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Fraction Simplifier — reduce to lowest terms

Reduce any fraction to its simplest form using the GCD. See the step-by-step working, a visual bar comparison, the decimal and mixed-number forms, and an AI explanation of why it works.

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Fraction Simplifier

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Quick answer

What does it mean to simplify a fraction?

Simplifying a fraction means dividing the numerator and denominator by their Greatest Common Divisor (GCD) until they share no common factor. For example, 18/24 simplifies to 3/4 because gcd(18, 24) = 6. The simplified fraction has exactly the same value — just smaller numbers.

Why this tool

Simplify with understanding

The bar diagram shows the original and reduced fractions are the same size — only the pieces differ.

One-step GCD method

We divide top and bottom by their GCD, the fastest route to lowest terms.

Visual bar comparison

Two bars prove the original and simplified fractions represent the same value.

Decimal & mixed forms

Get the decimal value and, where relevant, the mixed-number form too.

How it works

Simplify in three steps

Enter the fraction

Type a numerator and denominator, e.g. 18/24.

We find the GCD

The Greatest Common Divisor of both numbers is computed instantly.

Read the simplest form

Get the reduced fraction, decimal, mixed number, bars and AI insight.

Worked examples

Fraction simplifying examples

Tap any row to load it into the calculator.

Fraction	Simplest form	GCD
18/24	3/4	6
45/60	3/4	15
8/12	2/3	4
7/13	7/13	1 (already)
144/60	12/5	12
50/100	1/2	50
4/8	1/2	4
6/9	2/3	3
12/16	3/4	4
9/12	3/4	3
25/100	1/4	25

How to simplify a fraction

To reduce a fraction to lowest terms, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. The result has no common factor left, so it cannot be reduced further.

Worked example: 18/24

gcd(18, 24) = 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Both fractions equal 0.75 — the value never changes, only the representation.

Why dividing by the GCD works

Dividing the top and bottom by the same number is the same as multiplying the fraction by 1 (e.g. by 6/6), so its value is preserved. Using the greatest common divisor gets you to lowest terms in a single step.

A fraction is already in lowest terms when its numerator and denominator are coprime (GCD = 1), like 7/13.

Where simplifying fractions helps

Adding and comparing fractions with cleaner numbers.
Cooking and recipe scaling.
Gear, scale and aspect ratios.

FAQ

Frequently asked questions

How do you simplify a fraction?

Divide the numerator and denominator by their Greatest Common Divisor (GCD). For 18/24, the GCD is 6, so it reduces to 3/4.

What is the simplest form of a fraction?

A fraction is in simplest form when the numerator and denominator have no common factor other than 1 — that is, their GCD is 1.

Does simplifying change the value of a fraction?

No. Simplifying only changes how the fraction looks; 18/24 and 3/4 are exactly equal (both 0.75).

How do I convert to a mixed number?

Divide the numerator by the denominator: the whole-number quotient is the integer part and the remainder over the denominator is the fraction. The tool shows this automatically.

Can I simplify an improper fraction?

Yes. Improper fractions (like 144/60) simplify the same way and the tool also shows the mixed-number form, e.g. 2 2/5.

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