➗ Fraction Simplifier: Reduce Fractions to Lowest Terms

What is the Fraction Simplifier?

Simplifying a fraction means rewriting it with the smallest whole numbers that still represent the same value. The value never changes, only the way it is written: 18/24, 9/12, 6/8, and 3/4 are all the same amount, but 3/4 is the tidiest way to write it. A fraction simplifier reaches that tidy form by finding the greatest common divisor (GCD, also called the greatest common factor or GCF) of the top and bottom numbers and dividing both by it. Because 18 and 24 share a greatest common divisor of 6, dividing each by 6 turns 18/24 straight into 3/4 in a single step. Every fraction has infinitely many equivalent forms but only one simplest form, which is why teachers ask for it: it gives one canonical answer everyone can agree on.

The reliable way to find the greatest common divisor is the Euclidean algorithm, which is what this fraction simplifier uses under the hood. You repeatedly replace the larger number with the remainder of dividing it by the smaller number until the remainder is 0, and the last non-zero value is the GCD. For 18 and 24 that is 6, for 45 and 60 it is 15, and for 17 and 5 it is 1. When the GCD comes out as 1, the two numbers share no common factor and the fraction is already in its lowest terms, so nothing needs to change. The tool flags this case explicitly so you are never left wondering whether it did anything.

There is a second method worth knowing, because many worksheets teach it first: prime factorization. You break the numerator and denominator into their prime factors, cancel every factor that appears on both the top and the bottom, then multiply what is left. For 18/24 you write 18 as 2 times 3 times 3 and 24 as 2 times 2 times 2 times 3. The top and bottom share one 2 and one 3, so you cancel those, leaving 3 on top and 2 times 2 = 4 on the bottom, which is 3/4 again. Prime factorization and the GCD method always give the same answer; the GCD route is faster for big numbers, while factoring makes the shared factors visible, which helps when you are learning. You can also just divide by any common factor you spot and repeat until nothing divides evenly, but that takes more steps than dividing by the full GCD once.

Signs and improper fractions are the two details that trip people up, so this simplify fractions tool handles both. When either number is negative, it works with the absolute values to find the GCD, then places a single sign on the numerator and keeps the denominator positive, which is the standard convention. So -45/60 becomes -3/4, not 3/-4. When the fraction is top-heavy, meaning the numerator is at least as large as the denominator, it also shows the mixed number. The improper fraction 17/5 stays as 17/5 in lowest terms, but it also equals the mixed number 3 and 2/5, and both forms are displayed so you can copy whichever one your task needs.

Everything runs in your browser with exact integer arithmetic, so there is no rounding error and no data leaves your device. Alongside the reduced fraction the tool gives the decimal (3/4 = 0.75) and the percentage (75 percent), because those are the forms you often need next. A fraction simplifier is useful far beyond homework: cooks scale recipes, woodworkers and sewers read tape-measure fractions of an inch, engineers reduce ratios, and students check that a reduced answer matches the expected simplest form. Whatever the reason, reducing a fraction to lowest terms is always the same two moves, find the greatest common divisor and divide, and this reduce fractions tool shows both moves every time.

When to use it

• Reducing a homework answer like 18/24 to its simplest form 3/4 to match the expected worksheet result.
• Simplifying a tape-measure fraction such as 6/8 of an inch down to 3/4 for woodworking or sewing.
• Turning an improper fraction like 17/5 into the mixed number 3 and 2/5 for a recipe or a report.
• Checking whether a fraction such as 7/9 is already in lowest terms before writing it into a final answer.
• Simplifying a negative fraction like -45/60 to -3/4 while keeping the sign in the correct place.
• Teaching the greatest-common-divisor and prime-factorization steps so a student can see exactly how a fraction is reduced.

How to use the Fraction Simplifier

1. Type the numerator (the top number) into the first box, for example 18.
2. Type the denominator (the bottom number) into the second box, for example 24.
3. Read off the simplest form, the GCD used, the decimal value, the percentage, and the mixed number when the fraction is improper.
4. Use the sample buttons for quick examples, or Clear to start again. Negative numbers are allowed.
5. Press Copy to grab the reduced fraction for your notes, homework, or spreadsheet.

Formula & method

Worked examples

Common fractions and their simplest form (with the GCD used)

Tape-measure inch fractions reduced to simplest form

Improper fractions in lowest terms and their mixed numbers

Common mistakes to avoid

• Dividing by a common factor that is not the greatest one. Dividing 18/24 by 2 gives 9/12, which is smaller but still not finished, because 9 and 12 share another factor of 3. Simplifying in one clean step means dividing by the greatest common divisor, which is 6, to reach 3/4 directly. If you divide by a smaller factor, just keep going until nothing divides evenly.
• Thinking the value changes when you simplify. Reducing a fraction never changes its value, only how it looks. 18/24 and 3/4 are exactly the same amount, which is why both give the decimal 0.75. Simplifying is a rewrite, not a recalculation.
• Trying to cancel across addition instead of factors. You can only cancel factors that multiply the whole top and the whole bottom. In (2 + 4)/8 you cannot cancel the 2 or the 4 on their own; you must first add to get 6/8, then reduce to 3/4. Canceling parts of a sum is one of the most common fraction errors.
• Putting the minus sign on the denominator. The standard form keeps the denominator positive and puts a single sign on the numerator. So -45/60 should be written -3/4, not 3/-4 or -3/-4. Mixing sign positions can flip the value or make the fraction hard to read.
• Forgetting to give the mixed number for an improper fraction. An improper fraction like 17/5 is a perfectly valid answer in lowest terms, but many worksheets and recipes want the mixed number 3 and 2/5 instead. Simplest form and mixed number are two different requests, so check which one the task actually needs.
• Stopping before the fraction is fully reduced. A fraction is only in lowest terms when the numerator and denominator share no common factor except 1. 6/8 looks simpler than 12/16 but it is still not finished, because 6 and 8 both divide by 2. Always confirm the GCD is 1 before calling it done.

Glossary

Numerator

The top number of a fraction, showing how many parts you have.

Denominator

The bottom number of a fraction, showing how many equal parts make up one whole.

Greatest common divisor

The largest whole number that divides two numbers exactly, also called the greatest common factor (GCF). Dividing both parts of a fraction by it gives the lowest terms.

Lowest terms

A fraction in which the numerator and denominator share no common factor other than 1, such as 3/4. Also called simplest form or an irreducible fraction.

Prime factorization

Writing a number as a product of prime numbers, such as 24 = 2 x 2 x 2 x 3, used to spot the factors two numbers share.

Equivalent fractions

Different fractions that represent the same value, such as 3/4, 6/8, and 9/12, all found by multiplying or dividing top and bottom by the same number.

Improper fraction

A fraction whose numerator is at least as large as its denominator, such as 17/5, which is worth 1 or more.

Mixed number

A whole number written next to a proper fraction, such as 3 and 2/5, used to express an improper fraction.

Frequently asked questions

Sources

• Euclidean algorithm , Wikipedia
• Irreducible fraction , Wikipedia
• Greatest common divisor , Wikipedia