Calculated
Mixed Number Calculator
Sign up to favourite this calculatorEnter two mixed numbers and an operation. The answer comes back as a mixed number, with the improper-fraction working and the decimal beside it.
2 2/5 + 1 1/2
Working
12/5 + 3/2 = 24/10 + 15/10 = 39/10 = 3 9/10As an improper fraction
39/10As a decimal
3.9Result type
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Type the first mixed number as a whole number, a space, then the fraction:
2 2/5. - Choose add, subtract, multiply or divide.
- Type the second mixed number the same way.
- 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.
Working with plain fractions instead? The Fraction Calculator runs the same four operations without the mixed-number input.
What do I need to enter?
- First mixed number and Second mixed number — each as a whole number, a space, then a fraction, such as
2 2/5. A plain fraction, a whole number or a decimal also works, and a minus sign makes it negative. Numerators and denominators go up to 100,000,000, and a denominator cannot be zero. - Operation — + (add), − (subtract), × (multiply) or ÷ (divide). You cannot divide by zero.
What do the results show?
- Answer — the main figure, in lowest terms as a mixed number, headed by the sum you entered.
- Working — both numbers as improper fractions, the common denominator or products used, and the conversion back to a mixed number.
- As an improper fraction and As a decimal — the same answer in those two forms, with repeating digits shown in brackets.
- Result type — whether the answer is a whole number, a proper fraction or a mixed number.
- Common denominator — shown for addition and subtraction; not needed for multiplication or division.
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
| Sum | As improper fractions | Answer |
|---|---|---|
| 2 2/5 + 1 1/2 | 12/5 + 3/2 | 3 9/10 |
| 1 1/2 × 2 5/7 | 3/2 × 19/7 | 4 1/14 |
| 1 1/2 ÷ 2 5/7 | 3/2 ÷ 19/7 | 21/38 |
| 3 1/4 − 1 2/3 | 13/4 − 5/3 | 1 7/12 |
| 2 3/4 + 2 1/4 | 11/4 + 9/4 | 5 |
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.
Last updated 25 October 2026.