Name: ______________________________
Date: _________________________
Lesson 17
Opposites and Additive Inverses
Take a look at the number line below.
How far is the number 3 from 0? You are right: 3 units. What other number is 3 units from 0?
Right again: negative 3. This means that +3 and -3 are equidistant from 0. Two numbers that
are equidistant from 0 on a number line are opposites. Do you think you can name some
opposites? Sure you can.
Example 1
Below, write the opposite of each number.
a) 17
_____
b) -5
_____
c) +16 _____
Go on, see if you named all the opposites correctly.
Think about the opposites +3 and -3. What happens if you add them together? A number line
may help you to see what happens when you add these two numbers. Start at + 3 and add -3 to
it. If you add a negative number, which way do you go? You are correct: left. So where do you
end up?
You end up at 0. Would you get the same result if you started at -3 and added +3 to it? You
bet!
3 + (-3) = 0 or (-3) + 3 = 0
All opposites, when added together, equal ______________________
The sum of a number and its additive inverse is zero. In other words, the opposite of a number
is also its additive inverse. Any inverse "undoes," or cancels out, the other number -- the result
is 0. So what is the additive inverse of 23?
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Name: ______________________________
Date: _________________________
Lesson 17
The additive inverse is -23. (Adding -23 to 23 cancels it out, resulting in the sum of 0.)
What is the opposite of 23?
The opposite is -23. (-23 and 23 are equidistant from 0 on a number line.)
OK, here is one for you: What is the additive inverse of zero? Think about the definition of
additive inverse. When you add the additive inverse to a number, the sum is always 0. What
number can you add to zero to get zero? Seems like a ridiculous question, doesn't it? Zero is
the additive inverse of zero, which means that zero is also the opposite of zero.
Real-World Applications
Can you think of any real-world situations that involve both negative and positive numbers?
Hint: Think of the world of sports. Can you think of any sport in which scoring in the negatives
is a good thing? You got it: golf!
A golfer's score is dependent on par, or the number of strokes it usually takes a skilled golfer to
complete the hole. If a golfer scores under par, the score is negative. If the golfer scores above
par, the score is positive, and if the golfer scores even par, the score is 0. Take a look at the
scorecard below
Your task will be to determine the golfer's score. The addition will be easier if you use what
you know about additive inverses, or opposites. On the scorecard above, highlight in yellow all
the additive inverses.
+ 1 + (-1) + 1 + (-1) = 0 + 0 = 0
The three zeros don't add or subtract anything from the score. So what is the golfer's score after
nine holes of golf? Write the score in the blank below.
Score: ______
Example 2
a. In the blanks below, write your answers to the questions that follow. You go up six floors on
an elevator. What is the signed number that represents this situation? What is the opposite
situation? What is the signed number that represents the opposite situation? Write on the
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Name: ______________________________
Date: _________________________
Lesson 17
horizontal number line below to show that the two numbers are opposites.
Signed number representing going up six floors: _____
Opposite situation: _____
Signed number: _____
b. The temperature goes down by 8°. What is the signed number that represents this situation?
What is the opposite situation? What signed number represents the opposite situation? On the
vertical number line that follows, show that the two numbers are opposites.
Signed number representing 8° drop: _____
Opposite situation: _____
Signed number: _____
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