Lowest Terms Fraction Calculator
Reduce any fraction to its simplest form. See the greatest common divisor with every Euclidean algorithm step, the mixed-number form, and the decimal value.
Euclidean algorithm steps
| a | = | b | × | q | + | r |
|---|
The last non-zero remainder is the GCD. Dividing numerator and denominator by it gives the fraction in lowest terms.
Worked examples
Example 1: 4/8
8 = 4 × 2 + 0GCD(4, 8) = 4
Answer: 1/2
Divide 4 and 8 by their GCD 4.
Example 2: 12/18
18 = 12 × 1 + 612 = 6 × 2 + 0GCD(12, 18) = 6
Answer: 2/3
Divide 12 and 18 by their GCD 6.
Example 3: 7/3
7 = 3 × 2 + 13 = 1 × 3 + 0GCD(7, 3) = 1
Answer: 2 1/3
Already in lowest terms (GCD 1); shown as mixed number.
Example 4: -4/8
Work with |−4| and |8|: 8 = 4 × 2 + 0GCD(4, 8) = 4
Answer: -1/2
Sign stays on the numerator; only 4 and 8 are divided.
How it works
Reducing a fraction means dividing both the numerator and the denominator by their greatest common divisor (GCD) — the largest whole number that divides both. The calculator finds the GCD with the Euclidean algorithm: divide the larger number by the smaller one and keep the remainder, then repeat using the previous divisor and the remainder, until a remainder of 0 appears. The last non-zero remainder is the GCD.
What this tool is (and is not)
This tool simplifies fractions: 12/18 → 2/3. It does not do arithmetic with fractions (addition, subtraction, multiplication) — for that use the fraction calculator. It does not convert fractions to decimals as its main job — for that use the fraction-to-decimal converter. It does not sort lists of fractions — for that use the least-to-greatest fractions sorter.
Frequently asked questions
What does it mean to reduce a fraction to lowest terms?
How does the Euclidean algorithm find the greatest common divisor?
How do you simplify 12/18 step by step?
Can a fraction with a negative sign be reduced to lowest terms?
Why does this calculator reject a denominator of zero?
What is the difference between simplifying a fraction and converting it to a decimal?
How do I read a mixed-number answer like 2 1/3?
When is a fraction already in lowest terms?
Free tool by NRTechStudio