Page 166 - Basic College Mathematics with Early Integers

S E C T I O N 2.5 I MULTIPLYING AND DIVIDING INTEGERS 143

Examples Multiply. PRACTICE 1–4
#
1. -7 3 =-21 Multiply.
#
2. -21-52 = 10 1. -2 6 2. -41-32
#
#
3. 0 1-42 = 0 3. 0 1-102 4. 51-152
4. 101-82 =-80
Work Practice 1–4

Recall that by the associative and commutative properties for multiplication, we
may multiply numbers in any order that we wish. In Example 5, we multiply from
left to right.

Examples Multiply. PRACTICE 5–7
Multiply.
5. 7(–6)(–2)=–42(–2) 5. 71-221-42
=84 6. 1-521-621-12
7. 1-221-521-621-12
6. (–2)(–3)(–4)=6(–4)
=–24
7. 1-121-221-321-42 =-11-242 We have -24 from Example 6.
= 24
Work Practice 5–7

Concept Check What is the sign of the product of five negative numbers?
Explain.
# #
3
Recall from our study of exponents that 2 = 2 2 2 = 8. We can now work
with bases that are negative numbers. For example,
3
1-22 = 1-221-221-22 =-8

Example 8 Evaluate: 1-52 2 PRACTICE 8
4
Evaluate 1-32 .
Solution: Remember that 1-52 2 means 2 factors of -5.
2
1-52 = 1-521-52 = 25
Work Practice 8

Have you noticed a pattern when multiplying signed numbers?
If we let 1-2 represent a negative number and 1+2 represent a positive
number, then
1-21-2 = 1+2
Î
Î The product of an odd
The product of an even 1-21-21-2 = 1-2
number of negative numbers
number of negative Î 1-21-21-21-2 = 1+2 is a negative result.
numbers is a positive Î
1-21-21-21-21-2 = 1-2
result. Answers
1. -12 2. 12 3. 0 4. -75 5. 56
6. -30 7. 60 8. 81
2
Notice in Example 8 the parentheses around -5 in 1-52 . With these parenthe-
2
ses, -5 is the base that is squared. Without parentheses, such as -5 , only the 5 is Concept Check Answer
2
#
squared. In other words, -5 =-15 52 =-25 . Negative