OBJECTIVE 2 Find the product of two negative numbers. Look at another
pattern.
- 51 - 12 =?
- 5102 = 0
- 5112 =- 5
- 5122 =- 10
- 5132 =- 15
- 5142 =- 20
50 CHAPTER 1 The Real Number System
The products
increase by 5.The numbers in color on the left of the equals symbol decrease by 1 for each step
down the list. The products on the right increase by 5 for each step down the list. To
maintain this pattern, should be 5 more than or 5 more than 0, so
The pattern continues with
and so on, which suggests the next rule.
- 51 - 52 = 25 ,
- 51 - 42 = 20
- 51 - 32 = 15
- 51 - 22 = 10
- 51 - 12 = 5.
- 51 - 12 - 5102 ,
Multiplying Two Negative NumbersFor any positive real numbers xand y,
That is, the product of two negative numbers is positive.
Example: - 51 - 42 = 20
x 1 y 2 xy.
NOW TRY
EXERCISE 2
Find the product.
1
7
a-5
2
bNOW TRY ANSWER
- 145
Multiplying Two Negative NumbersFind each product, using the multiplication rule given in the box.
(a) (b)
(c) (d) NOW TRY
The following box summarizes multiplying signed numbers.
-
2
3
a-
3
2
b =
2
3
#^3
2
- 81 - 12 = 8 # 1 = 8 = 1
- 91 - 22 = 9 # 2 = 18 - 61 - 122 = 6 # 12 = 72
EXAMPLE 2
Multiplying Signed NumbersThe product of two numbers having the samesign is positive.
The product of two numbers having differentsigns is negative.
OBJECTIVE 3 Identify factors of integers.The definition of factor from
Section 1.1can be extended to integers. If the product of two integers is a third inte-
ger, then each of the two integers is a factorof the third. The table on the next page
shows examples.
http://www.ebook777.com
http://www.ebook777.com