Overview: What Are Fractions?
Fractions consist of a numerator, a, and a denominator, b, so that the fraction takes the form a/b. The denominator is the number of equal parts in a whole, and the numerator is the number of parts considered. For example, if a pizza is divided into 8 equal pieces, and 3 pieces are taken, the fraction to describe the relationship is 3/8. There is a close relationship between fractions and division, so that for any numbers a and b, and b is not equal to zero, a/b means that a is divided by b.
What Are Mixed Numbers and Improper Fractions?
In many fractions, the numerator is smaller than the denominator, so the fraction is less than 1. For example, 1/8 is less than 1. Using the division model, where a is divided by b to describe a fraction, the numerator can be larger than the denominator, such as 8/5. The number 8/5 can be represented 2 different ways, either as a mixed number 1 3/5, or an improper fraction 8/5. Think, 5/5 is equal to 1, and there are 3/5 left over. Even though the mixed number and the improper fraction mean the same thing, they are used in different circumstances.
What Are Common Denominators?
In order to compare fractions with each other, both must have the same denominator. In order to do that, find the least common multiple of both denominators. What is the common denominator for 1/6 and 1/4? The least common multiple is 12, so 1/6 x 2/2 would equal 2/12, and 1/4 x 3/3 would equal 3/12.
What Are Equal Fractions?
Fractions are equal when one fraction can be obtained from the other. The fractions 1/6 and 2/12 are equal because 2/12 means 1 X 2/6 X 2. Similarly, the fractions 1/4 and 3/12 are equal because 3/12 means 1 X 3/4 X 3. This can also be shown graphically with fraction bars, as 1/2 can be represented by 2/4, 4/8, 8/16 and so on. There are an infinite number of equal pairs of fractions.
What Are Unequal Fractions?
Although 1/6 and 1/4 can be transformed into equivalent fractions with the same common denominator, so that 1/6 is equal to 2/12 and 1/4 is equal to 3/12, 1/6 is not equal to 1/4. That can be shown clearly because 2/12 and 3/12 are not equal. The properties of equal fractions and unequal fractions together also illustrate the density of the number line, because there are an infinite number of fractions on the number line.
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