Fraction Simplifier & Mixed Number Converter

Q: How are the simplification steps generated?

The calculator logs the Euclidean algorithm: we compute gcd(|a|,|b|) with repeated division, then show how a/b becomes (a/g)/(b/g).

Q: Can I convert negative mixed numbers?

Yes. Toggle To Improper, enter the sign, whole part, remainder, and denominator; the sign is moved to the numerator and the denominator stays positive.

Q: What fraction format should I enter first?

Enter the numerator and denominator for a simple fraction, or switch to mixed-number mode when you have a whole part plus a remainder. Keep the denominator positive for the clearest steps.

Q: Why do other tools show an improper fraction or mixed number differently?

Some tools keep improper fractions, while others convert to mixed numbers automatically. Compare the reduced numerator and denominator first, then choose the display form your assignment requires.

Q: Are the decimal values exact?

Fraction reduction uses exact integer arithmetic. Decimal views are rounded only for display, so use the reduced fraction when you need an exact answer.

Fraction input

Numerator (a)

Denominator (b)

Mixed number input

Sign

Whole part (w)

Remainder (r)

Denominator (b)

Click "To Improper" for mixed-number inputs. Ensure 0 ≤ remainder < denominator.

Embed this calculator

Show steps Teacher mode

This calculator is provided for educational guidance only.

Static example before you calculate

This example is visible before the result area updates. It does not press a button or change the current inputs.

Simplify example: 8/12 has greatest common divisor 4, so it reduces to 2/3.
Mixed-number example: 1 3/4 converts to the improper fraction 7/4.
Reading the result: check the GCD first, then compare the simplified fraction, mixed form, decimal, and LaTeX output.

Results

Simplified: 2/3

Mixed form: 2/3

GCD: 4

Decimal: 0.666667

LaTeX: \frac{2}{3}

Steps

Start gcd(|8|, |12|).
12 = 8 × 1 + 4
8 = 4 × 2 + 0
gcd = 4.
Reduce: 8/12 = 2/3.

Visualization

Pie representation

Number line representation

FAQ

How are the simplification steps generated?

The calculator logs the Euclidean algorithm: we compute gcd(|a|,|b|) with repeated division, then show how a/b becomes (a/g)/(b/g).

Can I convert negative mixed numbers?

Yes. Toggle To Improper, enter the sign, whole part, remainder, and denominator; the sign is moved to the numerator and the denominator stays positive.

What fraction format should I enter first?

Enter the numerator and denominator for a simple fraction, or switch to mixed-number mode when you have a whole part plus a remainder. Keep the denominator positive for the clearest steps.

Why do other tools show an improper fraction or mixed number differently?

Some tools keep improper fractions, while others convert to mixed numbers automatically. Compare the reduced numerator and denominator first, then choose the display form your assignment requires.

Are the decimal values exact?

Fraction reduction uses exact integer arithmetic. Decimal views are rounded only for display, so use the reduced fraction when you need an exact answer.

Fraction simplification notes

Reduction method

The calculator finds the greatest common divisor of the numerator and denominator, then divides both parts by that same value.

Mixed and improper forms

A mixed number is easier to read for many classroom answers. An improper fraction is often better for algebra, multiplication, and spreadsheet work.

Negative fractions

The sign belongs on the whole value, not separately on both numerator and denominator. The calculator normalizes the sign so equivalent fractions stay comparable.

Common mistakes

Do not round the decimal and then rebuild a fraction from that rounded value. Reduce the exact numerator and denominator first.

Checking answers

Multiply the reduced numerator and denominator by the same common factor to confirm it returns to the original fraction.