Mixed Number Calculator
Add, subtract, multiply or divide mixed numbers such as 2 1/2 and 1 3/4, exactly, with the answer as a mixed number, an improper fraction and a decimal.
Result
Result: 4 1/4
Exact: fractions stay fractions until the decimal at the end.
- As an improper fraction
- 17/4
- As a decimal
- 4.25
https://calcgallery.com/algebra-numbers/mixed-number-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Mixed Number Calculator
- Enter the first mixed number as a whole number, a numerator and a denominator; for a plain fraction, leave the whole number at 0.
- Choose the operation, and enter the second mixed number the same way.
- Read the answer as a mixed number, an improper fraction and a decimal.
The method
a b/c = (a × c + b) ÷ ca/b + c/d = (ad + bc) ÷ bd a/b − c/d = (ad − bc) ÷ bda/b × c/d = ac ÷ bd a/b ÷ c/d = ad ÷ bcEvery answer is reduced to lowest terms by dividing top and bottom by their greatest common factor, then split into a whole number and a proper fraction.
Plain fractions
For a fraction with no whole part, such as 3/8, enter 0 as the whole number. A negative plain fraction can take its minus sign on the numerator. The fraction calculator handles plain fractions on their own.
With your numbers
- As improper fractions: 5/2 and 7/4
- Result: 17/4 = 4 1/4
Quick reference
Exact: fractions stay fractions until the decimal at the end.
| Example | Result |
|---|---|
| 2 1/2 + 1 3/4 | 4 1/4 |
| 2 1/2 − 1 3/4 | 3/4 |
| 2 1/2 × 1 3/4 | 4 3/8 |
| 2 1/2 ÷ 1 3/4 | 1 3/7 |
| −2 1/2 + 1 1/4 | −1 1/4 |
| 1 1/2 ÷ 0 | Not defined |
Common questions about the Mixed Number Calculator
- How do I add mixed numbers?
- Turn each into an improper fraction, add, and turn the answer back. 2 1/2 is 5/2 and 1 3/4 is 7/4; 5/2 + 7/4 = 10/4 + 7/4 = 17/4 = 4 1/4. The page does the same, exactly.
- How does a negative mixed number work?
- The minus sign applies to the whole thing: −2 1/2 means −(2 + 1/2) = −5/2, not −2 + 1/2. So −2 1/2 + 1 1/4 = −1 1/4. Reading it the other way gives 3/4, which is a common mistake.
- How do I divide mixed numbers?
- Turn both into improper fractions, then multiply by the reciprocal of the second: 5/2 ÷ 7/4 = 5/2 × 4/7 = 20/14 = 10/7 = 1 3/7.
- Why not just use decimals?
- Because many fractions have no exact decimal. A third is 0.333…, and adding three rounded thirds gives 0.999…, not 1. The page keeps everything as exact fractions until the final decimal.