Fractions

Technically, fractions express the relationship between two numbers set up as division. The numerator is the number on the top of the fraction. It represents the dividend in the division. The denominator is the bottom number of the fraction. It represents the divisor. Fractions in which the numerator is smaller than the denominator, represent less than a whole unit and are known as common or proper fractions. When a fraction’s denominator is equal to or less than the numerator, it represents one whole unit or more and is known as an improper fraction. A number that combines a whole number with a proper fraction is known as a mixed number. When a fraction has been reduced to the point where there are no common divisors left, other than 1, it is said to be reduced to lowest terms. The largest number that is a common divisor of a fraction is known as the greatest common divisor. It reduces the fraction to lowest terms in one step. Reducing fractions by inspection or observation is often a trial-and-error procedure. Sometimes a fraction’s common divisors are obvious; other times they are more difficult to determine. Reducing fractions by the greatest common divisor method. The best method for reducing a fraction to lowest terms is to divide the numerator and the denominator by the greatest common divisor because this accomplishes the task in one step. Sometimes it is difficult to determine which of two fractions is the larger or smaller number. By converting them to like fractions (same denominator), the answer will become evident. The least common denominator (LCD) is the smallest number that is a multiple of each of the given denominators.