Fractions may have numerators and denominators that are composite numbers. To keep the numbers small and easy to understand, we can simplify them. This will not change the value of the fraction.

Here is the most efficient way to simplify a fraction:

• Find the Greatest Common Factor (GCF) of the numerator and denominator
• Divide the numerator and the denominator by the GCF

Example: Simplify 42/54. Since 42 and 54 have a GCF of 6, we can divide both of them by 6, and get the result of 7/9.

However, sometimes it's not so easy to find the GCF right away. In that case, we can start with any common factor of the numerator and denominator, but we must repeat the process until we are sure there are no more common factors. Here are the steps:

• Find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly.
• Divide both the numerator and denominator by the common factor.
• Repeat this process until there are no more common factors.
• The fraction is simplified when no more common factors exist.

Example: Simplify 42/54. We might notice right away that both have a common factor of 2 because they are both even numbers. So we can start by dividing the 2 from both the numerator and denominator.

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However, we must check again for another common factor. We have it--three. Again, divide both the numerator and denominator.

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Now we are finished because 7 and 9 have no common factors aside from 1.

Simplifying fractions creates an equivalent fraction using smaller numbers. This works because of how we divide the numerator and denominator by the same factor. Any number over itself (e.g. 2/2, 3/3) is equivalent to 1, and multiplying or dividing by 1 does not change a number. This is known as the identity property of multiplication. Any number keeps its identity when it is multiplied or divided by 1.