Math
Simplify Fractions Calculator
Enter any fraction, improper fraction, mixed number, or decimal and get it in lowest terms.
The calculator factors the numerator and denominator into primes, finds the greatest common factor, divides it out, and shows the result as a simplified fraction, mixed number, decimal, and percent, plus a list of equivalent fractions and a strip picture.
Type a fraction (3/4), a mixed number (2 1/3), a whole number, or a decimal (1.75). Repeating decimals work too: 0.(3).
Try an example
Result
Simplified fraction
—
- Mixed number
- —
- Decimal
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- Percent
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- Greatest common factor
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
How to simplify a fraction
A fraction is in lowest terms (simplest form) when its The top number of a fraction; it counts how many parts you have. and The bottom number of a fraction; it says how many equal parts make one whole. share no factor bigger than 1. To get there, find the The largest number that divides evenly into every number in a set. (GCF) of the two numbers and divide both by it. Dividing top and bottom by the same number keeps the value the same because you are really multiplying by 1.
Finding the GCF with prime factors
Write each number as a product of A whole number above 1 whose only factors are 1 and itself.. 42 = 2 × 3 × 7 and 56 = 2^3 × 7. The primes they share are 2 (lowest power 2^1) and 7, so the GCF is 2 × 7 = 14, and 42/56 = 3/4. If you do not spot the GCF right away, divide by any common factor you see and repeat; you will reach the same answer in more steps.
| Fraction | GCF | Simplified | Decimal |
|---|---|---|---|
| 42/56 | 14 | 3/4 | 0.75 |
| 18/24 | 6 | 3/4 | 0.75 |
| 100/250 | 50 | 2/5 | 0.4 |
| 7/9 | 1 | 7/9 (already simplest) | 0.(7) |
| 45/10 | 5 | 9/2 = 4 1/2 | 4.5 |
| -12/16 | 4 | -3/4 | -0.75 |
Simplifying improper fractions and mixed numbers
A fraction whose top number is at least as big as its bottom number, like 7/3. simplify the same way; the result may still be improper, and the mixed-number form shows it as wholes plus a proper fraction. For a A whole number written next to a fraction, like 2 1/3., simplify only the fraction part: 4 6/8 = 4 3/4. The calculator accepts mixed numbers directly and shows both the improper and mixed forms of the answer.
How to use it
- Type the fraction (42/56), an improper fraction (45/10), a mixed number (4 6/8), or a decimal (0.375).
- Read the simplified fraction in the panel, with the mixed number and decimal beside it.
- Check the GCF tile and the prime factor tiles to see why that GCF is correct.
- Use the equivalent-fractions row when you need the same value with a different denominator.
How to read the answer
The simplified fraction is the same value as the original, written with the smallest possible whole numbers. A GCF of 1 means the fraction was already in lowest terms. The decimal and percent are the same amount in other notations, and the strip picture shades identical areas for both forms.
Common mistakes and edge cases
- Dividing by a common factor that is not the greatest one leaves the fraction unsimplified. 42/56 ÷ 2 gives 21/28, which still reduces to 3/4.
- Subtracting the same number from top and bottom changes the value. Only dividing (or multiplying) both parts by the same number is allowed.
- Cancelling digits is not simplifying: 16/64 = 1/4 is a coincidence, not a rule.
- Negative signs belong on the numerator or in front of the fraction; the denominator stays positive.
- A denominator of 0 is undefined; 0 in the numerator always simplifies to 0.
Worked examples
Typical
42/56
Simplified fraction
3/4
Already in lowest terms
7/9
Simplified fraction
7/9
Improper fraction
45/10
Simplified fraction
9/2
Negative fraction
-12/16
Simplified fraction
-3/4
Mixed number
4 6/8
Simplified fraction
19/4
Zero numerator
0/15
Simplified fraction
0
Large numbers
123456/789012
Simplified fraction
10288/65751
Zero denominator
5/0 is undefined
Simplified fraction
Error
Frequently asked questions
What does it mean to simplify a fraction?+
To write it with the smallest whole-number numerator and denominator that still give the same value. 42/56 and 3/4 are the same amount; 3/4 is the simplified form.
How do I know a fraction is fully simplified?+
The greatest common factor of the numerator and denominator is 1. The calculator shows the prime factors of both so you can confirm they share none.
Can I simplify an improper fraction?+
Yes. Divide by the GCF exactly as with a proper fraction. 45/10 becomes 9/2, which is 4 1/2 as a mixed number.
How do you simplify a mixed number?+
Simplify the fraction part and keep the whole number: 4 6/8 = 4 3/4. Or convert to an improper fraction, simplify, and convert back.
Does simplifying change the decimal value?+
No. 42/56 and 3/4 are both 0.75. Simplifying only changes how the fraction is written.
What are equivalent fractions?+
Fractions with the same value, such as 3/4, 6/8, and 9/12. Multiply or divide the numerator and denominator by the same nonzero number to move between them.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026