Explanation: Many fractions may be made into "equivalent" fractions having numbers that are less than 12. "Equivalent fractions" cover the same amount of space, such as 1/2 and 2/4. The first step is to consider the factors of the numerator (top number of a fraction) and denominator (bottom number on a fraction). Choose the greatest common factor, or "GCF", of the 2 numbers. Then rewrite each number as a multiplication problem in both the numerator and denominator, using the GCF as one of the factors. Then rewrite a multiplication problem of 2 separate fractions. The fraction with a GCF as the numerator and denominator is equivalent to 1. The problem is now 1 * the other fraction. The answer is simply the other fraction.

Examples:

4/16 GCF = 4 4/16 = (4*1)/(4*4) = 4/4 * 1/4 = 1 * 1/4 = 1/4

12/15 GCF = 3 12/15 = (3*4)/(3*5) = 3/3 * 4/5 = 1 * 4/5 = 4/5

Directions: For each problem in this problem set, you are to simplify the fraction completely. The denominators are less than 20. Strive for being able to do the problems with ease and then strive for speed. Good luck and enjoy the challenge!