What to keep in mind

The sign applies to the whole number: −3 2/5 is minus three and two fifths, not −3 + 2/5.
If a mixed number has a numerator larger than its denominator, the conversion still works and converting back gives a larger whole part.

FAQs

How do I write a mixed number as an improper fraction?

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

How do I write an improper fraction as a mixed number?

Divide the numerator by the denominator with a remainder: the quotient is the whole part and the remainder the numerator. 23/6: 23 ÷ 6 = 3 remainder 5, so 3 5/6.

What about negative numbers?

The minus applies to the whole number. −2 3/4 is −(2 + 3/4) = −11/4, not −2 + 3/4. Back again: −11/4 = −2 3/4.

What if the fraction divides exactly?

Then it is a whole number: 20/4 = 5, with no fraction part.

Why convert to an improper fraction at all?

Multiplying and dividing mixed numbers is easier with improper fractions: 1 1/2 × 2 1/3 = 3/2 × 7/3 = 7/2 = 3 1/2. Multiplying the whole parts and the fractions separately gives 2 1/6, which is wrong.

Why does the result sometimes simplify?

Because the numerator and denominator can share a factor. 2 2/4 becomes 10/4 and then 5/2. The calculator shows the simplified form on its own line.

Worked example

Three and two fifths

Input: 3 2/5

Output: 17/5

Note: 3 × 5 + 2 = 17 over the same denominator. Back again: 17 ÷ 5 gives 3 with 2 left over.

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