How do you simplify a fraction?

Divide the numerator and denominator by their greatest common divisor. For 42/56 the GCD is 14, so cancelling 14 gives 3/4. The value stays the same.

How can I tell if a fraction is already in simplest form?

Its numerator and denominator have GCD 1. For example, 7/12 is already simplest. This tool reports that test separately from normalizing a negative denominator.

Can you simplify a fraction with negative numbers or zero?

Yes. A negative sign is kept on the numerator: 42/−56 becomes −3/4, and −42/−56 becomes 3/4. Zero over any nonzero denominator becomes 0/1. A zero denominator is undefined and is rejected.

How do you simplify a mixed number?

Enter its whole part and proper fraction part. For 2 and 2/6, convert to (2 × 6 + 2)/6 = 14/6, then simplify to 7/3 or 2 1/3. A negative whole part makes the entire mixed number negative.

How do you know whether a fraction gives a repeating decimal?

Reduce first, then remove factors of 2 and 5 from the denominator. If 1 remains, the decimal terminates; otherwise it repeats. Thus 3/4 = 0.75, while 1/6 = 0.1(6), where parentheses indicate the repeating digit. Very long expansions receive a clearly marked preview limit.

Sumivo · Mathematics

Fraction Simplifier

Reduce one fraction to lowest terms. For a mixed number, add a whole part and a nonnegative proper fraction with positive denominator; the whole-part sign applies to the entire value (−2 and 1/3 means −7/3). For adding two fractions, use the Fraction Calculator linked below.

01 / inputs

Numerator

integer

Denominator (nonzero)

integer

Whole part (optional mixed number)

integer

02 / result

FRACTION IN LOWEST TERMS

3/4

Greatest common divisor: 14
Mixed number: 3/4
Exact decimal (parentheses repeat): 0.75
Decimal type: terminating
Already simplest?: No

Calculation trace

42 = 0 × 56 + 42
Euclid step 1
56 = 1 × 42 + 14
Euclid step 2
42 = 3 × 14 + 0
Euclid step 3
(14 × 3) / (14 × 4) = 3/4
Factor and cancel the greatest common divisor
4 = 2^2 × 5^0 × 1; terminating decimal
Classify the reduced denominator

Divide numerator and denominator by their positive GCD 14. The reduced denominator has no prime factors other than 2 and 5 (or equals 1), so its decimal terminates. Parentheses mark a complete repeating block when found. A mixed-number minus sign applies to the entire value.

How it works

An optional mixed number is converted to an improper fraction first. A negative denominator is moved to the numerator. Euclid’s algorithm repeatedly divides with remainder to find the positive greatest common divisor; dividing both terms by that GCD gives lowest terms. The factor-cancellation step shows the common factor explicitly. A reduced denominator with only factors 2 and 5 (or denominator 1) gives a terminating decimal; any remaining factor means it repeats. Exact long division tracks remainders to identify the repeating block, shown in parentheses. Quotient and remainder also give a mixed-number form.

Assumptions & limits

Single fractions accept signed integer numerators and nonzero signed integer denominators. Each field is limited to 1024 characters and 1000 digits; decimal points, E notation and expressions are rejected. Exact integer arithmetic preserves values beyond 2^53.
For mixed input, the fraction part must have a nonnegative numerator smaller than a positive denominator. Put the sign on the whole part: −2 with 1/3 means −(2 + 1/3) = −7/3. Use -0 with 1/2 for −1/2. Blank whole part means a single fraction.
Zero simplifies to 0/1 because gcd(0, d) = |d|. Already simplest means the input fraction, or converted improper fraction, has GCD 1; moving a denominator sign does not change this test.
The decimal preview is limited to 2000 fractional digits. An ellipsis marks an incomplete unrounded preview; the exact fraction and terminating/repeating classification remain valid. Parentheses are used only after a complete cycle is detected. At most 64 Euclid trace iterations are displayed; all iterations are computed and any omitted trace is disclosed.
This tool simplifies one fraction. The related Fraction Calculator adds two fractions and simplifies their sum; use that page for addition.

FAQ

How do you simplify a fraction?: Divide the numerator and denominator by their greatest common divisor. For 42/56 the GCD is 14, so cancelling 14 gives 3/4. The value stays the same.
How can I tell if a fraction is already in simplest form?: Its numerator and denominator have GCD 1. For example, 7/12 is already simplest. This tool reports that test separately from normalizing a negative denominator.
Can you simplify a fraction with negative numbers or zero?: Yes. A negative sign is kept on the numerator: 42/−56 becomes −3/4, and −42/−56 becomes 3/4. Zero over any nonzero denominator becomes 0/1. A zero denominator is undefined and is rejected.
How do you simplify a mixed number?: Enter its whole part and proper fraction part. For 2 and 2/6, convert to (2 × 6 + 2)/6 = 14/6, then simplify to 7/3 or 2 1/3. A negative whole part makes the entire mixed number negative.
How do you know whether a fraction gives a repeating decimal?: Reduce first, then remove factors of 2 and 5 from the denominator. If 1 remains, the decimal terminates; otherwise it repeats. Thus 3/4 = 0.75, while 1/6 = 0.1(6), where parentheses indicate the repeating digit. Very long expansions receive a clearly marked preview limit.

Related calculators

SOURCES

OpenStax, Rice University
Prealgebra 2e — 4.2 Multiply and Divide Fractions ↗
Section 4.2, Simplify Fractions: cancel common factors to obtain a fraction with no common factor other than 1. The exact Euclid implementation and display limits are calculator choices.
Accessed 2026-10-02
OpenStax, Rice University
Prealgebra 2e — 4.1 Visualize Fractions ↗
Section 4.1, Visualize Fractions: nonzero denominators, equivalent fractions, and conversion between improper fractions and mixed numbers. Signed mixed-input conventions are explicitly stated in this tool.
Accessed 2026-10-02