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Simplify Fractions Calculator

Simplify fractions online — free and step by step. Enter a numerator and denominator and the calculator divides by the greatest common divisor down to lowest terms.

Quick answer
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. Example: 18/24 — the GCD of 18 and 24 is 6, so 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4. Keep dividing until the numerator and denominator share no common factor other than 1.
The tool

Enter values — get full working

Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Simplify a fraction — 4 steps

Worked through “18/24”
  1. 1
    Step 1 of 4

    Write the numerator and denominator

    Write the fraction, e.g. 18/24. Numerator on top (18), denominator below (24).

  2. 2
    Step 2 of 4

    Find the greatest common divisor

    Look for the largest number that divides both 18 and 24. 18 = 2·3·3, 24 = 2·2·2·3, so the shared part is 2·3 = 6. The GCD is 6.

  3. 3
    Step 3 of 4

    Divide both by the GCD

    18 ÷ 6 = 3 and 24 ÷ 6 = 4. Always divide both by the same number, or the value changes.

  4. 4
    Step 4 of 4

    Check the result

    The reduced fraction is 3/4. Do 3 and 4 share a factor? No — done. 3/4 is in lowest terms.

Examples

Simplifying fractions — worked examples

Typical problems using the greatest common divisor
18/24
GCD(18, 24) = 6
18 ÷ 6 = 3
24 ÷ 6 = 4
3/4
12/16
GCD(12, 16) = 4
12 ÷ 4 = 3
16 ÷ 4 = 4
3/4
45/60
GCD(45, 60) = 15
45 ÷ 15 = 3
60 ÷ 15 = 4
3/4
7/14
GCD(7, 14) = 7
7 ÷ 7 = 1
14 ÷ 7 = 2
1/2
100/35
GCD(100, 35) = 5
100 ÷ 5 = 20
35 ÷ 5 = 7
20/7
9/28
GCD(9, 28) = 1
coprime
can’t reduce
9/28
Theory

What does “simplifying a fraction” mean?

Simplifying a fraction means dividing the numerator and denominator by the same number without changing the fraction’s value. 3/4 and 18/24 represent the same portion — they are equivalent. The simplified fraction is the cleanest way to write that value. The key is the greatest common divisor (GCD): dividing numerator and denominator by their GCD reduces the fraction to lowest terms in a single step. You can find the GCD by prime factorisation (picking out shared factors) or with the Euclidean algorithm (repeated division with remainder). A fraction is fully reduced when its numerator and denominator are coprime — sharing only 1 as a common divisor. Simplifying is the foundation for adding and comparing fractions and is part of the curriculum from grade 5–6 onward.

Pitfalls

Common mistakes when simplifying

Dividing only the numerator or only the denominator

Both must be divided by the same number. 18/24 becomes 3/4, not 3/24.

Cancelling across a plus sign

In (a + b)/c you can’t just cancel a and c. You cancel factors, never terms in a sum.

Not fully reduced

12/16 divided by 2 gives 6/8 — that still reduces. Using the GCD (4) lands directly on 3/4.

Confusing GCD with LCM

Simplifying needs the greatest common divisor, not the least common multiple (that’s for adding).
FAQ

Frequently asked questions about simplifying fractions

Glossary

Glossary — key terms explained simply

Numerator
The top number of a fraction.
Denominator
The bottom number of a fraction.
Greatest common divisor (GCD)
The largest number that divides two numbers with no remainder.
Coprime
Two numbers sharing no common factor other than 1.
Equivalent
Fractions with the same value, e.g. 3/4 = 18/24.
Lowest terms
A fraction that can’t be reduced any further.