Algebra Demystified 2nd Ed

82 algebra De mystif ieD

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

SOLUTIONS

1. −16 − 4 = −20


2. −70 − 19 = −89


3. −35 − 5 = −40


4. −100 − 8 = −108


5. −99 − 1 = −100

Double Negatives

A negative sign in front of a quantity can be interpreted to mean “opposite.”

For instance –3 can be called “the opposite of 3.” Viewed in this way, we can

see that –(–4) means “the opposite of –4.” But the opposite of –4 is +4, so

–(–4) = +4.

EXAMPLES

–(–25) = 25

–(–x) = x

–(–3y) = 3y

Rewriting a Subtraction Problem as an Addition Problem

Sometimes in algebra it is easier to think of a subtraction problem as an addi-

tion problem. One advantage to this is that we can rearrange the terms in an

addition problem but not a subtraction problem: 3 + 4 = 4 + 3 but 4 – 3 ≠ 3 – 4.

The minus sign can be replaced with a plus sign if we change the sign

of the number following it: 4 – 3 = 4 + (–3). The parentheses are used to show

that the sign in front of the number is a negative sign and not a minus sign.

The rule to rewrite a subtraction problem as an addition problem is

ab−=+−ab().

EXAMPLES

Rewrite as an addition problem.

–82 – 14 = –82 + (–14)

20 – (–6) = 20 + 6

x – y = x + (–y)

EXAMPLES

–(–25) = 25

EXAMPLES

Rewrite as an addition problem.

SOLUTIONS

1. −16 −