, and 1 × 5 = 5. Thus, any number divided or multiplied by a fraction equal to one will be itself. For example, 
and 
.The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
A fraction compares two numbers by division. To conduct basic operations, keep in mind that any number except 0 divided by itself is 1, and 1 times any number is itself. That is, , and 1 × 5 = 5. Thus, any number divided or multiplied by a fraction equal to one will be itself. For example, and .
When multiplying fractions, the numerators (top numbers) are multiplied together and the denominators (bottom numbers) are multiplied together. So 
. And 
.
To divide fractions, rewrite the problem as multiplying by the reciprocal (multiplicative inverse) of the divisor. So 
.
To add fractions that have the same, or a common, denominator, simply add the numerators, and use the common denominator. The figure below illustrates why this is true.
However, fractions cannot be added until they are written with a common denominator. The figure below shows why adding fractions with different denominators is incorrect.
To correctly add ½ and ⅓, common denominator must first be found. Usually, the least common multiple of the denominators (also called the least common denominator) is the best choice for the common denominator. In the example below, the least common multiple of the two denominators—2 and 3—is 6, so the least common denominator is 6. To convert the fractions, multiply ½ by 
(which is equivalent to 1) to get 
. Similarly, multiply ⅓ by 
(which is equivalent to 1) to get 
.
First 
And 
So 
, or 
To model this problem visually, divide a rectangle into halves horizontally, then into thirds vertically, creating six equal parts (see the figure below). Shade one-half in color to show ½, and then shade one-third in gray to show ⅓. Since, as the figure shows, the upper left square has been shaded twice, it must be "carried" (see arrow). Now five of six squares are shaded; therefore, 
.
Subtraction of fractions is similar to addition, in that the fractions being subtracted must have a common denominator. So 
.