Simplify Fractions Calculator
Reduce a fraction to its simplest form in one step. The calculator finds the greatest common factor, shows the prime factors behind it, and gives the result as a fraction, a mixed number and a decimal.
- Greatest common factor
- Prime factors shown
- Mixed numbers
- Very large numbers
Fraction to simplify
Enter a fraction such as 84/126, or a mixed number with the whole number in the first box.
- Simplified fraction
- 2/3
- Decimal
- 0.6 repeating
- Percentage
- 66.6 repeating%
A bar over digits means they repeat forever. In plain text this is written 0.(6).
Step-by-step working
Simplify by the greatest common factor
84 = 2² × 3 × 7126 = 2 × 3² × 7They share common factors 2 × 3 × 7 = 4284 over 126=84 ÷ 42 over 126 ÷ 42=2 over 3Divide the top and the bottom by the same number. The value does not change.
Convert to a decimal
2 ÷ 3=0.6 repeatingThe digits under the bar repeat forever.
Exact arithmetic for numbers of any size, with no rounding errors. Everything runs in your browser, and nothing you type leaves this page.
What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction means writing it with the smallest possible whole numbers while keeping its value. You do it by dividing the numerator and the denominator by their greatest common factor (GCF), also called the greatest common divisor (GCD). 84/126 and 2/3 are equivalent fractions, but 2/3 is in lowest terms because 2 and 3 share no factor other than 1. This simplifier shows the prime factorization of both numbers so you can see which factors cancel. For very large numbers it switches to the Euclidean algorithm, which finds the GCF quickly without factoring.
How to simplify a fraction with this calculator
- Type the numerator in the top box and the denominator in the bottom box. For a mixed number, add the whole number in the left box.
- The simplified fraction appears straight away, with the mixed number, decimal and percentage.
- Read the working: the prime factors of each number, the greatest common factor, and the division that reduces the fraction.
- Use the other tabs to add or multiply the simplified fraction, or turn it into a decimal.
Simplifying rules
- a/b = (a ÷ g)/(b ÷ g), g = GCF(a, b)
- 84/126 with g = 42 gives 2/3.
- GCF from prime factors
- Multiply the shared prime factors: 2² × 3 and 2 × 3² share 2 × 3 = 6.
- Euclidean algorithm
- GCF(126, 84): 126 = 1 × 84 + 42, 84 = 2 × 42 + 0, so the GCF is 42.
- Lowest terms test
- If GCF(a, b) = 1, the fraction is already in simplest form.
Why use this simplify fractions calculator
- Every step, freeThe full working is always on the page: common denominator, rewritten fractions, greatest common factor and the final simplification. No account, no premium tier and no daily limit.
- Exact answers at any sizeFractions are stored as exact whole numbers, so a 40-digit numerator stays exact. There is no floating-point rounding of the kind that turns 0.1 + 0.2 into 0.30000000000000004.
- Repeating decimals shown properly1/7 is shown as 0.142857 with a bar over the repeating block, instead of being cut off at 0.1428571429. You also get a rounded value to copy.
- Fast and privateThe answer updates as you type and is worked out on your device. Nothing you enter is sent to a server, and the calculator keeps working if your connection drops.
How it compares with other fraction calculators
| Feature | This calculator | Typical online calculators |
|---|---|---|
| More than two numbers in one problem | Yes, up to 10, with order of operations | Usually two |
| Fractions, mixed numbers, whole numbers and decimals together | Yes | Often separate calculators |
| Full step-by-step working | Always free | Often missing or behind a paywall |
| Repeating decimals | Exact, with a bar over the repeating digits | Rounded to a few places |
| Very large numbers | Exact at any size | Rounded or a separate big number tool |
| Decimal to fraction for repeating decimals | Type 0.1(6) or 0.1666... | Count the repeating digits yourself |
| Privacy | Runs in your browser, nothing sent | Inputs often sent to a server |
Common uses
- Final answers. Most teachers and tests expect fractions in lowest terms.
- Probability. Reduce 12/52 to 3/13 when counting cards or outcomes.
- Ratios and scale. Turn 1920/1080 into 16/9 or a recipe ratio into its simplest form.
- Measurements. Reduce 12/16 inch to 3/4 inch before marking a cut.
More math help: the percentage calculator for percent questions, the ratio calculator for simplifying and scaling ratios, and the math editor to type up your working as a neat equation.
Fraction words explained
- Numerator
- The top number. It counts how many parts you have.
- Denominator
- The bottom number. It says how many equal parts make one whole.
- Proper fraction
- The numerator is smaller than the denominator, such as 3/4.
- Improper fraction
- The numerator is as big as or bigger than the denominator, such as 7/4.
- Mixed number
- A whole number and a proper fraction together, such as 1 3/4.
- Equivalent fractions
- Different fractions with the same value, such as 1/2, 2/4 and 50/100.
- Least common denominator
- The smallest number all the denominators divide into.
- Greatest common factor
- The biggest number that divides both the numerator and the denominator.
- Reciprocal
- A fraction turned upside down. The reciprocal of 2/3 is 3/2.
- Repeating decimal
- A decimal whose digits repeat forever, such as 0.333... for 1/3.
For example, in 3 over 4 the numerator is 3 and the denominator is 4.
Worked example: simplify 84/126
Factor both numbers: 84 = 2 × 2 × 3 × 7 and 126 = 2 × 3 × 3 × 7. The factors they share are 2, 3 and 7, so the greatest common factor is 2 × 3 × 7 = 42. Divide the top and the bottom by 42: 84 ÷ 42 = 2 and 126 ÷ 42 = 3. So 84/126 = 2/3, which is 0.666... as a decimal.
What to expect from the result
Prime factors are listed for numbers up to 10 billion; above that the calculator shows the Euclidean algorithm instead, which works for numbers of any length. A fraction with a negative sign keeps the sign on the numerator, so 6/−8 simplifies to −3/4.
Simplify Fractions Calculator questions
How do you simplify a fraction?
Find the greatest common factor of the numerator and denominator and divide both by it. For 18/24 the GCF is 6, so 18/24 = 3/4. You can also divide by any shared factor repeatedly (by 2, then by 3) until nothing else divides both.
What is the simplest form of a fraction?
A fraction is in simplest form, or lowest terms, when the numerator and denominator have no common factor other than 1. 3/4 and 7/12 are in simplest form; 6/8 is not, because 2 divides both.
How do I find the greatest common factor?
List the prime factors of both numbers and multiply the ones they share. 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7 share 2, 3 and 7, so the GCF is 42. For large numbers, the Euclidean algorithm is faster: divide, keep the remainder, and repeat until the remainder is 0.
How do I simplify an improper fraction?
Simplify it like any other fraction, then turn it into a mixed number if you need to. 30/12 = 5/2 (dividing by 6) = 2 1/2.
Can a simplified fraction be a whole number?
Yes. If the denominator divides the numerator exactly, the fraction simplifies to a whole number. 12/4 = 3 and 45/9 = 5.
Does simplifying change the value of the fraction?
No. Dividing the top and the bottom by the same number is the same as dividing by 1, so 84/126 and 2/3 are exactly equal. Simplified fractions are just easier to read and compare.