Reduce fractions with exact arithmetic, GCD steps, and mixed numbers. View decimals and factor details. Export reports, compare forms, and learn faster every day.
| Input | Improper Form | Simplified Form | Mixed Form | Decimal |
|---|---|---|---|---|
| 8/12 | 8/12 | 2/3 | 2/3 | 0.666667 |
| 45/100 | 45/100 | 9/20 | 9/20 | 0.45 |
| 1 6/8 | 14/8 | 7/4 | 1 3/4 | 1.75 |
| -18/24 | -18/24 | -3/4 | -3/4 | -0.75 |
| 121/11 | 121/11 | 11 | 11 | 11 |
| 0/7 | 0/7 | 0 | 0 | 0 |
A fraction is simplified by dividing the numerator and denominator by their greatest common divisor. If the fraction is written as a mixed number, convert it to an improper fraction first.
Improper numerator: sign × ((|whole| × |denominator|) + |numerator|)
Greatest common divisor: gcd(a, b) = gcd(b, a mod b), with gcd(a, 0) = |a|
Simplified fraction: n′ = n / gcd(n, d), d′ = d / gcd(n, d)
Mixed number: whole = floor(|n′| / |d′|), remainder = |n′| mod |d′|
The calculator also shows the decimal value, percent value, equivalent fractions, and optional prime factor detail for both original and simplified values.
This calculator helps you reduce fractions into their lowest terms using exact integer arithmetic. It accepts standard fractions and mixed numbers, then converts everything into an improper fraction before simplification. That approach keeps the result mathematically consistent for whole numbers, negative fractions, and improper fractions.
The core method is the Euclidean algorithm. It finds the greatest common divisor quickly, even for large values. Once the divisor is known, the calculator divides both parts of the fraction by the same exact factor. Because both parts are reduced together, the simplified result preserves the original numeric value.
Advanced options make the tool more useful for study and checking work. You can keep the denominator positive, reveal the GCD steps, and inspect prime factor breakdowns. The equivalent fractions section is useful when comparing ratios or preparing classroom examples. Decimal and percent conversions add another way to confirm the result.
The result area appears directly below the header and above the form after submission. That placement makes it easier to review the answer without scrolling past other sections. The Plotly graph compares original and simplified numerators and denominators, giving a quick visual view of how far the fraction was reduced.
Export features are included for reporting and recordkeeping. The CSV option is suitable for spreadsheets, while the PDF option gives a compact text summary of the latest calculation. Together, these features make the page practical for homework, worksheets, tutoring sessions, and quick verification tasks.
It means reducing the numerator and denominator by their greatest common divisor. The new fraction has the same value, but uses the smallest whole-number terms possible.
Yes. Enter the whole part, numerator, and denominator. The calculator converts the mixed number to an improper fraction, then simplifies it and shows the mixed result again.
A fraction with denominator zero is undefined. The calculator checks for that case and shows an input error instead of returning an incorrect result.
The greatest common divisor is the largest factor shared by both numbers. Dividing by it removes every common factor in one step and guarantees the fraction is fully simplified.
Yes. It works with negative numerators, negative denominators, and negative mixed numbers. You can also choose to keep the denominator positive for a cleaner standard form.
Equivalent fractions help you compare forms that share the same value. They are useful for teaching, checking ratio scaling, and confirming that simplification did not change the fraction.
The graph compares the original numerator and denominator with the simplified numerator and denominator. It offers a quick visual snapshot of how much reduction occurred.
Yes. After you calculate, use the CSV button for spreadsheet-friendly output or the PDF button for a compact downloadable summary of the latest result.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.