How to solve it
- Convert each mixed number to an improper fraction.
- Apply the rule for the operation: common denominator to add or subtract, direct product to multiply, reciprocal to divide.
- Simplify the result.
- If it is improper, write it as a mixed number.
1 1/2 = (1 × 2 + 1)/2 = 3/2
2 2/3 = (2 × 3 + 2)/3 = 8/3
3/2 + 8/3 = 9/6 + 16/6 = 25/6
25/6 = 4 1/6
Result: 25/6
Common mistake:Wrong: 1 1/2 + 2 1/2 = 3 2/4.Right: 1 1/2 + 2 1/2 = 4.When you add equal parts the denominator does not change, and 2/2 completes a whole: 1/2 + 1/2 = 1, so the total is 4.
A complete example
To add two mixed numbers, convert them to improper fractions, add them, and write the result as a mixed number again. If you only need to convert one number, mixed number to fraction does it without any operation, and improper fraction to mixed number puts a result you already have as a fraction into mixed form.
Worked example: 2 1/3 + 1 5/6
Add these two mixed numbers and write the result in both forms.
- Convert each mixed number. 2 1/3 = (2 × 3 + 1)/3 = 7/3, and 1 5/6 = (1 × 6 + 5)/6 = 11/6.
- Find the common denominator. The least common multiple (LCM) of 3 and 6 is 6, and 7/3 = 14/6.
- Add the numerators. 14/6 + 11/6 = 25/6.
- Since 25 and 6 have no common factors, the fraction is already in lowest terms. Dividing 25 ÷ 6 gives 4 with a remainder of 1, so 25/6 = 4 1/6.
The result is 25/6, or 4 1/6 as a mixed number.
Check: the whole numbers add up to 2 + 1 = 3 and the fractions to 1/3 + 5/6 = 7/6, which is 1 1/6. In total, 3 + 1 1/6 = 4 1/6.
Subtraction, multiplication and division follow the same path, and only the rule in step 3 changes.
One rule for each operation
Each operation is applied to the improper fractions. For subtraction you find a common denominator, for multiplication you multiply the numerators and the denominators, and for division you multiply by the reciprocal of the divisor. The table gathers one case of each kind.
| Operation | With improper fractions | Result | As a mixed number |
|---|---|---|---|
| 6 1/8 − 2 5/8 | 49/8 − 21/8 = 28/8 | 7/2 | 3 1/2 |
| 1 1/2 × 2 2/3 | 3/2 × 8/3 = 24/6 | 4 | 4 |
| 3 3/5 ÷ 1 4/5 | 18/5 × 5/9 = 90/45 | 2 | 2 |
| −1 1/2 + 1/4 | −6/4 + 1/4 | −5/4 | −1 1/4 |
The last row shows the effect of the sign: it applies to the whole 3/2, not just to the whole number.
If the calculation mixes different operations or has parentheses, use the fraction expressions calculator, which respects the order of operations.
When to carry a 1 when adding separately
Adding the whole numbers and the fractions separately is valid, but if the fractions add up to more than one unit, you have to carry the 1 over to the whole numbers.
Subtraction has something similar with borrowing, and with negative signs the shortcut no longer works. With improper fractions there are no special cases: it is the same calculation every time. The Wikipedia article Fraction (mathematics) points out that in algebra, mixed notation is usually replaced by improper fractions, which are easier to compute with (consulted October 16, 2026).
Where to go next
To tell mixed, improper and proper fractions apart, the guide on types of fractions compares them with examples. The mixed number worksheets have exercises with answers for practicing by hand. After practicing, use this calculator to check your results and see at which step you went wrong.
Frequently asked questions
Can I mix mixed numbers with decimals?
In this calculator, every row is a mixed number. To combine a decimal with a mixed number, use the “Mixed numbers and decimals” mode of the main calculator, which accepts both formats. For example, 0.75 + 2 1/5 = 3/4 + 11/5 = 15/20 + 44/20 = 59/20, which is 2 19/20 as a mixed number.
What happens if I subtract a larger mixed number from a smaller one?
The result is negative, and that is valid. The first row is the minuend, the second is the subtrahend, and the order of the rows matters. With 1 2/5 − 2 7/10 you get 14/10 − 27/10 = −13/10, which as a mixed number is −1 3/10. If you need the difference as a positive number, swap the rows.
How do you write a negative mixed number?
The sign goes in front of the entire mixed number: −2 3/4 means −(2 + 3/4) = −11/4. To write −29/8 as a mixed number, divide 29 by 8, which gives 3 with a remainder of 5, and put the sign in front: −3 5/8. In the calculator, choose the negative sign on that row and leave the whole part, numerator and denominator unsigned.