Convert between mixed numbers and improper fractions.
This mixed number to improper fraction calculator converts in both directions. Turn a mixed number like 3 2/5 into an improper fraction for multiplying or dividing, or turn an improper fraction like 17/5 back into a mixed number for a final answer. Each conversion shows its steps and the decimal value.
Quick answer: to turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator: 3 2/5 = (3 × 5 + 2)/5 = 17/5. To go back, divide: 17 ÷ 5 = 3 remainder 2, so 3 2/5.
How to Use the Mixed Number Calculator
Mixed → Improper
- Enter the whole number, the numerator and the denominator. For 3 2/5, enter 3, 2 and 5.
- Read the improper fraction and the decimal.
Improper → Mixed
- Enter the numerator and denominator. For 17/5, enter 17 and 5.
- Read the mixed number and the decimal.
How to Convert a Mixed Number to an Improper Fraction
- Multiply the whole number by the denominator.
- Add the numerator.
- Keep the same denominator.
3 2/5: 3 × 5 = 15, then 15 + 2 = 17, so 3 2/5 = 17/5.
How to Convert an Improper Fraction to a Mixed Number
- Divide the numerator by the denominator.
- The whole number is the answer to the division.
- The remainder becomes the new numerator, over the same denominator.
17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.
More Examples
- 2 3/4 = (2 × 4 + 3)/4 = 11/4
- 1 1/2 = (1 × 2 + 1)/2 = 3/2
- 22/7 = 3 remainder 1 = 3 1/7
- 9/3 = 3 remainder 0 = 3, a whole number
Why Convert at All?
- Multiplying and dividing fractions is much easier with improper fractions. 1 1/2 × 2 2/3 becomes 3/2 × 8/3 = 4.
- Final answers are usually written as mixed numbers, because 3 2/5 is easier to picture than 17/5.
- Measurements such as 2 3/4 inches or 1 1/2 cups are mixed numbers, but scaling them is easier as improper fractions.
To add, subtract, multiply or divide mixed numbers, use the fraction calculator. It accepts mixed numbers directly and converts them for you.
Negative Mixed Numbers
−2 1/3 means −(2 + 1/3), not −2 + 1/3. So −2 1/3 = −7/3. The calculator keeps the minus sign on the whole value.
Related Fraction Tools
- Reduce the answer to lowest terms with the simplify fractions calculator.
- Turn a mixed number into a decimal with the fraction to decimal calculator.
Mixed Number FAQs
What is a mixed number?
A whole number and a proper fraction written together, such as 3 2/5. It means 3 + 2/5.
What is an improper fraction?
A fraction whose numerator is equal to or larger than its denominator, such as 17/5 or 4/4. Its value is 1 or more.
Is 7/7 an improper fraction?
Yes. Its value is exactly 1, so as a mixed number it is just the whole number 1.
Should the answer be simplified?
Yes. The fraction part of a mixed number should be in simplest form, so 2 4/6 should be written as 2 2/3. The calculator does this for you.
How we checked this page: every conversion was worked in both directions by hand and matches the calculator.