SECTION 1.6 Multiplying and Dividing Real Numbers^49
OBJECTIVES
Multiplying and Dividing Real Numbers
1.6
1 Find the product of
a positive number
and a negative
number.
2 Find the product of
two negative
numbers.
3 Identify factors of
integers.
4 Use the reciprocal
of a number to
apply the definition
of division.
5 Use the rules for
order of operations
when multiplying
and dividing signed
numbers.
6 Evaluate expressions
involving variables.
7 Translate words and
phrases involving
multiplication and
division.
8 Translate simple
sentences into
equations.The result of multiplication is called the product.We know that the product of two
positive numbers is positive. We also know that the product of 0 and any positive
number is 0, so we extend that property to all real numbers.
Multiplication by Zero
For any real number x, x# 0 0.OBJECTIVE 1 Find the product of a positive number and a negative
number.Look at the following pattern.
3 # 1 - 12 =?
3 # 0 = 0
3 # 1 = 3
3 # 2 = 6
3 # 3 = 9
3 # 4 = 12
3 # 5 = 15
The products
decrease by 3.What should equal? The product represents the sum
so the product should be 3. Also,
and
These results maintain the pattern in the list, which suggests the following rule.
31 - 32 =- 3 + 1 - 32 + 1 - 32 = - 9.
31 - 22 =- 2 + 1 - 22 + 1 - 22 = - 6
-
- 1 + 1 - 12 + 1 - 12 = - 3 ,
31 - 12 31 - 12
Multiplying Numbers with Different SignsFor any positive real numbers xand y,
and
That is, the product of two numbers with opposite signs is negative.
Examples: 61 - 32 =- 18 and 1 - 623 =- 18
x 1 y 2 1 xy 2 1 x 2 y 1 xy 2.
NOW TRY
EXERCISE 1
Find each product.
(a) - 11192 (b)3.1 1 - 2.5 2
Multiplying a Positive Number and a Negative NumberFind each product, using the multiplication rule given in the box.
(a) (b)
(c) (d)
NOW TRY- 9 a 6.2 1 - 4.1 2 =- 1 6.2#4.1 2 =-25.42
1
3
b =-a 9 #
1
3
b =- 3
81 - 52 = - 18 # 52 = - 40 1 - 524 =- 15 # 42 =- 20
EXAMPLE 1
NOW TRY ANSWERS
- (a)- 99 (b) -7.75