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Chapter 3—Fractions 31 Introducing Fractions
When you complete the work for this section, you should be able to:  Show where fractions occur on a number line.
 Explain how fractions indicate a specific portion of a whole object.
 Identify the numerator and denominator of a fraction.
 Define and identify proper fractions and improper fractions.
 Define and identify mixed numbers.
 Whole numbers and integers can be plotted on number lines . Fractions, however, allow us to plot points between the numbers—half way between 2 and 3, for example; or between –1 and –2. There is no limit to how finely you can divide the space between two whole numbers or integers.  Fractions allow you to plot values between whole numbers and integers.  A First Look at Fractions These squares are divided into four tiles.  In the first example, one of the four tiles is red. This can be written as the fraction ^{1}/_{4}.
 In the second instance, two of the four tiles are red. This can be written as the fraction ^{2}/_{4}.
 In the third instance, three of the four tiles are red. This can be written as the fraction ^{3}/_{4}.
 In the fourth instance, four of the four tiles are red. This can be written as the fraction ^{4}/_{4}.
The fraction ^{1}/_{4} is spoken as "one over four" or "one fourth" The fraction ^{3}/_{4} is spoken as "three over four" or "three fourths." Fractions are written as two numbers, one over the other, and separated by a bar. Definition  The upper number in a fraction is the numerator.
 The lower number in a fraction is the denominator
  Proper Fractions Definition A proper fraction is one where the absolute value of the numerator is smaller than the absolute value of the denominator.  Examples: This is an animated set of examples. Watch a few of them before moving on.   More Examples: Proper fractions: ^{1}/_{2}, ^{1}/_{3}, ^{2}/_{3}, ^{–5}/_{8} Fractions that are not proper fractions: ^{3}/_{2}, ^{4}/_{3}, ^{7}/_{3}, ^{–15}/_{8} Improper Fractions and Mixed Numbers Definitions  An improper fraction is one where the absolute value of the numerator is greater than, or equal to, the absolute value of the denominator.
Examples: ^{3}/_{2}, ^{8}/_{3}, ^{16}/_{5}, ^{7}/_{7}  A mixed number is one that includes an integer as well as a fractional part.
Examples: 1^{1}/_{2}, 2 ^{3}/_{4}, 6 ^{5}/_{8}, –4^{ 1}/_{4}  Three halves of these tiles are colored blue. A mixed number expresses fractional parts that are greater than 1.The blue tiles in these squares represent a total of three halves. There are two sets of tiles. Both halves of the first tile are colored blue. Examples and Exercises Introducing Fractions Select the response that best describes the given fraction or mixed number. Continue the work until you can complete at least ten examples without making any errors.  
