**Equivalent fractions can be found by either dividing or multiplying both the numerator and denominator by the same nonzero number.** For example, when the top, or numerator, and bottom, or denominator, of the fraction 2/4 is divided by 2, the result is the equivalent fraction 1/2. When the top and bottom of 2/4 is multiplied by 2, the equivalent fraction is 4/8.

Equivalent fractions are fractions that represent the same value, although the numbers in the fraction are different. When a fraction can no longer be divided by a whole number, the fraction has been reduced to its simplest form, or simplified. For example, 1/2 can no longer be divided by a whole number. Other equivalent fractions of 2/4 are 6/12, 8/16 and 10/20. Equivalent fractions can only be found by multiplying or dividing, not by adding or subtracting.

Other types of fractions include proper, improper, reciprocal and mixed number. Proper fractions are fractions when the numerator is a smaller number than the denominator. Examples of proper fractions include 1/2, 4/5 and 5/25. Improper fractions are fractions that have a smaller denominator than numerator. Examples of these include 9/1, 8/3 and 6/4. Fractions that have an equal numerator and denominator, such as 10/10, are also improper fractions. Reciprocal fractions are fractions that when multiplied, equal 1. For example, 4/3 and 3/4 are reciprocals because 3/4*4/3 is equal to 12/12, or 1. Mixed numbers are comprised of a whole number, such as 6, and a proper fraction, such as 1/5, which together are written as 6 1/5.