What Does it Mean to "Reduce Fractions?"
One of the concepts that is central to working with fractions in math is that as long as you perform the same operation on both the numerator (top) and denominator (bottom), you won't change the underlying value of the fraction.
For example, if you begin the fraction 1/2, and multiply the top and bottom of the fraction by, say 5, you will not change the underlying value of the fraction no matter how many times you repeat the multiplication.
| 1 | = | 1 x 5 | = | 5 | = | 5 x 5 | = | 25 | = | 25 x 5 | = | 125 |
| 2 | 2 x 5 | 10 | 10 x 5 | 50 | 50 x 5 | 250 |
125 ÷ 250 = .50 = 1/2
Now, since 125/250 is the same as 1/2, 1/2 would be the simplified version of 125/250 (or 500/1000, 2500/5000, etc.). And since working with smaller numbers is easier than working with larger numbers, it always makes sense to reduce fractions to their simplest form before working with them.
How To Simply Fractions
The easiest way to simplify fractions is to use the fraction reducer calculator on this page. Otherwise, if you would like to simplify fractions manually, there are a couple of different ways:
The Trial and Error Method
To use the trial and error method of simplifying fractions you just start by attempting to divide the numerator and denominator by a small number that you believe to a common factor to both (usually 2) and then continue to work your way up. After each successful reduction, you then need to repeat the process until the numerator and denominator have no other factors in common.
| 8 | = | 8 ÷ 2 | = | 4 | = | 4 ÷ 2 | = | 2 |
| 12 | 12 ÷ 2 | 6 | 6 ÷ 2 | 3 |
The Greatest Common Factor Method
To use the greatest common factor method of simplifying fractions you first need to find the greatest common factor of the numerator and denominator. Next, you simply divide the numerator and denominator by their greatest common factor.
Using the fraction 8/12 from above, we find that the greatest common factor of the numerator and denominator is 4.
| 8 | = | 8 ÷ 4 | = | 2 |
| 12 | 12 ÷ 4 | 3 |
Regardless of which manual method you choose, using them to reduce fractions can be extremely tedious and time-consuming. Therefore I would suggest you bookmark the fraction reducer calculator and use it any time you are working with fractions.
How to Convert Improper Fraction to Mixed Number
An improper fraction is a fraction that has a numerator that is greater than its denominator. Typically, when you are asked to simplify fractions, and a simplified fraction turns out to be an improper fraction, you would need one final step before the simplification was considered complete. And that would be to convert the improper fraction to a mixed number (a b/c).
To convert an improper fraction to a mixed number (the fraction reducer calculator does this for you), you first divide the numerator by the denominator. The number of full times the denominator goes into the numerator becomes the whole number, the remainder becomes the numerator, and the denominator remains unchanged.
Here is how you would convert the improper fraction 5/3 into a mixed number.
| 5 | >>> | 5 ÷ 3 = 1 with remainder of 2 | >>> | 1 | 2 |
| 3 | 3 |
How to Convert Mixed Numbers Into Improper Fractions
To convert a mixed number to an improper fraction, multiply the denominator by the whole number portion of the mixed number, add that result to numerator to get the improper numerator, and keep the denominator the same.
Here is how you would convert the mixed number 1-2/3 into an improper fraction.
| 1 | 2 | >>> | (3 × 1) + 2 = 5 | >>> | 5 |
| 3 | 3 |
Happy simplifying!