Calculator
Enter two mixed numbers. Choose auto comparison or test a specific inequality.
Plotly Graph
The graph places both mixed numbers on a number line.
Example Data Table
| Left Mixed Number | Operator Tested | Right Mixed Number | Actual Relation | Left Decimal | Right Decimal |
|---|---|---|---|---|---|
| 2 1/3 | < | 3 1/4 | True | 2.33333333 | 3.25000000 |
| -1 2/5 | > | -2 1/4 | True | -1.40000000 | -2.25000000 |
| 4 3/6 | = | 4 1/2 | True | 4.50000000 | 4.50000000 |
| 5 1/8 | ≥ | 5 2/8 | False | 5.12500000 | 5.25000000 |
Formula Used
Each mixed number becomes an improper fraction first.
1) Convert mixed number to improper fraction:
Improper Numerator = (Whole × Denominator) + Numerator
Apply the sign after conversion.
2) Compare two fractions:
For a/b and c/d, compare a×d with c×b.
If a×d < c×b, then a/b < c/d.
If a×d > c×b, then a/b > c/d.
If both cross products match, both values are equal.
The calculator also finds decimal values, exact difference, and absolute difference for a fuller inequality review.
How to Use This Calculator
- Choose the sign for the first mixed number.
- Enter its whole number, numerator, and denominator.
- Select auto compare or a specific inequality symbol.
- Enter the second mixed number the same way.
- Press Compare Mixed Numbers.
- Read the result panel above the form.
- Review decimals, fractions, difference, and the graph.
- Export the result as CSV or PDF.
FAQs
1) What does this mixed number inequality calculator do?
It compares two mixed numbers and shows whether one is less than, greater than, or equal to the other. It also tests custom inequality symbols, converts values, shows decimals, and calculates differences.
2) Can I compare negative mixed numbers?
Yes. Choose the negative sign for either mixed number. The calculator applies that sign to the full mixed value before comparison, so negative fractions and negative wholes are handled correctly.
3) Why does the calculator convert mixed numbers first?
Mixed numbers are easier to compare accurately after converting them into improper fractions. That creates a consistent form for cross multiplication, decimal conversion, simplification, and exact difference calculations.
4) What is auto compare?
Auto compare ignores any preset test and simply reveals the true relation between the two mixed numbers. It is useful when you want the actual answer without checking a specific statement.
5) Why are cross products shown?
Cross products prove the comparison step. When comparing a/b and c/d, the calculator checks a×d and c×b. Larger cross product means the larger fraction, assuming positive denominators.
6) Does the calculator simplify fractions?
Yes. Improper fractions and difference fractions are reduced to simplest form. That keeps the output cleaner and makes the final inequality review easier for homework or lesson notes.
7) What does the graph show?
The graph places both values on a number line. This visual comparison helps you see distance, order, and whether the two mixed numbers sit on the same point or different locations.
8) Can I export the result?
Yes. Use the CSV button for spreadsheet-friendly output or the PDF button for a printable summary. The export uses the current calculation displayed in the result panel.