Simplify Fractions Calculator — Reduce to Lowest Terms (Free)
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To simplify a fraction, divide the numerator and the denominator by their greatest common factor (GCF). For 48/60 the GCF is 12, so 48 ÷ 12 = 4 and 60 ÷ 12 = 5, and 48/60 in lowest terms is 4/5 (0.8, or 80%). The simplify fractions calculator below does this for fractions, mixed numbers, negatives, decimals and complex fractions, and shows every step.
Show steps
- List the factorsFactors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- Find the greatest common factorCommon factors: 1, 2, 3, 4, 6, 12. The greatest is 12.
- Divide top and bottom by 1248 ÷ 12 = 4 and 60 ÷ 12 = 5, so 4860 = 45.
Next: add, subtract, multiply or divide fractions · GCF and LCM calculator · fraction, decimal and percent converter
How to use the simplify fractions calculator
- Type the numerator (top) and denominator (bottom). For a mixed number such as 2 9/6, also fill in the Whole box.
- Pick how you want the steps explained: by the greatest common factor, by prime factorization, or by dividing out common factors one at a time. All three give the same answer.
- Read the fraction in lowest terms, the GCF, the mixed number, decimal and percent. The fraction bars show that the original and the simplified fraction cover the same length.
- Optional: type your own answer in Check your answer. The calculator tells you whether it is correct, equal but not fully simplified, or not equal.
Use the Type it tab for 0.375, −2 9/6, 1.5/3, complex fractions such as (1/2)/(3/4) or powers such as 2^3/2^5, and the A list tab to simplify a whole homework set at once.
How to simplify a fraction
- Find the greatest common factor of the numerator and the denominator.
- Divide both numbers by the GCF.
- Check that the new numerator and denominator have no common factor other than 1. If they do not, the fraction is in lowest terms (also called simplest form).
Example: simplify 24/36. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 and the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The greatest common factor is 12, so 24/36 = (24 ÷ 12)/(36 ÷ 12) = 2/3. In the same way, 18/42 has GCF 6 and simplifies to 3/7.
Simplifying never changes the value. 4/5, 8/10, 12/15 and 48/60 are equivalent fractions: they name the same point on the number line, and 4/5 is the one with the smallest numbers.
Three ways to find the common factor
Greatest common factor
For small numbers, list the factors and pick the largest shared one. For large numbers, the Euclidean algorithm is faster: divide the larger number by the smaller and keep the remainder until it is 0. For 462/1071: 1071 = 2 × 462 + 147, 462 = 3 × 147 + 21, 147 = 7 × 21 + 0. The last non-zero remainder, 21, is the GCF, so 462/1071 = 22/51.
Prime factorization
Write both numbers as products of primes and cancel the primes they share. 84 = 2 × 2 × 3 × 7 and 126 = 2 × 3 × 3 × 7. The common primes 2, 3 and 7 multiply to 42, and what is left is 2 over 3, so 84/126 = 2/3.
Divide step by step
Divide by any common factor you can see, then repeat. 48/60 ÷ 2 = 24/30, then ÷ 6 gives 4/5. Dividing by 2 and then by 6 is the same as dividing once by 12, the GCF. This is the quickest method in your head, as long as you keep going until no common factor is left.
Simplifying improper fractions and mixed numbers
An improper fraction has a numerator at least as large as its denominator. Simplify it first, then turn it into a mixed number if you need one: 18/12 = 3/2 (GCF 6), and 3 ÷ 2 = 1 remainder 1, so 3/2 = 1 1/2.
For a mixed number, keep the whole number aside and simplify only the fraction part: 3 6/8 = 3 3/4. If the fraction part is improper, carry the extra whole: in 2 9/6, 9/6 = 3/2 = 1 1/2, so 2 9/6 = 3 1/2.
Negative, decimal and complex fractions
- Negative signs: a negative over a negative is positive, so −10/−20 = 1/2. With one minus sign, put it in front or on the numerator: 3/−9 = −1/3.
- Decimals: multiply the top and bottom by a power of 10 to clear the decimals, then simplify. 1.5/3 = 15/30 = 1/2, and 0.375 = 375/1000 = 3/8.
- Complex fractions: divide by multiplying by the reciprocal. (1/2)/(3/4) = 1/2 × 4/3 = 4/6 = 2/3.
