A mixed number (also called a mixed fraction) is a whole number and a fraction together, such as 2 1/3. An improper fraction has a top number that is as big as or bigger than the bottom, such as 7/3. They can show the same amount: 2 1/3 = 7/3. To switch, use whole × denominator + numerator, or divide.
In short: Mixed to improper: multiply the whole number by the denominator, add the numerator, and keep the denominator. Improper to mixed: divide the top by the bottom; the answer is the whole number and the remainder is the new numerator.
In this guide
What Is a Mixed Number?
| Type | What it means | Example |
|---|---|---|
| Proper fraction | Top is smaller than the bottom (less than 1) | 3/4 |
| Improper fraction | Top is equal to or bigger than the bottom (1 or more) | 7/3 |
| Mixed number | A whole number plus a proper fraction | 2 1/3 |
You read 2 1/3 as “two and one third”. It means 2 + 1/3.
How to Change a Mixed Number to an Improper Fraction
- Multiply the whole number by the denominator: 2 × 3 = 6.
- Add the numerator: 6 + 1 = 7.
- Keep the denominator: 7/3.
Example: 4 2/3 as a fraction: (4 × 3 + 2)/3 = 14/3.
Example: 3 1/2 as a fraction: (3 × 2 + 1)/2 = 7/2.
How to Change an Improper Fraction to a Mixed Number
- Divide the numerator by the denominator: 17 ÷ 5 = 3 remainder 2.
- The whole number is the answer: 3.
- The remainder goes over the same denominator: 2/5. So 17/5 = 3 2/5.
Example: 22/7: 22 ÷ 7 = 3 remainder 1, so 22/7 = 3 1/7.
When to Use Each Form
- Use improper fractions to calculate. They make multiplying and dividing much easier, and they avoid borrowing when you subtract.
- Use mixed numbers for the final answer in everyday problems, such as 2 1/2 cups of flour, because they are easier to picture.
- Simplify the fraction part. 3 2/4 should be written as 3 1/2. See how to simplify fractions.
Common Examples
| Mixed number | Working | Improper fraction |
|---|---|---|
| 2 1/3 | (2 × 3 + 1)/3 | 7/3 |
| 3 1/2 | (3 × 2 + 1)/2 | 7/2 |
| 4 2/3 | (4 × 3 + 2)/3 | 14/3 |
| 3 2/5 | (3 × 5 + 2)/5 | 17/5 |
| 1 3/4 | (1 × 4 + 3)/4 | 7/4 |
Try it
Type a mixed number such as 4 2/3, or an improper fraction such as 22/7, and see both forms and the decimal.
FAQ
What is a mixed fraction?
A mixed fraction, or mixed number, is a whole number and a proper fraction written together, such as 2 1/3. It means 2 + 1/3.
What is 4 and 2/3 as a fraction?
4 2/3 = (4 × 3 + 2)/3 = 14/3.
What is 3 1/2 as a fraction?
3 1/2 = (3 × 2 + 1)/2 = 7/2.
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number answer is the whole part and the remainder is the new numerator. 17/5 = 3 remainder 2 = 3 2/5.
Is an improper fraction wrong?
No. Improper fractions are correct and are often easier to work with. Many teachers ask for the final answer as a mixed number, so check what your class expects.
Sources and Further Reading
- OpenStax, Prealgebra 2e, Section 4.3: Multiply and Divide Mixed Numbers and Complex Fractions, Rice University.
- OpenStax, Prealgebra, Section 4.6: Add and Subtract Mixed Numbers.
More fraction guides: How to add fractions, How to subtract fractions, How to multiply fractions, How to divide fractions. Or check any answer with the fraction calculator.
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