Page 87 - MarceAlgebra Demystified

74 CHAPTER 4 Negative Numbers

3 3 6 3 5 1
9: 5 ¼ ¼ ¼
6 5 5 5 6 2
5

10: 28 ð 4Þ¼ 7
Negating a variable does not automatically mean that the quantity will be
negative: x means ‘‘the opposite’’ of x. We cannot conclude that x is a
negative number unless we have reason to believe x itself is a positive num-
ber. If x is a negative number, x is a positive number. (Although in practice
we verbally say ‘‘negative x’’ for ‘‘ x’’ when we really mean ‘‘the opposite of
x.’’)
The same rules apply when multiplying ‘‘negative’’ variables.

Examples

3ð5xÞ¼ 15x 5ð xÞ¼ 5x

12ð 4xÞ¼ 48x xð yÞ¼ xy

2xð3yÞ¼ 6xy xð yÞ¼ xy

16xð 4yÞ¼ 64xy 4ð 1:83xÞð2:36yÞ¼ 17:2752xy

3ð xÞ¼ 3x

Practice

1: 18ð 3xÞ¼

2: 4ð2xÞð 9yÞ¼

3: 28ð 3xÞ¼

4: 5xð 7yÞ¼

5: 1ð 6Þð 7xÞ¼

6: 1:1xð2:5yÞ

7: 8:3ð4:62xÞ¼