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Reduce 8/12 to 2/3: Fraction Simplifier and Reducer
Use this free fraction reducer to simplify any fraction to its simplest form. Enter a numerator and denominator, and the simplified fraction calculator shows you the step-by-step process: finding the GCD, dividing both numbers, and confirming the result is fully reduced. It works as a fraction simplifier for proper fractions, improper fractions, mixed numbers, and very large numbers, and it tells you when a fraction is already the simplest fraction it can be.
Quick Tips
- A fraction is in simplest form when the numerator and denominator have no common factors other than 1
- The Greatest Common Divisor (GCD) is the largest number that divides both numerator and denominator evenly
- To simplify a fraction, divide both numerator and denominator by their GCD
- Mixed numbers should be converted to improper fractions before simplifying
- Results are always shown in proper fraction form (simplified)
What Is Simplest Form?
"Write your answer in simplest form." Every test says it, and barely any textbook explains it. Here is the plain-English version: a fraction is in its simplest form when no number other than 1 divides evenly into both the top and the bottom. That is the whole idea. Some textbooks call it lowest terms or say the fraction is fully reduced; all three phrases mean exactly the same thing.
How do you know a fraction is in simplest form?
Check the greatest common divisor (GCD) of the numerator and denominator. If the GCD is 1, you are done. If it is anything larger than 1, there is still reducing to do. A quick shortcut: if both numbers are different primes, the fraction is always already in simplest form. That is why 7/11 needs no work at all, and neither do 5/8, 3/7, or 13/15.
Worked examples
| Fraction | GCD | Divide both by the GCD | Simplest form |
|---|---|---|---|
| 6/8 | 2 | 6 ÷ 2 = 3, 8 ÷ 2 = 4 | 3/4 |
| 10/15 | 5 | 10 ÷ 5 = 2, 15 ÷ 5 = 3 | 2/3 |
| 12/18 | 6 | 12 ÷ 6 = 2, 18 ÷ 6 = 3 | 2/3 |
| 24/36 | 12 | 24 ÷ 12 = 2, 36 ÷ 12 = 3 | 2/3 |
| 48/180 | 12 | 48 ÷ 12 = 4, 180 ÷ 12 = 15 | 4/15 |
| 7/11 | 1 | Nothing to divide | 7/11 |
The GCD method, step by step
The number you are looking for is the greatest common divisor, sometimes called the greatest common factor (GCF). It is simply the largest number that goes evenly into both the numerator and the denominator.
- List the factors of the numerator. For 12: 1, 2, 3, 4, 6, 12.
- List the factors of the denominator. For 18: 1, 2, 3, 6, 9, 18.
- Find the common factors: 1, 2, 3, 6. The greatest of them is 6, so GCD(12, 18) = 6.
- Divide both numbers by the GCD: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12/18 reduces to 2/3.
For large numbers, listing every factor gets tedious. The Euclidean algorithm is faster: divide the larger number by the smaller, note the remainder, then repeat with the smaller number and that remainder until the remainder is 0. The last non-zero remainder is the GCD. For 48 and 180: 180 ÷ 48 = 3 remainder 36, 48 ÷ 36 = 1 remainder 12, 36 ÷ 12 = 3 remainder 0, so the GCD is 12.
The common mistake: stopping too early
Most wrong answers come from dividing by a common factor instead of the greatest one. Simplify 24/36 by dividing both by 2 and you get 12/18, which looks simpler but is not fully reduced: 12 and 18 still share a factor of 6. Always divide by the GCD. If you did divide by a smaller factor, just repeat the process on the result until the GCD is 1.
Why simplest form matters
- 2/3 is far easier to add to another fraction than 200/300.
- Reducing before you multiply keeps you out of enormous numbers.
- It is the standard form: 4/6, 6/9, and 10/15 all look different even though they are equal, while everyone who sees 2/3 knows they are talking about the same amount.
Understanding Fraction Simplification
What is Fraction Simplification?
Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.
Why Simplify Fractions?
- Simplified fractions are easier to understand and work with
- They help identify equivalent fractions more easily
- They make calculations simpler and reduce the chance of errors
- They provide a standard form for comparing fractions
Pro Tip:
Always simplify your final answer when working with fractions to ensure you've found the most reduced form.
Finding the Greatest Common Divisor (GCD)
The GCD is the key to simplifying fractions. It's the largest number that divides both the numerator and denominator evenly.
Methods to Find the GCD:
- List all factors of both numbers and find the largest one they share
- Use the Euclidean algorithm (divide the larger number by the smaller, then repeat with the remainder)
- Use prime factorization (find the common prime factors and multiply them)
Pro Tip:
For large numbers, the Euclidean algorithm is much faster than listing all factors!
The Simplification Process
Once you have the GCD, simplifying a fraction is straightforward.
