ToolnozaConvert before you calculate
A mixed number combines a whole number and a proper fraction, such as 2 1/3. To make arithmetic consistent, convert it to an improper fraction: multiply the whole number by the denominator, add the numerator and keep the denominator. Thus 2 1/3 becomes 7/3.
Addition example
Add 2 1/3 and 1 1/4. First convert to 7/3 and 5/4. Find the common denominator 12: 28/12 + 15/12 = 43/12 = 3 7/12. The key is finding a common denominator, not simply adding top and bottom numbers.
Division example
Divide 2 1/3 by 1 1/4. Convert first: (7/3) ÷ (5/4) = (7/3) × (4/5) = 28/15 = 1 13/15. Dividing by a fraction means multiplying by its reciprocal, provided the divisor is not zero.
Check your result
Estimate the answer with decimals: 2.33 + 1.25 is about 3.58, matching 3 7/12. A quick estimate catches sign errors and misplaced denominators. Use Toolnoza's fraction calculator to verify the equivalent improper-fraction operation.
Frequent mistakes
Do not add denominators. Simplify only by dividing numerator and denominator by the same nonzero common factor. Convert negative mixed numbers consistently; −2 1/3 conventionally means −(2 + 1/3).
Frequently asked questions
What is an improper fraction? One with a numerator whose absolute value is at least as large as its denominator.
Can denominators be zero? No.
Do I have to convert back to a mixed number? Not unless your context or teacher requests that representation.