Simplify Fractions Calculator
History
Your results will appear here. Tap Use on any of them to carry it into the next calculation, in this calculator or another one. History is kept while this tab is open.
To simplify fractions, divide the numerator and the denominator by their greatest common factor (GCF): 12/16 becomes 3/4. This fraction simplifier takes mixed numbers too. Press Simplify to see the simplest form, the mixed number and the decimal.
How to Simplify a Fraction
Simplifying fractions and reducing fractions mean the same thing. Here is how you reduce a fraction:
- Find the greatest common factor of the numerator and the denominator.
- Divide both of them by it.
- Check that the new pair shares no factor other than 1.
a/b = (a ÷ GCF)/(b ÷ GCF)
For 12/16, the GCF is 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4, so 12/16 = 3/4.
If the GCF isn't obvious, divide by any common factor and keep going: 12/16 → 6/8 → 3/4. More steps, same answer. Some textbooks split both numbers into prime factors instead; that also ends at 3/4.
The line under the result shows the one-step version: GCF 4 · 12 ÷ 4 = 3 · 16 ÷ 4 = 4 · 0.75.
Greatest Common Factor
The GCF is the largest number that divides both the numerator and the denominator. With small numbers, list the factors of the smaller one and keep those that also divide the larger. The factors of 12 are 1, 2, 3, 4, 6 and 12. Of these, 1, 2 and 4 divide 16, so the GCF is 4.
For bigger numbers, Euclid's algorithm is quicker. Divide, keep the remainder, repeat until it's 0: 16 = 1 · 12 + 4, then 12 = 3 · 4 + 0. The last non-zero remainder, 4, is the GCF. The calculator finds it for you.
Simplest Form and Lowest Terms
A fraction is in simplest form when its numerator and denominator have no common factor greater than 1, that is, when their GCF is 1. Lowest terms is another name for it, so a simplest form calculator and a lowest terms calculator give the same result. Enter 3/4 and the line under the result reads "3/4 is already in simplest form".
An improper fraction in simplest form stays improper. 18/8 reduces to 9/4 and no further. The mixed number 2 1/4 is the same value written another way, and the display shows it beside the fraction: 9/4 = 2 1/4.
Simplified Fractions Are Equivalent Fractions
Simplifying doesn't change the value. 12/16 and 3/4 are equal, and both come to 0.75.
To go the other way, multiply the numerator and the denominator by the same number. Every fraction you get is an equivalent fraction: 3/4 = 6/8 = 12/16. The calculator only reduces, so you build up a fraction with a bigger denominator by hand.
To turn a decimal into a fraction, or a fraction into a decimal, use the decimal to fraction calculator.
Examples
Each row is one calculation as the display shows it: what you enter, the simplified fraction and the line under the result.
| You enter | Result | Line under the result |
|---|---|---|
| 12/16 | 3/4 | GCF 4 · 12 ÷ 4 = 3 · 16 ÷ 4 = 4 · 0.75 |
| 4/12 | 1/3 | GCF 4 · 4 ÷ 4 = 1 · 12 ÷ 4 = 3 · 0.333333333333 |
| 18/8 | 9/4 = 2 1/4 | GCF 2 · 18 ÷ 2 = 9 · 8 ÷ 2 = 4 · 2.25 |
| 18/6 | 3 | GCF 6 · 18 ÷ 6 = 3 · 6 ÷ 6 = 1 |
| 3/4 | 3/4 | 3/4 is already in simplest form |
| −8/12 | −2/3 | GCF 4 · −8 ÷ 4 = −2 · 12 ÷ 4 = 3 · −0.666666666667 |
| 2 4/8 | 5/2 = 2 1/2 | 2 4/8 = 20/8 · GCF 4 · 20 ÷ 4 = 5 · 8 ÷ 4 = 2 · 2.5 |
For a negative fraction, press ± before the numbers. To add, subtract, multiply or divide two fractions, use the fraction calculator.
As a percent, 3/4 is 0.75 × 100 = 75%. For percent problems, use the percentage calculator.
FAQ
What is a simplified fraction?
It's a fraction whose numerator and denominator can't both be divided by any number greater than 1. It equals the original: 12/16 simplified is 3/4, and both are 0.75.
Can 3/4 be simplified?
No. The only common factor of 3 and 4 is 1, so 3/4 is already in simplest form.
What is the simplest way to simplify fractions?
Divide the numerator and the denominator by their GCF, and you're done in one step. If you can't spot the GCF, divide by any common factor and repeat until none is left, as in How to Simplify a Fraction.
How do you simplify 4/12?
The GCF of 4 and 12 is 4: 4 ÷ 4 = 1 and 12 ÷ 4 = 3, so 4/12 = 1/3. The ratio 4 : 12 simplifies the same way, to 1 : 3; for ratios, use the ratio calculator.
How do you simplify an improper fraction?
Reduce it like any other fraction, then write it as a mixed number if you need one: 18/8 = 9/4 = 2 1/4. Enter a mixed number such as 2 4/8, and the calculator first turns it into 20/8, then reduces it to 5/2 = 2 1/2. Converting between improper fractions and mixed numbers is explained on the fraction calculator.