Step-by-Step Guide:
- Find the GCD of the numerator and denominator
- Divide both the numerator and denominator by the GCD
- The result is the simplified fraction
Remember:
A fraction is fully simplified when the GCD of its numerator and denominator is 1.
Share Your Learning Journey
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- Share simplified fractions with classmates
- Help others understand the simplification process
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- Create practice problems for students
Related Tools
Fractions people simplify most
Every one of these has its own page with the full working, the decimal, and the percentage.
- 2/4 = 1/2
- 2/6 = 1/3
- 3/6 = 1/2
- 4/6 = 2/3
- 2/8 = 1/4
- 4/8 = 1/2
- 6/8 = 3/4
- 3/9 = 1/3
- 6/9 = 2/3
- 2/10 = 1/5
- 4/10 = 2/5
- 5/10 = 1/2
- 6/10 = 3/5
- 8/10 = 4/5
- 2/12 = 1/6
- 3/12 = 1/4
- 4/12 = 1/3
- 6/12 = 1/2
- 8/12 = 2/3
- 9/12 = 3/4
- 10/12 = 5/6
- 2/14 = 1/7
- 4/14 = 2/7
- 6/14 = 3/7
- 7/14 = 1/2
- 8/14 = 4/7
- 10/14 = 5/7
- 12/14 = 6/7
- 3/15 = 1/5
- 5/15 = 1/3
- 6/15 = 2/5
- 9/15 = 3/5
- 10/15 = 2/3
- 12/15 = 4/5
- 2/16 = 1/8
- 4/16 = 1/4
- 6/16 = 3/8
- 8/16 = 1/2
- 10/16 = 5/8
- 12/16 = 3/4
- 14/16 = 7/8
- 2/18 = 1/9
- 3/18 = 1/6
- 4/18 = 2/9
- 6/18 = 1/3
- 8/18 = 4/9
- 9/18 = 1/2
- 10/18 = 5/9
- 12/18 = 2/3
- 14/18 = 7/9
- 15/18 = 5/6
- 16/18 = 8/9
- 2/20 = 1/10
- 4/20 = 1/5
- 5/20 = 1/4
- 6/20 = 3/10
- 8/20 = 2/5
- 10/20 = 1/2
- 12/20 = 3/5
- 14/20 = 7/10
- 15/20 = 3/4
- 16/20 = 4/5
- 18/20 = 9/10
- 3/21 = 1/7
- 6/21 = 2/7
- 7/21 = 1/3
- 9/21 = 3/7
- 12/21 = 4/7
- 14/21 = 2/3
- 15/21 = 5/7
- 18/21 = 6/7
- 2/22 = 1/11
- 4/22 = 2/11
- 6/22 = 3/11
- 8/22 = 4/11
- 10/22 = 5/11
- 11/22 = 1/2
- 12/22 = 6/11
- 14/22 = 7/11
- 16/22 = 8/11
- 18/22 = 9/11
- 20/22 = 10/11
- 2/24 = 1/12
- 3/24 = 1/8
- 4/24 = 1/6
- 6/24 = 1/4
- 8/24 = 1/3
- 9/24 = 3/8
- 10/24 = 5/12
- 12/24 = 1/2
- 14/24 = 7/12
- 15/24 = 5/8
- 16/24 = 2/3
- 18/24 = 3/4
- 20/24 = 5/6
- 21/24 = 7/8
- 22/24 = 11/12
- 5/25 = 1/5
- 10/25 = 2/5
- 15/25 = 3/5
- 20/25 = 4/5
- 13/26 = 1/2
- 9/27 = 1/3
- 18/27 = 2/3
- 7/28 = 1/4
- 14/28 = 1/2
- 21/28 = 3/4
- 5/30 = 1/6
- 6/30 = 1/5
- 10/30 = 1/3
- 12/30 = 2/5
- 15/30 = 1/2
- 18/30 = 3/5
- 20/30 = 2/3
- 24/30 = 4/5
- 25/30 = 5/6
- 8/32 = 1/4
- 16/32 = 1/2
- 24/32 = 3/4
- 11/33 = 1/3
- 22/33 = 2/3
- 17/34 = 1/2
- 7/35 = 1/5
- 14/35 = 2/5
- 21/35 = 3/5
- 28/35 = 4/5
- 6/36 = 1/6
- 9/36 = 1/4
- 12/36 = 1/3
- 18/36 = 1/2
- 24/36 = 2/3
- 27/36 = 3/4
- 30/36 = 5/6
- 19/38 = 1/2
- 13/39 = 1/3
- 26/39 = 2/3
