This document provides examples and definitions for finding opposite numbers. It begins with examples of finding the opposite of situations, such as a deposit becoming a withdrawal. It then gives examples of finding the opposite of numbers on a number line by changing the sign. Further examples show finding the opposite of absolute values and additive inverses. Definitions provided state that opposite numbers differ only in sign and are the same distance from zero on a number line but in opposite directions. The procedure for finding opposites is given as changing the sign of the original number.

1. Opposite Numbers
GUIDED EXAMPLE 1 Find the opposite of each situation.
SITUATION
a. A deposit of $38.25 into a
checking account
OPPOSITE
b. A population growth of
1394 people
c. Losing 15 pounds of weight
d. A loss of 8 yards in a
football game
e. Climbing up (ascending) a
mountain that is 2135 feet
in elevation
A withdrawal of $38.25 from the
checking account
A population decline of 1394 people
Gaining 15 pounds of weight
A gain of 8 yards in a
football game
Climbing down (descending) a
mountain that is 2135 feet in
elevation

2. Finding the Opposite of a Number
GUIDED EXAMPLE 2 Find the opposite of the number using a
number line.
SOLUTION
STEP RESULT
The opposite of is
Locate the number on a
number line.
Find the number that is the
same distance from zero,
but on the opposite side of
the number line.
Answer

3. Finding the Opposite of a Number
GUIDED EXAMPLE 3 Find the opposite of each of the following
numbers.
REAL NUMBER INSERT A MINUS SIGN OPPOSITE
a.
b.
c.
d.
e.
f.

4. Finding the Opposite of an Absolute Value
GUIDED EXAMPLE 4 Find the opposite of each of the following
absolute values.
ABSOLUTE VALUE INSERT A MINUS SIGN OPPOSITE
a.
b.
c.
d.
e.
f.

5. Additive Inverses
GUIDED EXAMPLE 5 Find the additive inverse, or opposite, of each
number. Then add the additive inverse to the number.
REAL NUMBER ADDITIVE INVERSE (OPPOSITE) SUM
a.
b.
c.
d.
e.
f.

6. Study Guide
In everyday life, we consider positive numbers as the opposite of
negative numbers.
• A gain of 5 yards in a football game is the opposite of…
• A check written for $28.50 on a checking account is the
opposite of…
Definition: OPPOSITE NUMBERS
Opposite numbers are two numbers that differ only in sign. They are the
same distance from zero on a number line but in opposite directions.
Each positive number has an opposite negative number.
Similarly, each negative number has an opposite positive number.
Note: The opposite of a number is the negative of that number.
The symbol for “the opposite of” a number is the minus (or negative)
sign, “–”.
If a is a real number, then the opposite of a, denoted equals
The opposite of is

7. Study Guide
Procedure: FINDING THE OPPOSITE OF A NUMBER
To find the opposite of a number, change the sign of the number.
The absolute value of a number is its distance from zero on
a number line. The symbol for absolute value is .
Notice that for any real number a, but
Be careful to notice that these two expressions are not equal.
Note: Any pair of opposite numbers has the same absolute value
since they are the same distance from 0 on a number line.
Note: Any number plus its opposite is equal to zero.
Definition: ADDITIVE INVERSE
Two numbers are additive inverses, or opposites, if they add to equal zero.