Simplify Fractions Calculator

How to use the simplify fractions calculator

1. Enter the numerator and denominator. Negative numerators are fine: −18/24 simplifies to −3/4. Improper fractions such as 56/32 work too.
2. Read the simplest form. The note underneath names the greatest common factor the calculator divided by.
3. Optionally enter a target denominator. This is the box to use when you need a common denominator to add fractions, or when a worksheet asks for “an equivalent fraction with a denominator of 21.” If no whole-number numerator fits, the calculator tells you so.

The list at the bottom shows the fraction multiplied by 2, 3, 4, 5 and 10. All of them have the same value, which the decimal line confirms.

Simplifying: divide by the greatest common factor

A fraction is in simplest form when its numerator and denominator have no common factor other than 1. To get there in one step, divide both by their greatest common factor (GCF).

The open textbook Prealgebra 2e from OpenStax (section 4.2) shows the method on several fractions:

• 10/15: both are multiples of 5, so 10/15 = 2/3 (Example 4.19).
• −18/24: the GCF is 6, so −18/24 = −3/4. The negative sign stays in front (Example 4.20).
• −56/32: the GCF is 8, so −56/32 = −7/4. An improper fraction stays improper unless you want a mixed number, which would be −1 3/4 (Example 4.21).
• 210/385: factor both: 210 = 2 × 3 × 5 × 7 and 385 = 5 × 7 × 11. The shared factors are 5 and 7, so the GCF is 35 and the fraction is 6/11 (Example 4.22).

You can also simplify in stages, dividing by any common factor you spot and repeating until none is left. 48/72 ÷ 2 = 24/36, ÷ 2 again = 12/18, ÷ 6 = 2/3. It takes more steps but gets to the same place. The greatest common factor calculator shows how to find the GCF directly with prime factors or Euclid’s algorithm.

Equivalent fractions: multiply top and bottom

The Equivalent Fractions Property says that multiplying the numerator and the denominator by the same nonzero number doesn’t change the value of a fraction. One half of a pizza is the same amount whether it is cut into 2, 4 or 20 slices.

OpenStax Example 4.14 finds three fractions equal to 2/5 by multiplying by 2, 3 and 5: 4/10, 6/15 and 10/25.

Finding a specific denominator. Example 4.15 asks for a fraction equivalent to 2/7 with a denominator of 21. Since 21 ÷ 7 = 3, multiply the top by 3 as well: 2/7 = 6/21. In general, divide the target denominator by the current one to get the multiplier. If the result isn’t a whole number, there is no whole-number equivalent with that denominator. 3/4 can’t be written over 10, because 10 ÷ 4 = 2.5 and the numerator would be 7.5.

The calculator reduces your fraction first, so a target denominator works if it is any multiple of the reduced denominator. 18/24 reduces to 3/4, which can be rewritten over 20 as 15/20, even though 20 isn’t a multiple of 24.

Are two fractions equivalent? Cross-multiply

To check whether a/b and c/d are equal, compare the cross products a × d and b × c. If they match, the fractions are equivalent. 6/15 and 10/25: 6 × 25 = 150 and 15 × 10 = 150, so they are equal. 2/3 and 5/8: 2 × 8 = 16 and 3 × 5 = 15, so 2/3 is the larger by a small amount.

Reducing both to simplest form also works: two fractions are equivalent if and only if they reduce to the same thing. That is how the calculator decides, and it is the reason simplest form is useful. It gives every value a single standard name.

Where simplifying helps

Adding and subtracting fractions. You need a common denominator. Rewriting 1/4 and 1/6 over their least common multiple, 12, gives 3/12 + 2/12 = 5/12. Use the target-denominator box for each fraction, or the mixed fraction calculator to do the whole sum.

Measurements. A tape measure reads in sixteenths, so a cut list might say 12/16 inch. That is 3/4 inch, which is easier to find on a ruler and to read aloud on a job site.

Scores and ratios. 18 correct out of 24 is 3/4, which makes it easy to see as 75%. A recipe that calls for 6 cups of flour to 8 cups of water is the same proportion as 3 to 4.

Homework answers. Most teachers and answer keys expect fractions in simplest form, and a mismatched form is the most common reason a correct answer gets marked wrong.

Common mistakes

• Cancelling digits instead of factors. Crossing out the 6s in 16/64 happens to leave the right answer, 1/4, and the same luck works for 26/65 = 2/5. Try it on 13/36 and you get 1/6, which is wrong: 13/36 is already in lowest terms. Only common factors cancel, not shared digits.
• Adding instead of multiplying. Adding 1 to the top and bottom changes the value: 1/2 becomes 2/3.
• Stopping too early. 12/18 → 6/9 still has a common factor of 3. Dividing by the GCF in one step avoids this.
• Dividing only one part. Every step has to treat the numerator and the denominator the same way.

Simplifying fractions with large numbers

When the numbers are too large to spot common factors, use Euclid’s algorithm to find the GCF. For 391/667: 667 = 1 × 391 + 276, 391 = 1 × 276 + 115, 276 = 2 × 115 + 46, 115 = 2 × 46 + 23, and 46 = 2 × 23 + 0. The GCF is 23, so 391/667 = 17/29. Neither number is even or a multiple of 3, 5, 7, 11 or 13, so trial division by small primes would have taken a while. The greatest common factor calculator prints these steps for any pair.

Simplifying mixed numbers

Only the fraction part needs simplifying: 3 6/8 = 3 3/4. If the fraction is improper, such as 2 9/6, simplify it to 3/2, then carry the extra whole: 2 + 1 1/2 = 3 1/2. Entering 2 9/6 as the improper fraction 21/6 gives the same result here: 7/2, or 3 1/2.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Simplest form divides numerator and denominator by their greatest common factor.
• The sign is carried on the numerator; the denominator is positive.
• Equivalent fractions multiply top and bottom by the same nonzero whole number.
• A target denominator works only if it is a multiple of the reduced denominator.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 4.1 Visualize Fractions. The Equivalent Fractions Property, Example 4.14 (2/5 = 4/10 = 6/15 = 10/25) and Example 4.15 (2/7 = 6/21).
2. OpenStax (Rice University), Prealgebra 2e, 4.2 Multiply and Divide Fractions. Simplifying by removing common factors: 10/15 = 2/3, −18/24 = −3/4, −56/32 = −7/4 and 210/385 = 6/11 (Examples 4.19–4.22).

Last reviewed November 2, 2026. Whether to show an improper fraction as a mixed number is a matter of style; both are simplified.