Fraction Tool
Add, subtract, multiply, divide, compare and simplify fractions, including mixed numbers and negative values. View exact results, decimal and percentage equivalents, worked steps, a value table, and interactive fraction bars or number lines. Export your results.
Fraction visualiser
Step-by-step solution
Value breakdown
| Value | Fraction | Decimal | Percentage |
|---|
Table of Contents
Highlights
- Eight operations covering arithmetic, comparison and fraction forms
- Supports mixed numbers, improper fractions and negative values
- Exact simplified answers with step-by-step working
- Interactive fraction bars and signed number-line views
- Decimal and percentage breakdowns with CSV, text and SVG exports
How Fraction Tool Works?
Every fraction represents a ratio of two integers. In a/b, a is the numerator and b is the non-zero denominator. A mixed number combines a whole part and a fraction, so a positive mixed number such as 1 2/3 equals 5/3. Negative whole parts or numerators are treated as negative values.
For addition and subtraction, cross-multiply to obtain a common denominator:
Multiplication uses the product of the numerators over the product of the denominators. Division multiplies by the reciprocal of the second fraction, which must not be zero.
Comparison is determined from the cross-products ad and bc. Simplification divides the numerator and denominator by their greatest common divisor (GCD). Decimal values come from numerator divided by denominator; percentages multiply that quotient by 100.
| Operation | Example | Result |
|---|---|---|
| Add | 1/2 + 1/3 | 5/6 |
| Subtract | 3/4 − 1/2 | 1/4 |
| Multiply | 2/3 × 3/5 | 2/5 |
| Divide | 3/4 ÷ 1/2 | 3/2 |
| Compare | 2/3 and 3/4 | 2/3 < 3/4 |
| Simplify | 12/18 | 2/3 |
Results are displayed as simplified fractions and, where applicable, mixed numbers. Choose 2, 4, 6, 8, 10 or 12 decimal places for the decimal and percentage display. Fraction bars and a number line offer alternate visual views.
Practical Use Cases
Students: Check homework involving fraction arithmetic, negative fractions and mixed numbers, then follow the worked steps to understand the result.
Teachers and tutors: Demonstrate equivalent values and comparisons using fraction bars or a number line, and discuss why a simplified answer is unchanged in value.
Home cooks: Add or subtract fractional ingredient quantities, such as 1/2 plus 3/4, when adjusting a recipe.
Woodworkers and craft makers: Combine or compare fractional measurements used in plans and cutting lists while retaining exact fractional answers.
Parents helping with homework: Show how a mixed number becomes an improper fraction and compare two fractions with different denominators.
Accuracy and Limitations
Fraction arithmetic and simplification use integer-based rational calculations, so the fraction result is exact for valid integer inputs. Each entered integer is limited to 35 digits, and denominators cannot be zero; division also requires a non-zero second fraction. Decimal and percentage outputs use JavaScript floating-point approximations rounded to the selected 2–12 decimal places. Extremely large values can exceed the numeric range used for decimal displays and charts. The visual bars show absolute magnitudes, while the number line shows approximate signed positions. A negative whole part or numerator makes the entire mixed-number input negative.
