Add, subtract, multiply, and divide mixed numbers and fractions instantly with simplified results.
Enter two mixed numbers and select an operation. Leave the whole number as 0 for simple fractions.
First Mixed Number
Second Mixed Number
A mixed number (also called a mixed fraction) combines a whole number and a proper fraction into one value. For example, 2¾ means "two and three-quarters." Mixed numbers appear frequently in everyday measurements — cooking recipes, construction dimensions, and time calculations. They're a natural way to express quantities that fall between whole numbers.
Mixed numbers are typically introduced in 4th grade mathematics and remain important throughout middle school and high school. The Khan Academy fraction arithmetic course provides comprehensive lessons on working with mixed numbers. For simpler fraction operations, try our Fraction Calculator.
Before performing any operation, convert each mixed number to an improper fraction using this formula:
Example: Convert 3²⁄₅ to an improper fraction
(3 × 5 + 2) / 5 = 17/5
Simplify the result using the GCF of the numerator and denominator, then convert back to a mixed number if needed.
Full Example: 2¹⁄₃ + 1³⁄₄
Convert: 2¹⁄₃ = 7/3 and 1³⁄₄ = 7/4
Common denominator (LCD = 12): 28/12 + 21/12 = 49/12
Convert back: 49/12 = 4¹⁄₁₂
According to the National Council of Teachers of Mathematics, common mistakes with mixed numbers include forgetting to convert to improper fractions before calculating, and not finding a common denominator before adding or subtracting. Always convert first, then calculate, then simplify — and use our calculator to verify your work!
A mixed number has a whole part and a fraction part (like 2¾). An improper fraction has a numerator larger than or equal to the denominator (like 11/4). They represent the same value — 2¾ = 11/4.
Yes! A negative mixed number like -2½ means negative two and a half, or -5/2 as an improper fraction. The negative sign applies to the entire mixed number.
Separate the whole part from the decimal part. Convert the decimal to a fraction (e.g., 0.75 = 75/100 = 3/4). Combine: 2.75 = 2¾.
A mixed number combines a whole number with a proper fraction, written as 2 and 3/4. It expresses the same value as the improper fraction 11/4, but in a form that is easier to picture, which is why measurements, recipes and construction plans use it. A mixed numbers calculator converts between the two forms and performs arithmetic on them.
Multiplying 1 and 1/2 by 2 and 1/2 by combining the whole parts and the fraction parts separately gives 2 and 1/4, which is wrong. The correct answer is 3 and 3/4. Mixed numbers must be converted to improper fractions before any multiplication or division.
Step 1: Convert both to improper fractions
Step 2: Multiply
Step 3: Convert back
The answer is 3 and 3/4, not the 2 and 1/4 the shortcut would suggest
Addition and subtraction can be done either by converting to improper fractions or by handling the whole and fractional parts separately. The second method is often quicker mentally, but requires care when borrowing.
Convert to improper fractions
Find a common denominator and add
Convert back
The total is 4 and 5/12
Subtracting mixed numbers sometimes requires borrowing from the whole number, in the same way column subtraction borrows from the next place value.
The answer is 2 and 1/2
| Mixed Number | Improper Fraction | Decimal |
|---|---|---|
| 1 and 1/2 | 3/2 | 1.5 |
| 1 and 3/4 | 7/4 | 1.75 |
| 2 and 1/3 | 7/3 | 2.333... |
| 2 and 5/8 | 21/8 | 2.625 |
| 3 and 1/4 | 13/4 | 3.25 |
| 4 and 2/3 | 14/3 | 4.666... |
The reliable workflow for any mixed number arithmetic is the same three steps: convert everything to improper fractions, do the arithmetic, then convert the answer back to a mixed number. It is slightly longer than shortcuts but it never produces the errors that shortcuts do.
Imperial measurement runs on mixed numbers. Timber is sold as 2 and 1/4 inches, spanners come in fractional sizes, and drill bits step in sixteenths. Recipes use them because 2 and 1/2 cups is immediately meaningful in a way that 5/2 cups is not. In each case the mixed form communicates the quantity clearly, even though calculations happen in improper form.
This calculator is provided for educational purposes.