Simplify Fractions Calculator
Reduce any fraction to its lowest terms — with prime factorisation steps shown.
Step by step calculations
Enter a fraction in the calculator to see the step by step calculations.
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Simplify Fractions Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Why simplifying matters in practice
A survey reports 120 out of 360 people preferred a product. Writing 120/360 is clunky — simplifying to ⅓ tells the story instantly. A recipe uses 6 out of 8 tablespoons of sugar — that's ¾ of the recommended amount. Probability of rain: 15/20 = ¾. Simplified fractions communicate clearly; unsimplified ones hide the pattern.
Worked example
"Simplify 18/24."
Step 1: Find GCD(18, 24)
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
GCD = 6
Step 2: 18 ÷ 6 = 3, 24 ÷ 6 = 4
Result: 3/4
Verify: 3/4 × 6/6 = 18/24 ✓
Common mistake to avoid
- ✗ Dividing by a common factor instead of the GCD: 18/24 ÷ 2 = 9/12, which is correct but not fully simplified. You'd need to divide again (by 3) to reach 3/4. Finding the GCD first does it in one step.
What does 'simplify a fraction' mean?
Simplifying a fraction means writing it in its simplest form, also known as reducing it to its lowest terms. This is when the numerator (top number) and the denominator (bottom number) have no common factors other than 1.
For example, the fraction 2/4 can be simplified to 1/2 because both 2 and 4 can be divided by 2. The fraction 1/2 cannot be simplified further because 1 and 2 only share 1 as a common factor.
How to simplify a fraction using prime factorisation
Find the prime factors of the numerator
Break down the numerator into its prime factors. Prime factors are prime numbers that multiply together to give the original number (e.g., the prime factors of 12 are 2 × 2 × 3).
Find the prime factors of the denominator
Do the same for the denominator, breaking it down into its prime factors.
Identify common prime factors and find the HCF
Look for any prime factors that appear in both the numerator's list and the denominator's list. Multiply these common prime factors together to find the Highest Common Factor (HCF).
Divide both by the HCF
Divide both the original numerator and the original denominator by the HCF you found in Step 3. This will give you the fraction in its simplest form.
Convert to a mixed number (if improper)
If your simplified fraction is an improper fraction (where the numerator is larger than the denominator), you can convert it into a mixed number (a whole number and a proper fraction).
Common mistakes to avoid
- Simplifying 10/15 to 5/10:You must divide both the numerator and the denominator by the same number. Here, it looks like 5 was subtracted from both, or the numerator was divided by 2 and the denominator by 1. The HCF of 10 and 15 is 5. 10/15 = 2/3 (divide both by 5)
- Simplifying 12/18 to 6/9:While 12 and 18 are both divisible by 2 (giving 6/9), 6 and 9 still share a common factor (3). You need to divide by the Highest Common Factor (HCF) to simplify in one step, or keep dividing until no common factors remain. 12/18 = 2/3 (HCF of 12 and 18 is 6)
- Simplifying 20/30 by just cancelling out the '0's to get 2/3:While cancelling zeros works here, it's a shortcut for dividing by 10. The proper method is to find the HCF (which is 10) and divide both by it. Relying on 'cancelling zeros' can lead to errors in other situations (e.g., 21/31 cannot be simplified by 'cancelling 1s'). 20/30 = 2/3 (HCF of 20 and 30 is 10)