86 algebra De mystif ieD

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 4

4. 62 ÷ (−2) = −31
   5.^1
   2

3

7

3

14

−







=−

6. (−4)(6)(−3) = 72

7.

(^43)
21
4
3
1
2
4
3
2
1
8
3
8
− 3
=÷− =⋅
−

−
=−

8. (−2)(5)(−6)(−8) = −480

9.

−

− =

− ÷− =− ⋅

−

=

53

56

3

5

6

5

3

5

5

6

1

2

10. −28 ÷ (−4) = 7

Negating Variables

Negating a variable does not automatically mean that the quantity is negative:

• x means “the opposite” of x. We can’t conclude that –x is a negative number
  unless we have reason to believe x itself is a positive number. If x is a negative
  number, −x is a positive number. (Although in practice we verbally say “nega-
  tive x” for “−x” when we really mean “the opposite of x.”)
  The same rules above apply when multiplying “negative” variables.

EXAMPLES

Use the rules for negating numbers in a product to rewrite the product.

−3(5x) = −15x 5(−x) = −5x

−12(−4x) = 48x −x(−y) = xy

−2x(3y) = −6xy x(−y) = −xy

−16x(−4y) = 64 xy 4(−1.83x)(2.36y) = −17.2752xy

−3(−x) = 3x

EXAMPLES

Use the rules for negating numbers in a product to rewrite the product.