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Chapter 3—Fractions

3-5 Multiplying Fractions and Mixed Numbers
When you complete the work for this section, you should be able to:
  • Demonstrate your ability to multiply fractions and mixed numbers.
  • Demonstrate your ability to simplify and reduce the results of a multiplication operation.

You've probably thought that addition is simpler than multiplication. It usually is ... for whole numbers and integers. Not for fractions. You will find that multiplication of fractions is a lot simpler than adding and subtracting them. So let's do the easier stuff first.

Multiplying Fractions

Procedure

To multiply fractions:
  1. Multiply the numerators to get the numerator for the product.
  2. Multiply the denominators to get the denominator for the product.
  3. Reduce or simplify the result as necessary.
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Example 1

Problem

1/2 x 3/4 = _____
Procedure
  1. Multiply the numerators.

1/2 x 3/4 =  3/?
  1. Multiply the denominators.

1/2 x 3/4 = 3/8
Solution

1/2 x 3/4 =  3/8

Example 2

Problem

1/2 x 2/3 = _____
Procedure
  1. Multiply the numerators.

1/2 x 2/3 =  2/?
  1. Multiply the denominators.

1/2 x 2/3 = 2/6
  1. Reduce or simplify the result as necessary.

2/6 = 1/3

Solution

1/2 x 2/3 = 1/3

Examples and Exercises

Multiplying Simple Fractions

Use these interactive examples and exercises to strengthen your understanding and build your skills: Complete the multiplication and reduce the result if necessary.

Multiplying Mixed Numbers

Procedure

To multiply mixed numbers:

  1. Convert the mixed fractions to improper fractions.
  2. Multiply the numerators and denominators.
  3. Reduce or simplify the result as necessary.

Example 3

Problem

3/8 x 5 =  _____

  
Procedure
  1. Convert the mixed fractions to improper fractions.

3/8 x 5 = 3/8 x 5/1
  1. Multiply the numerators.

3/8 x 5/1 =  15/?
  1. Multiply the denominators.

3/8 x 5/1 = 15/8
  1. Reduce or simplify the result as necessary.

15/8 = 1 7/8
Solution

3/8 x 5 =  1 7/8

  

Example 4

Problem

5 1/2 x 3 3/4 = _____

   
Procedure
  1. Convert the mixed fractions to improper fractions.

5 1/2 x 3 3/4 = 11/2 x 3 3/4

5 1/2 x 3 3/4 = 11/2 x  15/4
  1. Multiply the numerators.

11/2 x 15/4 =  165/?
  1. Multiply the denominators.

11/2 x 15/4 = 165/8
  1. Reduce or simplify the result as necessary.

165/8 = 20 5/8
Solution

5 1/2 x 3 3/4 = 20 5/8

  

Examples and Exercises

Multiplying Fractions and Mixed Numbers

Use these interactive examples and exercises to strengthen your understanding and build your skills: Complete the multiplication and reduce the result if necessary.

Author: David L. Heiserman
Publisher: SweetHaven Publishing Services

Copyright © 2007, David L. Heiserman
All Rights Reserved