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Mixed Number Calculator

Enter two mixed numbers and an operation. The answer comes back as a mixed number, with the improper-fraction working and the decimal beside it.

Your mixed numbers

A whole number, a space, then the fraction — 2 2/5. A plain fraction or whole number works too.
Operation
As improper fractions
12/5 + 3/2
Common denominator
10
2 2/5 + 1 1/2
3 9/10
Working
12/5 + 3/2 = 24/10 + 15/10 = 39/10 = 3 9/10
As an improper fraction
39/10
As a decimal
3.9
Result type
Mixed number

How to use this calculator

  1. Type the first mixed number as a whole number, a space, then the fraction:2 2/5.
  2. Choose add, subtract, multiply or divide.
  3. Type the second mixed number the same way.
  4. Read the answer, then check the working line. It shows both numbers as improper fractions, the common denominator where one is needed, and the conversion back.

A plain fraction or a whole number can go in either field, so the tool also covers2 1/2 + 3 and 4 ÷ 1 1/3 without any special handling.

How to calculate with mixed numbers

Mixed numbers are awkward to calculate with directly, so the method is to leave them as quickly as possible. Convert, calculate, convert back.

w n/d = (w × d + n) / d
  • w — the whole number, e.g. 2
  • n/d — the fraction part, e.g. 2/5
  • Result — the improper fraction, e.g. 12/5

Once both numbers are improper fractions, the usual rules apply: a common denominator for addition and subtraction, straight across for multiplication, and multiply by the reciprocal for division.

Coming back the other way is a division with a remainder. 39/10 is 3 remainder 9, so the answer is 3 9/10. When the remainder is zero the answer is a whole number, which is why 2 3/4 + 2 1/4 is simply 5.

Worked examples

Mixed-number sums, with the improper-fraction stage shown
SumAs improper fractionsAnswer
2 2/5 + 1 1/212/5 + 3/23 9/10
1 1/2 × 2 5/73/2 × 19/74 1/14
1 1/2 ÷ 2 5/73/2 ÷ 19/721/38
3 1/4 − 1 2/313/4 − 5/31 7/12
2 3/4 + 2 1/411/4 + 9/45

Row four is the borrowing case: 1/4 is smaller than 2/3, so the whole numbers cannot simply be subtracted. Over a denominator of 12 it becomes 39/12 − 20/12 = 19/12, which is 1 7/12.

Frequently asked questions

How do I add mixed numbers?

Convert each to an improper fraction, put them over a common denominator, add, then convert back. For 2 2/5 + 1 1/2: the improper fractions are 12/5 and 3/2, which over 10 become 24/10 and 15/10, giving 39/10 — that is 3 9/10.

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

Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 3 1/4: 3 × 4 = 12, plus 1 is 13, so it is 13/4. This is the step to get right, because everything after it is ordinary fraction arithmetic.

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

Divide the numerator by the denominator. The whole part of the answer is the whole number and the remainder goes over the same denominator. 17/6 is 2 remainder 5, so it is 2 5/6.

Can I add the whole parts and the fractions separately?

For addition and subtraction, yes, as long as you handle borrowing correctly — 3 1/4 − 1 2/3 needs a whole unit broken up, which is where the method usually goes wrong. It does not work at all for multiplication or division, so converting to improper fractions first is the method worth learning.

Why is the answer sometimes a plain fraction?

Because the result is smaller than 1, so there is no whole part to show. 1 1/2 ÷ 2 5/7 comes to 21/38, which is a proper fraction. The improper-fraction row beside the answer always shows the same number in the other form.

Does it handle negative mixed numbers?

Yes. Put the minus sign at the front, as in −2 1/2, and it applies to the whole mixed number rather than only the fraction part. That is the usual convention: −2 1/2 is −2.5, not −2 + 0.5.