Common fractions in lowest terms
| Fraction | GCF | Lowest terms | Decimal | Percent |
|---|---|---|---|---|
| 2/4 | 2 | 1/2 | 0.5 | 50% |
| 6/8 | 2 | 3/4 | 0.75 | 75% |
| 8/12 | 4 | 2/3 | 0.666… | 66.67% |
| 10/15 | 5 | 2/3 | 0.666… | 66.67% |
| 12/16 | 4 | 3/4 | 0.75 | 75% |
| 15/20 | 5 | 3/4 | 0.75 | 75% |
| 18/24 | 6 | 3/4 | 0.75 | 75% |
| 20/25 | 5 | 4/5 | 0.8 | 80% |
| 45/60 | 15 | 3/4 | 0.75 | 75% |
| 25/100 | 25 | 1/4 | 0.25 | 25% |
| 36/48 | 12 | 3/4 | 0.75 | 75% |
| 14/21 | 7 | 2/3 | 0.666… | 66.67% |
Common mistakes when simplifying fractions
- Stopping too early. 48/60 ÷ 2 = 24/30 is not finished; 24 and 30 still share 6.
- Dividing only one number. Whatever you divide the top by, divide the bottom by the same number.
- Subtracting instead of dividing. Taking 2 off the top and bottom of 6/8 gives 4/6, which is a different value.
- Cancelling digits. In 16/64 you cannot cross out the 6s; the correct answer, 1/4, comes from the GCF 16.
- Leaving a mixed number half done. 2 9/6 is not simplified until the fraction part is proper: 3 1/2.
Check your work, by hand or with the calculator
For homework, work the problem first, then enter it and compare. A simplified answer passes two checks: it has the same value as the original (cross-multiply: 48 × 5 = 240 = 60 × 4), and its numerator and denominator have a GCF of 1. Use the calculator for large numbers, long lists or to check your steps, and simplify by hand when the common factor is easy to spot, such as halving 2/4 or dividing by 5 when both numbers end in 0 or 5.
Simplified fractions are easier to compare, add and read. Recipes, measurements (6/8 inch is 3/4 inch), probabilities (2/6 is a 1/3 chance) and test answers are all usually written in lowest terms.
Simplifying fractions practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
The GCF of 36 and 54 is 18, and 36 ÷ 18 = 2, 54 ÷ 18 = 3, so 36/54 = 2/3. Answers such as 4/6 or 6/9 are equal but not fully simplified.
42 = 2 × 3 × 7 and 56 = 2 × 2 × 2 × 7. The shared primes are 2 and 7, so the GCF is 14.
15 = 3 × 5 and 28 = 2 × 2 × 7 share no prime, so the GCF is 1. The others share 7, 3 and 5.
A negative divided by a negative is positive, and the GCF of 21 and 35 is 7, so −21/−35 = 3/5.
Multiply by the reciprocal: 3/4 × 10/9 = 30/36, and the GCF of 30 and 36 is 6, so the answer is 5/6.
Quiz complete
Frequently asked questions
How can I simplify fractions?
Divide the numerator and the denominator by their greatest common factor. If you do not know the GCF, divide by any common factor (2, 3, 5 and so on) and repeat until the only common factor left is 1.
Can you simplify fractions on a calculator?
Yes. This calculator gives the answer in lowest terms with the steps. Many scientific and graphing calculators also have a fraction key or a function that converts a division into a simplified fraction.
How do you simplify fractions without a calculator?
Use divisibility rules to spot common factors: even numbers share 2, numbers ending in 0 or 5 share 5, and numbers whose digits add to a multiple of 3 share 3. Divide both numbers by the factor and repeat. For example, 45/60 ÷ 5 = 9/12, then ÷ 3 = 3/4.
How do you simplify improper fractions?
Simplify them like any other fraction, by dividing by the GCF, then convert to a mixed number if needed. 18/12 = 3/2 = 1 1/2.
How do you simplify mixed fractions?
Keep the whole number and simplify the fraction part: 3 6/8 = 3 3/4. If the fraction part is improper, add the extra whole to the whole number: 2 9/6 = 2 + 1 1/2 = 3 1/2.
How do you simplify a fraction on a TI-84 calculator?
Type the fraction as a division, such as 24 ÷ 36, press MATH, choose 1: ►Frac and press ENTER. The screen shows 2/3. The same steps turn a decimal into a fraction: 0.375 ►Frac gives 3/8.
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