Simplify a fraction to its lowest terms, or convert a fraction — including mixed numbers like 3 3/8 — to its decimal value.
24/36 is divided by its greatest common divisor (12) to reach the simplest form 2/3.
Fractions represent a part of a whole using a numerator (top number) and denominator (bottom number). Adding, subtracting, multiplying, and dividing fractions each follow distinct rules, and results are typically simplified to their lowest terms for clarity.
The Greatest Common Divisor (GCD) is the largest number that divides both numerator and denominator evenly. For example, 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6.
| Operation | Example | Result |
|---|---|---|
| Addition | 1/4 + 1/6 | 5/12 |
| Subtraction | 3/4 − 1/3 | 5/12 |
| Multiplication | 2/3 × 3/5 | 2/5 |
| Division | 2/3 ÷ 4/9 | 3/2 |
Fractions can only be directly added or subtracted once they share the same denominator, since the denominator defines the "size" of each part being counted. Using the Least Common Multiple (LCM) of the denominators keeps the resulting numbers as small as possible before simplifying.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.3% |
| 3/4 | 0.75 | 75% |
| 5/8 | 0.625 | 62.5% |
To convert a fraction to a decimal, divide the numerator by the denominator; to convert a decimal to a percentage, multiply by 100.
| Mixed number | Decimal |
|---|---|
| 3 3/8 | 3.375 |
| 8 5/8 | 8.625 |
| 4 3/4 | 4.75 |
| 5 5/8 | 5.625 |
| 2/3 | 0.6667 |
Enter the whole number, numerator, and denominator above (leave "Whole" blank for a simple fraction) to convert any mixed number to its decimal value.
Why do I need a common denominator to add fractions but not to multiply them? Addition combines like-sized parts, which requires equal denominators; multiplication scales both numerator and denominator directly, so no common base is needed.
Why simplify a fraction at all? A simplified fraction is easier to interpret and compare, and it's the conventional way to express a final answer.
How do I divide by a fraction? Dividing by a fraction is the same as multiplying by its reciprocal (flipping numerator and denominator).
How do I add a mixed number and a fraction? Convert the mixed number to an improper fraction first (multiply the whole number by the denominator and add the numerator), then apply the normal addition rule with a common denominator.
What's the difference between the LCM and just multiplying the denominators? Multiplying denominators always works but can produce larger numbers than necessary; using the Least Common Multiple keeps the intermediate numbers smaller and easier to simplify.
Can a fraction have a negative numerator or denominator? Yes — a negative sign can sit on the numerator, denominator, or in front of the whole fraction; all three represent the same negative value, though convention usually places the sign on the numerator or in front.
How do repeating decimals convert back to fractions? A repeating decimal like 0.333... converts to a fraction (1/3 in this case) using algebraic methods that isolate and cancel the repeating part — a distinct process from simple terminating-decimal conversion.
What is 3 3/8 as a decimal? 3.375 — divide 3 by 8 to get 0.375, then add the whole number 3.
What is 8 5/8 in decimal form? 8.625 — 5 divided by 8 is 0.625, added to the whole number 8.
What is 4 3/4 as a decimal, and what is 5 5/8 as a decimal? 4 3/4 equals 4.75, and 5 5/8 equals 5.625.
18/24 has a greatest common divisor of 6 (since 18 = 6×3 and 24 = 6×4), so it simplifies to 3/4 — dividing both numerator and denominator by their GCD always produces the simplest equivalent fraction.
Numerator: The top number of a fraction, representing the number of parts.
Denominator: The bottom number of a fraction, representing the total number of equal parts.
Greatest common divisor (GCD): The largest number that evenly divides both the numerator and denominator.
How is the GCD found?
This calculator uses the Euclidean algorithm, a fast method of repeated division that finds the greatest common divisor of two numbers.