Simplifying Fractions

To express a fraction in its simplest form, divide both the numerator and denominator by their greatest common factor (GCF).

Example: Find the simplest form of 10/25.

The GCF of 10 and 25 is 5.
Divide both the numerator and the denominator by 5.
10/25 divided by 5/5 = 2/5

The simplest form of 10/25 is 2/5.

If the numerator of a fraction is bigger than the denominator, the fraction is an Improper Fraction.

You can simplify any improper fraction:
First, divide the numerator and the denominator by the GCF.
Then, change the fraction to a mixed number.

Example: Find the simplest form of 42/12.

The GCF of 42 and 12 is 6.
42/12 divided by 6/6 = 7/2

Change 7/2 to a mixed number by dividing 7 by 2.

The simplest form of 42/12 is 3 & 1/2.

Two fractions are EQUIVALENT if they have the same value in simplest form.

3/12, 2/8, and 1/4 are equivalent fractions because the simplest form of each fraction is 1/4.