Simplify Fractions Calculator: Lowest Terms, Mixed Number, Decimal
A fraction in lowest terms with the common factor shown, plus its mixed number, decimal and percentage.
Inputs
- Numerator18(75%)
- Remainder6(25%)
- Working
- The greatest common factor of 18 and 24 is 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4
- Decimal
- 0.75
- Percentage
- 75.00%
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What each Simplify Fractions input means
- Numerator
- The top number — how many of the equal parts you have. Whole numbers only, negatives allowed. For a fraction with a decimal in it, such as 2.5/4, multiply both numbers by 10 first and enter 25/40.
- Denominator
- The bottom number — how many equal parts make one whole. It cannot be 0. A negative denominator is fine: the sign moves to the top, so 3/−12 comes out as −1/4.
Simplify Fractions formula
simplified = (numerator ÷ GCF) / (denominator ÷ GCF), where GCF is the greatest common factor
A fraction is in lowest terms when the top and bottom share no factor but 1. OpenStax's method is to write both as products of their factors and remove the factors they share — the Equivalent Fractions Property says that does not change the value. Doing it in one step means dividing both by their greatest common factor: 18/24 shares a 6, so it is 3/4. The page shows that factor, then the fraction as a mixed number when it is more than 1, as a decimal and as a percentage.
Simplify Fractions worked example
18 and 24 are both divisible by 6, their greatest common factor: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4 — 0.75, or 75%. OpenStax's example, 10/15, works the same way with a common factor of 5: 2/3.
More Simplify Fractions examples
45 minutes out of an hour, 45/60. The greatest common factor of 45 and 60 is 15, and 45 ÷ 15 = 3 while 60 ÷ 15 = 4, so it is 3/4 of an hour: 0.75, or 75%. Dividing by a smaller shared factor first, such as 5 (giving 9/12), also works; it just needs a second step, ÷ 3, to finish.
An improper fraction, 22/8. Both numbers are even and 2 is their greatest common factor, so it reduces to 11/4. As a mixed number that is 2 3/4, because 4 goes into 11 twice with 3 left over; as a decimal it is 2.75.
Where the Simplify Fractions calculator can give the wrong answer
- A denominator of zero is rejected; division by zero is undefined.
- The sign is kept on the numerator: −3/12 becomes −1/4.
- Improper fractions are shown as a mixed number too: 7/4 is 1 3/4.
- Only whole-number numerators and denominators are simplified; for a decimal like 0.375, use the decimal-to-fraction calculator.
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Simplify Fractions reference table
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/12 | 0.0833… | 8.33% |
| 1/16 | 0.0625 | 6.25% |
Simplify Fractions FAQ
- Divide the numerator and denominator by their greatest common factor. 18/24: the GCF is 6, so 3/4.
- When the numerator and denominator have no common factor except 1. 3/4 is; 6/8 is not, since both divide by 2.
- Divide: the whole-number answer is the whole part and the remainder sits over the same denominator. 11/4 is 2 remainder 3, so 2 3/4.
- Divide the top by the bottom and multiply by 100. 3/8 = 0.375 = 37.5%.
- Divide the top and bottom by any number that goes into both, and repeat until nothing does. 48/72: halve to 24/36, halve again to 12/18, then divide by 6 to get 2/3. The greatest common factor, 24 here, simply does it in one step.
- Multiply the top and bottom by 10, 100 or whatever clears the decimals, then simplify the whole numbers. 1.5/4.5 becomes 15/45, which is 1/3.
- Rewrite them over a common denominator — the least common multiple of the bottoms — then add or subtract the tops and simplify. 1/4 + 1/6: the LCM of 4 and 6 is 12, so 3/12 + 2/12 = 5/12.
- Multiply the tops together and the bottoms together, then simplify: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the second fraction turned upside down: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. OpenStax Prealgebra cancels common factors before multiplying, which keeps the numbers small.
- Yes, and it equals 0: zero parts of anything is nothing. 5/0 is different — it is undefined, because no number multiplied by 0 gives 5.