Mixed Number Calculator
Mixed Number Tips
Mixed to Improper
Multiply whole by denominator, add numerator: 2½ = (2×2+1)/2 = 5/2
Improper to Mixed
Divide numerator by denominator: 7/3 = 2 R1 = 2⅓
Example Problems
Related Calculators
Understanding Mixed Numbers
What Is a Mixed Number?
A mixed number combines a whole number with a proper fraction. For example, 2½ represents 2 whole units plus ½ of another unit. Mixed numbers are commonly used in everyday measurements, cooking, and carpentry.
Mixed Number Parts
- Whole part: 2
- Numerator: 3 (top of fraction)
- Denominator: 4 (bottom of fraction)
Converting Mixed Numbers
Mixed → Improper
Multiply whole by denominator, add numerator, keep denominator.
Improper → Mixed
Divide numerator by denominator. Quotient = whole, remainder = numerator.
Operations with Mixed Numbers
Adding Mixed Numbers
- Convert to improper fractions
- Find a common denominator
- Add the numerators
- Simplify and convert back to mixed number
Subtracting Mixed Numbers
- Convert to improper fractions
- Find a common denominator
- Subtract the numerators
- Simplify and convert back to mixed number
Multiplying Mixed Numbers
- Convert to improper fractions
- Multiply numerators together
- Multiply denominators together
- Simplify and convert back to mixed number
Dividing Mixed Numbers
- Convert to improper fractions
- Flip the second fraction (reciprocal)
- Multiply instead of divide
- Simplify and convert back to mixed number
Common Equivalent Forms
| Mixed | Improper | Decimal |
|---|---|---|
| 1½ | 3/2 | 1.5 |
| 2¼ | 9/4 | 2.25 |
| 3⅓ | 10/3 | 3.333... |
| 4¾ | 19/4 | 4.75 |
Tips for Working with Mixed Numbers
- Always convert to improper fractions before calculating
- Find the LCD (Least Common Denominator) for addition and subtraction
- Remember: dividing by a fraction means multiplying by its reciprocal
- Simplify your final answer by finding the GCD of numerator and denominator
- Check your work by converting back to decimal
Frequently Asked Questions
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, 2 3/4 becomes: (2 x 4 + 3) / 4 = 11/4. This works because 2 3/4 means 2 + 3/4 = 8/4 + 3/4 = 11/4.
Why do you need to convert mixed numbers before calculating?
Converting to improper fractions simplifies calculations because you can apply standard fraction rules (same denominator for add/subtract, multiply straight across for multiply/divide) without tracking whole numbers separately.
How do you multiply mixed numbers?
Convert both to improper fractions, multiply numerators together, multiply denominators together, then simplify and convert back to a mixed number. Example: 2 1/4 x 1 1/3 = 9/4 x 4/3 = 36/12 = 3.
What is the difference between a mixed number and an improper fraction?
A mixed number has a whole number and a proper fraction (2 3/4). An improper fraction has a numerator larger than or equal to its denominator (11/4). They represent the same value but in different forms. Mixed numbers are easier to visualize; improper fractions are easier to calculate with.