Mixed Number Calculator
Add, subtract, multiply, and divide mixed numbers. Get results as mixed numbers, improper fractions, and decimals.
Result (Mixed Number)
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Result (Improper Fraction) —
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Result (Mixed)
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Result (Improper) —
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Result
Result (Mixed Number) —
Result (Improper Fraction) —
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Math Details
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How to Use This Calculator
Enter the whole number, numerator, and denominator for each mixed number, select the operation, and click Calculate. Results appear as a mixed number, improper fraction, and decimal.
Formula
Convert a b/c → (ac+b)/c, perform fraction arithmetic, convert result back to mixed number.
Example
2½ + 1¾ = 5/2 + 7/4 = 17/4 = 4¼ = 4.25
Frequently Asked Questions
- A mixed number is a number written as a whole-number part plus a proper fraction, such as 2½ (meaning 2 + 1/2 = 2.5) or 3¾ (meaning 3 + 3/4 = 3.75). Mixed numbers represent values between consecutive integers and are common in everyday measurements: recipes (1½ cups), lengths (5¾ inches), and time (2¼ hours). Formally, a mixed number a b/c is equivalent to the improper fraction (a×c + b) / c. They are easier to read for large values but harder to compute with than improper fractions.
- The most reliable method is to convert each mixed number to an improper fraction first, then add using a common denominator, and finally convert the result back. Example: 2½ + 1¾ = 5/2 + 7/4 = 10/4 + 7/4 = 17/4 = 4¼. Alternatively, add the whole-number parts and fraction parts separately: 2 + 1 = 3, and ½ + ¾ = 2/4 + 3/4 = 5/4 = 1¼. Then combine: 3 + 1¼ = 4¼. The first method (improper fractions) is generally safer because it avoids separate cases for when the fractional parts sum to more than 1.
- Multiply the whole-number part by the denominator, then add the numerator. The denominator stays the same. Formula: a b/c = (a×c + b) / c. Examples: 2½ → (2×2 + 1)/2 = 5/2. 3¾ → (3×4 + 3)/4 = 15/4. 5 2/3 → (5×3 + 2)/3 = 17/3. Converting to an improper fraction before arithmetic keeps all operations on simple fractions, making multiplication, division, and finding common denominators straightforward.
- Divide the numerator by the denominator. The integer quotient is the whole-number part, and the remainder over the denominator is the fractional part. Example: 17/4 → 17 ÷ 4 = 4 remainder 1 → mixed number 4¼. Another example: 22/7 → 22 ÷ 7 = 3 remainder 1 → 3 1/7. After converting, check that the fraction part is fully simplified (divide numerator and denominator by their GCD). Always simplify the final fractional part.
- Yes — enter a negative whole number to represent a negative mixed number. For example, to represent −2½, enter whole = −2, numerator = 1, denominator = 2. The value is −2 − ½ = −2.5. Be careful: −2½ is the same as −5/2, not −3/2. The negative sign applies to the entire mixed number, including the fractional part. All four arithmetic operations work correctly with negative mixed numbers — the calculator handles the sign logic automatically.