OpenStax-CNX module: m34867
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Multiplication and Division of
Whole Numbers: Properties of
Multiplication
∗
Wade Ellis
Denny Burzynski
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 3.0
†
Abstract
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr.
This
module discusses properties of multiplication of whole numbers. By the end of the module students should
be able to understand and appreciate the commutative and associative properties of multiplication and
understand why 1 is the multiplicative identity.
1 Section Overview
• The Commutative Property of Multiplication
• The Associative Property of Multiplication
• The Multiplicative Identity
We will now examine three simple but very important properties of multiplication.
2 The Commutative Property of Multiplication
Commutative Property of Multiplication
The product of two whole numbers is the same regardless of the order of the factors.
2.1 Sample Set A
Example 1
Multiply the two whole numbers.
∗ Version
1.2: Aug 18, 2010 8:45 pm -0500
† http://creativecommons.org/licenses/by/3.0/
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6 · 7 = 42
7 · 6 = 42
The numbers 6 and 7 can be multiplied in any order. Regardless of the order they are multiplied,
the product is 42.
2.2 Practice Set A
Use the commutative property of multiplication to nd the products in two ways.
Exercise 1
(Solution on p. 7.)
Exercise 2
(Solution on p. 7.)
3 The Associative Property of Multiplication
Associative Property of Multiplication
If three whole numbers are multiplied, the product will be the same if the rst two are multiplied rst and
then that product is multiplied by the third, or if the second two are multiplied rst and that product is
multiplied by the rst. Note that the order of the factors is maintained.
It is a common mathematical practice to use parentheses to show which pair of numbers is to be combined
rst.
3.1 Sample Set B
Example 2
Multiply the whole numbers.
(8 · 3) · 14 = 24 · 14 = 336
8 · (3 · 14) = 8 · 42 = 336
3.2 Practice Set B
Use the associative property of multiplication to nd the products in two ways.
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Exercise 3
(Solution on p. 7.)
Exercise 4
(Solution on p. 7.)
4 The Multiplicative Identity
The Multiplicative Identity is 1
The whole number 1 is called the multiplicative identity,
changed.
since any whole number multiplied by 1 is not
4.1 Sample Set C
Example 3
Multiply the whole numbers.
12 · 1 = 12
1 · 12 = 12
4.2 Practice Set C
Multiply the whole numbers.
Exercise 5
(Solution on p. 7.)
5 Exercises
For the following problems, multiply the numbers.
Exercise 6
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(Solution on p. 7.)
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Exercise 7
Exercise 8
(Solution on p. 7.)
Exercise 9
Exercise 10
(Solution on p. 7.)
Exercise 11
Exercise 12
(Solution on p. 7.)
Exercise 13
Exercise 14
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(Solution on p. 7.)
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Exercise 15
Exercise 16
(Solution on p. 7.)
Exercise 17
For the following 4 problems, show that the quantities yield the same products by performing the multiplications.
Exercise 18
(4 · 8) · 2 and 4 · (8 · 2)
(Solution on p. 7.)
Exercise 19
(100 · 62) · 4 and 100 · (62 · 4)
Exercise 20
23 · (11 · 106) and (23 · 11) · 106
(Solution on p. 7.)
Exercise 21
1 · (5 · 2) and (1 · 5) · 2
Exercise 22
(Solution on p. 7.)
The fact that (a rst number · a second number)· a third number = a rst number ·(a second number · a third number
an example of the
property of multiplication.
Exercise 23
property of
The fact that 1 · any number = that particular numberis an example of the
multiplication.
Exercise 24
(Solution on p. 7.)
Use the numbers 7 and 9 to illustrate the commutative property of multiplication.
Exercise 25
Use the numbers 6, 4, and 7 to illustrate the associative property of multiplication.
5.1 Exercises for Review
Exercise 26
() In the number 84,526,098,441, how many millions are there?
Exercise 27
(Solution on p. 7.)
85
() Replace the letter m with the whole number that makes the addition true. + m
97
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OpenStax-CNX module: m34867
Exercise 28
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(Solution on p. 7.)
() Use the numbers 4 and 15 to illustrate the commutative property of addition.
Exercise 29
() Find the product. 8, 000, 000 × 1, 000.
Exercise 30
(Solution on p. 7.)
() Specify which of the digits 2, 3, 4, 5, 6, 8,10 are divisors of the number 2,244.
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Solutions to Exercises in this Module
Solution to Exercise (p. 2)
15 · 6 = 90 and 6 · 15 = 90
Solution to Exercise (p. 2)
432 · 428 = 184, 896 and 428 · 432 = 184, 896
Solution to Exercise (p. 2)
168
Solution to Exercise (p. 3)
165,564
Solution to Exercise (p. 3)
843
Solution to Exercise (p. 3)
234
Solution to Exercise (p. 4)
4,032
Solution to Exercise (p. 4)
326,000
Solution to Exercise (p. 4)
252
Solution to Exercise (p. 4)
21,340
Solution to Exercise (p. 5)
8,316
Solution to Exercise (p. 5)
32 · 2 = 64 = 4 · 16
Solution to Exercise (p. 5)
23 · 1, 166 = 26, 818 = 253 · 106
Solution to Exercise (p. 5)
associative
Solution to Exercise (p. 5)
7 · 9 = 63 = 9 · 7
Solution to Exercise (p. 5)
6
Solution to Exercise (p. 6)
4 + 15 = 19
15 + 4 = 19
Solution to Exercise (p. 6)
2, 3, 4, 6
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