To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). For 18/24, the GCF is 6, so 18/24 = 3/4. A fraction is in simplest form, or lowest terms, when the top and bottom share no common factor except 1.
In short: Find the greatest common factor of the top and bottom, divide both by it, and you are done in one step. You can also divide by small common factors (2, 3, 5…) again and again until none is left.
In this guide
Simplify With the Greatest Common Factor
- List the factors of both numbers. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- Pick the greatest one they share: 6.
- Divide the top and bottom by it: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4.
Simplifying does not change the value. 6/8 and 3/4 are equivalent fractions; the simplified one just uses fewer, bigger pieces.
Divide in Small Steps
If you cannot see the GCF straight away, divide by any common factor, then check again.
Example: 45/60: both end in 0 or 5, so divide by 5 to get 9/12. Both are divisible by 3, so divide again: 3/4. (The GCF of 45 and 60 is 15, and 45 ÷ 15 = 3, 60 ÷ 15 = 4.)
Quick checks for common factors: both even → divide by 2; digits of both add up to a multiple of 3 → divide by 3; both end in 0 or 5 → divide by 5.
How to Simplify Big Fractions
For large numbers, use the Euclidean method: divide the bigger number by the smaller and keep the remainder, then repeat until the remainder is 0. The last divisor is the GCF.
Example: 84/126: 126 ÷ 84 = 1 remainder 42, then 84 ÷ 42 = 2 remainder 0. The GCF is 42, so 84/126 = 2/3.
Simplifying Mixed Numbers and Improper Fractions
Simplify only the fraction part of a mixed number: 3 6/8 = 3 3/4. An improper fraction simplifies the same way as any other: 10/4 = 5/2 = 2 1/2.
Common Examples
| Fraction | GCF | Simplest form |
|---|---|---|
| 6/8 | 2 | 3/4 |
| 12/16 | 4 | 3/4 |
| 18/24 | 6 | 3/4 |
| 45/60 | 15 | 3/4 |
| 84/126 | 42 | 2/3 |
| 10/4 | 2 | 5/2 = 2 1/2 |
Try it
Type any fraction, such as 84/126, and the calculator shows the GCF and the simplest form.
FAQ
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For 18/24 the GCF is 6, so 18/24 = 3/4.
How do you know a fraction is in simplest form?
It is in simplest form when the top and bottom have no common factor other than 1, such as 3/4 or 5/6.
How do you simplify a big fraction?
Find the GCF with the Euclidean method: divide the larger number by the smaller, keep the remainder and repeat. For 84/126 the GCF is 42, giving 2/3.
Does simplifying change the value of a fraction?
No. A simplified fraction is equivalent to the original. 6/8 and 3/4 are the same amount.
What is 12/16 in simplest form?
The GCF of 12 and 16 is 4, so 12/16 = 3/4.
Sources and Further Reading
- OpenStax, Prealgebra 2e, Section 4.2: Multiply and Divide Fractions (equivalent fractions and simplifying), Rice University.
More fraction guides: Mixed numbers and improper fractions, How to add fractions, Fraction, decimal and percent chart, How to do fractions on a calculator. Or check any answer with the fraction calculator.
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