Copyright © Cengage Learning. All rights reserved. 1 Basic Concepts Functions Copyright © Cengage Learning. All rights reserved.

Review of Operations with Fractions Unit 1B Review of Operations with Fractions Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved. 1.8 Multiplication and Division of Fractions Copyright © Cengage Learning. All rights reserved.

Multiplication and Division of Fractions Multiplying Fractions To multiply fractions, multiply the numerators and multiply the denominators. Then reduce the resulting fraction to lowest terms.

Example 1 Multiply: To simplify the work, consider the following alternative method: This method divides the numerator by 15, or (5  3), and the denominator by 15, or (5  3). It does not change the value of the fraction.

Multiplication and Division of Fractions Dividing Fractions To divide a fraction by a fraction, invert the fraction (interchange numerator and denominator) that follows the division sign (). Then multiply the resulting fractions.

Example 5 Divide: Invert and multiply.

Multiplication and Division of Fractions When both multiplication and division of fractions occur, invert only the first fraction that follows a division sign (). Then proceed according to the rules for multiplying fractions.

Applications Involving Multiplication and Division of Fractions

Applications Involving Multiplication and Division of Fractions Lumber is usually measured in board feet. One board foot is the amount of wood contained in a piece of wood that measures one inch thick and one square foot in area, or its equivalent. (See Figure 1.28.) One board foot Figure 1.28

Applications Involving Multiplication and Division of Fractions The number of board feet in lumber may be found by the formula The 12 in the denominator comes from the fact that the simplest form of one board foot can be thought of as a board that is 1 in. thick  12 in. wide  1 ft long.

Applications Involving Multiplication and Division of Fractions Lumber is either rough or finished. Rough stock is lumber that is not planed or dressed; finished stock is planed on one or more sides. When measuring lumber, we compute the full size. That is, we compute the measure of the rough stock that is required to make the desired finished piece. When lumber is finished or planed, in. is taken off each side when the lumber is less than in. thick.

Applications Involving Multiplication and Division of Fractions If the lumber is in. or more in thickness, in. is taken off each side. (Note: Lumber for framing houses usually measures in. less than the name that we call the piece. For example, a “two-by-four,” a piece 2 in. by 4 in., actually measures in. by in.)

Example 11 Find the number of board feet contained in 6 pieces of lumber 2 in.  8 in.  16 ft (Figure 1.29). Figure 1.29

Example 11 cont’d