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Chapter 3—Fractions

3-1 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.

fig030103.gif (1636 bytes)

Fractions allow you to plot values between whole numbers and integers.

A First Look at Fractions

fig0301_01.jpg (21026 bytes)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.

fig0301_03.jpg (4757 bytes)

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: 11/2, 2 3/4, 6 5/8, –4 1/4

fig0301_04.jpg (11425 bytes)

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.

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015