Pre-Algebra Demystified

Each integer has anopposite. The opposite of a given integer is the cor-

responding integer, which is exactly the same distance from the origin as

the given integer. For example, the opposite of
4isþ4 or 4. The opposite

of 0 is 0.

The positive distance any number is from 0 is called theabsolute valueof

the number. The symbol for absolute value is | |. Hence, |
6|¼6 and |þ10|¼

10. In other words, the absolute value of any number except 0 is positive. The
    absolute value of 0 is 0, i.e., |0|¼0.

Math Note: Do not confuse the concepts of opposite and absolute

value. With the exception of zero, to find the opposite of an integer,

change its sign and to find the absolute value of an integer,

make it positive.

EXAMPLE

Find the opposite of 12.

SOLUTION

The opposite of 12 is
12 since we change the sign.

EXAMPLE

Find |12|.

SOLUTION

|12|¼12 since the absolute value of this number is 12.

EXAMPLE

Find the opposite of
3.

SOLUTION

The opposite of
3isþ3 or 3 since we change the sign.

EXAMPLE

Find |
3|.

SOLUTION

|
3|¼3 since the absolute value is positive.

Sometimes a negative sign is placed outside a number in parentheses. In

this case, it means the opposite of the number inside the parentheses. For

example,
ð
 6 Þmeans the opposite of
6, which is 6. Hence,
ð
 6 Þ¼6.

Also,
ðþ 8 Þmeans the opposite of 8, which is
8. Hence,
ðþ 8 Þ¼
8.

18 CHAPTER 2 Integers