To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). The result is an equivalent fraction in lowest terms. For example, 18/24 simplified is 3/4 because the GCF of 18 and 24 is 6. Use the free calculator below for instant step-by-step results with any fraction — including improper fractions, negative numbers, and large values.
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Step-by-Step Solution
How Do You Simplify a Fraction Step by Step?
Simplifying (or reducing) a fraction means rewriting it so the numerator and denominator are as small as possible while the fraction keeps the same value. The standard approach is the GCF method:
Find the Greatest Common Factor (GCF). The GCF is the largest number that divides evenly into both the numerator and the denominator. You can find it by listing factors or by using the GCF Calculator.
Divide both parts by the GCF. When you divide the numerator and the denominator by the same number, the value of the fraction stays the same, but the numbers get smaller.
Verify the result. The fraction is fully simplified when the only common factor between the new numerator and denominator is 1. For more detail, see How to Simplify Fractions.
What Does It Mean to Simplify a Fraction?
Every fraction has infinitely many equivalent forms. For example, 2/4, 3/6, and 50/100 all equal the same value — one half. Among all equivalent forms, the simplest is the one with the smallest possible whole-number numerator and denominator: 1/2.
Simplifying doesn't change what a fraction is worth; it just makes the numbers easier to read and work with. Teachers often require answers in simplified form, and standardized tests expect it. In real life, reduced fractions are simpler to compare, add, or convert to decimals.
What Are Some Examples of Simplifying Fractions?
Easy
Simplify 6/9
The GCF of 6 and 9 is 3. Divide both: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. Result: 2/3.
Easy
Simplify 15/25
The GCF of 15 and 25 is 5. Divide both: 15 ÷ 5 = 3 and 25 ÷ 5 = 5. Result: 3/5.
Medium
Simplify 48/64
The GCF of 48 and 64 is 16. Divide both: 48 ÷ 16 = 3 and 64 ÷ 16 = 4. Result: 3/4.
Larger Numbers
Simplify 126/210
Using the Euclidean algorithm: GCF = 42. Divide both: 126 ÷ 42 = 3 and 210 ÷ 42 = 5. Result: 3/5.
Common Questions About Simplifying Fractions
Simplifying a fraction means reducing it to lowest terms by dividing the numerator and denominator by their greatest common factor (GCF). The simplified version uses the smallest possible whole numbers while keeping the same value. For instance, 8/12 becomes 2/3 because the GCF of 8 and 12 is 4.
Yes. Improper fractions where the numerator is larger than the denominator are simplified the same way — divide both numbers by their GCF. For example, 18/12 simplifies to 3/2. You can then convert 3/2 to the mixed number 1½ if needed.
List every factor of each number and pick the largest one they share. Alternatively, use the Euclidean algorithm: divide the larger number by the smaller, take the remainder, and repeat until the remainder is zero. The last non-zero remainder is the GCF. Try our GCF Calculator for an instant answer.
Zero works as a numerator — any fraction with a zero numerator equals zero (for example, 0/7 = 0). However, zero cannot be a denominator because dividing by zero is mathematically undefined and produces no valid result.
No. A simplified fraction is equivalent to the original — it represents exactly the same amount. Simplifying only makes the numbers smaller and easier to work with. For example, 4/8 and 1/2 are the same value expressed in different terms.
There is no difference. "Simplify" and "reduce" mean the same thing when applied to fractions — both refer to dividing the numerator and denominator by their GCF to reach lowest terms. The terms are interchangeable in all math textbooks and standardized tests.
For large numbers, use the Euclidean algorithm instead of listing factors. Divide the larger number by the smaller, then divide the previous divisor by the remainder. Repeat until the remainder is zero. The last non-zero remainder is the GCF. For example, GCF(126, 210) = 42, so 126/210 simplifies to 3/5.
Yes. Simplify the fraction by ignoring the signs — find the GCF of the absolute values and divide both parts. Then place the negative sign in front of the numerator by convention. For example, −18/24 simplifies to −3/4 because the GCF of 18 and 24 is 6.
A fraction is fully simplified — also called "in lowest terms" — when the numerator and denominator share no common factor other than 1. If you can still find a number greater than 1 that divides evenly into both, the fraction can be reduced further.
The simplest form (or lowest terms) of a fraction is the version where the numerator and denominator are the smallest possible whole numbers that still represent the same value. You reach simplest form by dividing both by their greatest common factor. For example, the simplest form of 20/30 is 2/3.