- 8/40 = 1/5
- 10/40 = 1/4
- 16/40 = 2/5
- 20/40 = 1/2
- 24/40 = 3/5
- 30/40 = 3/4
- 32/40 = 4/5
- 7/42 = 1/6
- 14/42 = 1/3
- 21/42 = 1/2
- 28/42 = 2/3
- 35/42 = 5/6
- 11/44 = 1/4
- 22/44 = 1/2
- 33/44 = 3/4
- 9/45 = 1/5
- 15/45 = 1/3
- 18/45 = 2/5
- 27/45 = 3/5
- 30/45 = 2/3
- 36/45 = 4/5
- 23/46 = 1/2
- 8/48 = 1/6
- 12/48 = 1/4
- 16/48 = 1/3
- 24/48 = 1/2
- 32/48 = 2/3
- 36/48 = 3/4
- 40/48 = 5/6
- 10/50 = 1/5
- 20/50 = 2/5
- 30/50 = 3/5
- 40/50 = 4/5
- 17/51 = 1/3
- 34/51 = 2/3
- 13/52 = 1/4
- 39/52 = 3/4
- 9/54 = 1/6
- 18/54 = 1/3
- 36/54 = 2/3
- 45/54 = 5/6
- 11/55 = 1/5
- 22/55 = 2/5
- 33/55 = 3/5
- 44/55 = 4/5
- 14/56 = 1/4
- 42/56 = 3/4
- 19/57 = 1/3
- 38/57 = 2/3
- 10/60 = 1/6
- 12/60 = 1/5
- 15/60 = 1/4
- 20/60 = 1/3
- 24/60 = 2/5
- 36/60 = 3/5
- 40/60 = 2/3
- 45/60 = 3/4
- 48/60 = 4/5
- 50/60 = 5/6
- 21/63 = 1/3
- 42/63 = 2/3
- 16/64 = 1/4
- 48/64 = 3/4
- 13/65 = 1/5
- 26/65 = 2/5
- 39/65 = 3/5
- 52/65 = 4/5
- 11/66 = 1/6
- 22/66 = 1/3
- 44/66 = 2/3
- 55/66 = 5/6
- 17/68 = 1/4
- 51/68 = 3/4
- 23/69 = 1/3
- 46/69 = 2/3
- 14/70 = 1/5
- 28/70 = 2/5
- 42/70 = 3/5
- 56/70 = 4/5
- 12/72 = 1/6
- 18/72 = 1/4
- 24/72 = 1/3
- 48/72 = 2/3
- 54/72 = 3/4
- 60/72 = 5/6
- 15/75 = 1/5
- 30/75 = 2/5
- 45/75 = 3/5
- 60/75 = 4/5
- 19/76 = 1/4
- 57/76 = 3/4
- 13/78 = 1/6
- 65/78 = 5/6
- 16/80 = 1/5
- 20/80 = 1/4
- 32/80 = 2/5
- 48/80 = 3/5
- 60/80 = 3/4
- 64/80 = 4/5
- 14/84 = 1/6
- 21/84 = 1/4
- 63/84 = 3/4
- 70/84 = 5/6
- 17/85 = 1/5
- 34/85 = 2/5
- 51/85 = 3/5
- 68/85 = 4/5
- 22/88 = 1/4
- 66/88 = 3/4
- 15/90 = 1/6
- 18/90 = 1/5
- 36/90 = 2/5
- 54/90 = 3/5
- 72/90 = 4/5
- 75/90 = 5/6
- 23/92 = 1/4
- 69/92 = 3/4
- 19/95 = 1/5
- 38/95 = 2/5
- 57/95 = 3/5
- 76/95 = 4/5
- 16/96 = 1/6
- 24/96 = 1/4
- 72/96 = 3/4
- 80/96 = 5/6
- 20/100 = 1/5
- 40/100 = 2/5
- 60/100 = 3/5
- 80/100 = 4/5
- 17/102 = 1/6
- 85/102 = 5/6
- 21/105 = 1/5
- 42/105 = 2/5
- 63/105 = 3/5
- 84/105 = 4/5
- 18/108 = 1/6
- 90/108 = 5/6
- 22/110 = 1/5
- 44/110 = 2/5
- 66/110 = 3/5
- 88/110 = 4/5
- 19/114 = 1/6
- 95/114 = 5/6
- 23/115 = 1/5
- 46/115 = 2/5
- 69/115 = 3/5
- 92/115 = 4/5
- 20/120 = 1/6
- 24/120 = 1/5
- 48/120 = 2/5
- 72/120 = 3/5
- 96/120 = 4/5
- 100/120 = 5/6
- 21/126 = 1/6
- 105/126 = 5/6
- 22/132 = 1/6
- 110/132 = 5/6
- 23/138 = 1/6
- 115/138 = 5/6
- 24/144 = 1/6
- 270/810 = 1/3
- 88/7744 = 1/88
Fractions that are already in simplest form
These have a greatest common factor of 1, so they cannot be reduced any further.
Frequently Asked Questions
Common questions about simplifying fractions