How to convert a mixed number
A mixed number like 2 3/4 combines a whole part and a fraction. To write it as an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the denominator: (2 × 4 + 3) / 4 = 11/4.
The reason this works is that the whole part must first be rewritten in quarters. Two wholes are 8 quarters, and adding the existing 3 quarters gives 11 quarters. The denominator never changes because you are only renaming the whole number in the same-sized pieces the fraction already uses. An improper fraction converts straight to a decimal with the fraction to decimal calculator.
How to use this calculator
Enter the whole number, the numerator and the denominator. The denominator cannot be zero. The result is the equivalent improper fraction, with the working shown. To reduce that result further, use the fraction simplifier calculator.
A common error is adding the whole number to the numerator without multiplying by the denominator first, which would wrongly turn 2 3/4 into 5/4. Another is changing the denominator during the conversion — it always stays the same.
Improper fractions and mixed numbers
An improper fraction has a numerator larger than its denominator. It represents the same value as the mixed number — 11/4 and 2 3/4 are equal. Improper fractions are easier to multiply and divide, which is why they are often the preferred form in algebra.
Going the other way, divide the numerator by the denominator: 11 ÷ 4 gives 2 remainder 3, which reassembles into 2 3/4. Mixed numbers are easier to picture and are preferred in measurements and recipes, while improper fractions are the working form for calculation. Going back the other way is a division with a remainder, which the long division calculator lays out.
Frequently asked questions
- What is 2 3/4 as an improper fraction?
- 11/4. Multiply 2 by 4 to get 8, add 3 to get 11, and keep the denominator 4.
- What is the formula?
- Improper fraction = (whole × denominator + numerator) ÷ denominator.
- Can the denominator be zero?
- No. A zero denominator is undefined, so the calculator requires a non-zero denominator.
- What is an improper fraction?
- A fraction whose numerator is greater than or equal to its denominator, such as 11/4.
- How do I convert a negative mixed number?
- Convert the size of the number first and then apply the minus sign to the whole result. For −2 3/4, work out 2 3/4 = 11/4 and write the answer as −11/4 — the negative applies to the entire quantity, not just the whole part.