Enter mixed numbers
Formula used
Convert a mixed number: a b/c = (a × c + b) / c
Subtract fractions: p/q − r/s = (ps − rq) / qs
Simplify: Divide the numerator and denominator by their greatest common divisor.
The least common denominator method produces smaller intermediate numbers. The calculator uses it before reducing the final fraction. Signed values are handled automatically throughout every calculation.
How to use this calculator
- Select the sign for each mixed number.
- Enter each whole number, numerator, and denominator.
- Choose the improper fraction or regrouping method.
- Select Calculate to view the simplified answer and steps.
- Use CSV, copy, print, or PDF controls as needed.
Worked examples
| First number | Second number | Result | Notes |
|---|---|---|---|
| 5 3/4 | 2 1/4 | 3 1/2 | No borrowing required |
| 4 1/3 | 2 5/6 | 1 1/2 | Borrowing is required |
| 2 1/4 | 5 1/2 | −3 1/4 | Negative result |
| 3 2/5 | 3 2/5 | 0 | Equal values |
| 7 0/1 | 2 3/8 | 4 5/8 | Whole number input |
Understanding mixed-number subtraction
A mixed number combines a whole number and a proper fraction. Subtraction becomes easier when both values use a consistent fraction form. The calculator performs these conversions without changing each value.
The improper fraction method converts every mixed number first. It then finds a common denominator and subtracts corresponding numerators. This method also handles negative numbers and improper fractional parts.
The regrouping method resembles traditional written subtraction. One whole can be exchanged for denominator-sized fractional pieces when necessary. This approach is especially useful for classroom practice and review.
Always check denominators before calculating. A denominator of zero is undefined and cannot represent a fraction. Final answers should also be reduced to simplest terms.
Common mistakes
- Subtracting denominators instead of finding a common denominator.
- Forgetting to multiply the whole number during improper conversion.
- Applying a negative sign only to the whole-number part.
- Skipping simplification after obtaining the fraction result.
- Borrowing one whole without adding one denominator to the numerator.
Frequently asked questions
1. What is a mixed number?
A mixed number contains a whole number and a fractional part, such as 3 1/2.
2. Can this calculator handle negative mixed numbers?
Yes. Select a negative sign for either input, and the calculator applies it to the complete value.
3. What happens when the answer is negative?
The negative sign appears before the complete simplified mixed number and improper fraction.
4. Why is a common denominator necessary?
Fractions must describe equal-sized parts before their numerators can be subtracted correctly.
5. Does the calculator simplify answers automatically?
Yes. It divides the result by the greatest common divisor and converts improper fractions into mixed numbers.
6. Can I enter an improper fraction in the numerator field?
Yes. The calculator accepts it, converts the entire input correctly, and displays a warning.
7. What does regrouping mean?
Regrouping exchanges one whole for a fraction equal to that whole, allowing fractional subtraction to continue.
8. Can I subtract a mixed number from a whole number?
Yes. Enter zero as the numerator and one as the denominator for the whole-number input.
9. How do I save the solution as a PDF?
Calculate the result, select Print / Save PDF, and choose the PDF option in your browser.