Transcript 1-3 Integers and Absolute Value Key Terms

1-3 Integers and Absolute
Value
Key Terms
Integer
 Opposite
 Additive inverse
 Absolute value

Objective

Learn to compare and order integers
and to evaluate expressions containing
absolute value.

Integers are the set of whole numbers
and their opposites.
– Examples: …,-4, -3, -2, -1, 0, 1, 2, 3, 4,…
Think and Discuss

Explain how integers are used in real
life to manage a bank account.
On a number line, opposites, or additive
inverses, are numbers that are the
same distance from 0, but on opposite
sides of 0 on the number line.
 Remember: numbers on a number line
increase in value as you move from left
to right!

Example 1: Finding Additive
Inverses
Find the additive inverse of each integer.
a) -7
7 is the same distance from 0 as -7 is on
the number line.
b) 23
-23 is the same distance from 0 as 23 is
on the number line.
c) 1.5
-1.5 is the same distance from 0 as 23 is
on the number line.
Think and Discuss
Are
-1, -4, and 5 are additive
inverses? Why or why not?
Example 2:
Use <, >, or = to compare the scores.
Kim’s score is 4, and Trevor’s score is –1.
Place the scores on the number line.
•
–5
–4
–3
–1 < 4
–2
–1
•
0
1
2
3
–1 is to the left of 4.
Trevor’s score is less than Kim’s.
4
5
Example 3:
Use <, >, or = to compare the scores.
List the golf scores in order from the
lowest to the highest. The scores are –4,
2, 5, and –3.
Place the scores on the number line and read
them from left to right.
•
–5
–4
•
•
–3
–2
–1
0
1
2
•
3
4
5
In order from the lowest score to the highest
score, the scores are –4, –3, 2, and 5.
Example 4: Ordering Integers
Write the integers 8, –5, and 4 in order from
t least to greatest.
8 > –5,
8 > 4,
Compare each pair of
integers.
and –5 < 4
–5, 4, and 8.
–5 is less than both
4 and 8.
Absolute Value
A number’s absolute value is its distance
from 0 on a number line. “The absolute
value of –4” is written as 4 . Additive
inverses have the same absolute value.
4 units
4 units

–5
–4
–3
–2
–4 = 4 = 4.
–1
0
1
2
3
4
Both 4 and –4 are 4
units from 0.
5
Think and Discuss
Can there exist a negative measure of
distance?
 Can absolute value be negative? Why
or why not?

Example 5: Evaluating AbsoluteValue Expressions
Evaluate each expression.
A. –8 + –5
–8 = 8
–8 is 8 units from 0.
–5 = 5
–5 is 5 units from 0.
8 + 5 = 13
B. 5 – 6
–1 = 1
–1 is 1 units from 0.
In-class Problem 1

The boiling point of nitrogen is -196
degrees Celsius. The boiling point of
oxygen is -183 degrees Celsius. Which
element has the greater boiling point?
Explain your answer.
Oxygen!

Oxygen has a greater boiling point than
nitrogen because -183 > -196.
In-class Problem 2
Can any number replace n to make the
following equation true? Explain your
reasoning.
n  1
No!

There is no value for n that could make
the expression true, because the
absolute value of a number represents
a distance. A distance cannot be
negative.
Resources

Copyright © by Holt, Rinehart and
Winston.