Simplifying a fraction means writing it in its lowest terms — the smallest numerator and denominator that represent exactly the same value. A fraction like 6/9 and its simplified form 2/3 are equivalent fractions: they describe the same amount, just written differently. Simplified fractions are easier to read, easier to compare, and are expected in math class.
There are two reliable methods for simplifying fractions. Both work — the one you choose depends on the numbers involved.
Method 1: Divide by Any Common Factor (Step by Step)
This method is good when you can spot a shared factor quickly, even if it's not the largest one. You keep dividing until there's nothing left to divide.
The rule: divide the numerator (top number) and denominator (bottom number) by the same whole number. Repeat until the only shared factor is 1.
12/30 = 2/5
This approach works well when the numbers are large and a smaller factor (like 2, 3, or 5) is obvious. The downside is that it takes a few more steps.
Method 2: Divide by the GCF (One Step)
The fastest way to simplify a fraction in one move is to find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by it. The GCF is the largest number that divides evenly into both.
How to find the GCF
List all the factors of each number, then find the largest one they share.
36/48 = 3/4
This is the same calculation your calculator uses. See it in action on the 36 ÷ 4 and 48 ÷ 4 pages — you're essentially dividing both parts of the fraction by the same number.
After simplifying, verify your answer: the GCF of the new numerator and denominator should be 1. If there's still a shared factor greater than 1, the fraction isn't fully reduced yet.
Which Method Should You Use?
| Method | Best for | Trade-off |
|---|---|---|
| Step-by-step (any factor) | Large numbers where a small factor (2, 5, 10) is obvious | Takes multiple steps |
| GCF method (one step) | Smaller numbers where listing factors is quick | Finding the GCF takes more upfront work |
In practice, most people use a mix of both: spot a small common factor, divide once or twice, then check if they've fully reduced. Either way, you reach the same answer.
Worked Examples
8/24 = 1/3
100/10 = 10/1 = 10 (a whole number)
When the denominator simplifies to 1, the fraction becomes a whole number. This makes sense: if 10 equal parts make up the whole, and you have all 10, you have 1 complete whole.
54/6 = 9
Try this calculation on our 54 ÷ 6 calculator to see the division behind the simplification.
Simplifying Improper Fractions
An improper fraction has a numerator larger than its denominator — for example, 18/12 or 72/8. The simplification process is identical: find the GCF and divide both numbers by it.
72/8 = 9
Once simplified, an improper fraction can also be converted to a mixed number by dividing the numerator by the denominator. The quotient is the whole number, and any remainder becomes the new numerator. For a step-by-step look at what remainders mean, see our guide on understanding remainders in division.
A Real-World Example
Imagine you cut a pizza into 12 slices and eat 8 of them. You ate 8/12 of the pizza. That's technically correct — but 2/3 is much clearer and easier to visualise. To simplify: the GCF of 8 and 12 is 4, so 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving you 2/3.
The pizza is the same pizza. You ate the same amount. Simplifying just makes it easier to communicate.
Three Things That Cannot Be Simplified
Not every fraction can be reduced. A fraction is already in its simplest form when:
1. The GCF is already 1. For example, 7/10 — the factors of 7 are just 1 and 7, and 10 is not divisible by 7. Nothing to cancel.
2. The numerator is 1. A fraction like 1/8 cannot be reduced further because 1 shares no factors with any other number except 1.
3. Both numbers are prime. If both the numerator and denominator are prime numbers and they are different, the fraction is already in lowest terms. For example, 3/7 — 3 and 7 are both prime and not equal, so no simplification is possible.
Understanding divisibility helps here. If you know the divisibility rules, you can quickly rule out common factors like 2, 3, 5, and 9 without doing any division.