Transcript 1-4

1-4 Integers and Absolute Value
Open your notebook
and write today’s date.
We are doing sec 1.4 today.
1-4 Integers and Absolute Value
Warm Up
Evaluate each expression for the given
values of the variables.
1. 2x – 3y for x = 17 and y = 6
2. 5(x + 3) + 4y for x = 3 and y = 2
3. 5x – 4y for x = 0.3 and y = 0.2
1-4 Integers and Absolute Value
Warm Up
Evaluate each expression for the given
values of the variables.
1. 2x – 3y for x = 17 and y = 6
2. 5(x + 3) + 4y for x = 3 and y = 2
3. 5x – 4y for x = 0.3 and y = 0.2
16
38
0.7
1-4 Integers and Absolute Value
Learn to compare and order integers and to
evaluate expressions containing absolute
value.
1-4 Integers and Absolute Value
Vocabulary
integer
opposite
additive inverse
absolute value
1-4 Integers and Absolute Value
Integers are the set of whole numbers and their
opposites. Opposites, or additive inverses, are
numbers that are the same distance from 0, but
on opposite sides of 0 on the number line.
1-4 Integers and Absolute Value
Additional Example 1A: Sports Application
Use <, >, or = to compare the scores.
Aaron’s score is 4, and Felicity’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.
4
5
1-4 Integers and Absolute Value
Additional Example 1B: Sports Application
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.
1-4 Integers and Absolute Value
Check It Out: Additional Example 1A
Use <, >, or = to compare the scores.
Fran’s score is –2, and Joaquin’s score is –3.
Place the scores on the number line.
–5
–4
•
•
–3
–2
–3 < –2
–1
0
1
2
3
4
–3 is to the left of –2.
5
1-4 Integers and Absolute Value
Check It Out: Additional Example 2
Write the integers 7, –12, and 13 in order
from least to greatest.
13 > –12, 13 > 7, and
–12 < 7
Compare each pair of
integers.
–12, 7, and 13.
–12 is less than both
7 and 13.
1-4 Integers and Absolute Value
Additional Example 3: Finding Additive Inverses
Find the additive inverse of each integer.
A. 6
–6
–6 is the same distance from 0 as 6 is on the
number line.
B. –14
14 14 is the same distance from 0 as –14 is on
the number line.
C. 0.5
–0.5 –0.5 is the same distance from 0 as 0.5 is
on the number line.
1-4 Integers and Absolute Value
A number’s absolute value is its distance
from 0 on a number line. Absolute value is
always positive or 0 because distance cannot
be negative. “The absolute value of –4” is
written as |–4|. Additive inverses have the
same absolute value.
4 units
–5
–4
–3
–2
–4 = 4 = 4.
4 units
–1
0
1
2
3
4
5
Both 4 and –4 are 4 units from 0.
1-4 Integers and Absolute Value
8 8
8  8
0 0
1-4 Integers and Absolute Value

   or 0
0
1-4 Integers and Absolute Value
Additional Example 4: Simplifying Absolute-Value
Expressions
Simplify 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.
1-4 Integers and Absolute Value
Check It Out: Additional Example 4
Simplify each expression.
A. –2 + –9
–2 = 2
–2 is 2 units from 0.
–9 = 9
–9 is 9 units from 0.
2 + 9 = 11
B. 1 – 1
0 =0
0 is 0 units from 0.
1-4 Integers and Absolute Value
Try these problems.
Write the integers in order from least to greatest.
1. –17, –26, 23
2. 0, 5, –4
Simplify each expression.
3. The sum of 3 and the additive inverse of –8
4. |–4| + |–2|
5. At the end of the course, your golf score was –2.
Your friend’s score was 7. Use <, >, or = to compare the
scores.
1-4 Integers and Absolute Value
Answers
Write the integers in order from least to greatest.
1. –17, –26, 23
–26, –17, 23
2. 0, 5, –4
–4, 0, 5
Simplify each expression.
3. The sum of 3 and the additive inverse of –8
11
4. |–4| + |–2| 6
5. At the end of the course, your golf score was –2.
Your friend’s score was 7. Use <, >, or = to compare the
scores.
–2 < 7
1-4 Integers and Absolute Value
Try this problem.
1. Which of the following represents the given
integers in order from least to greatest?
–24, 16, –13
A. –24, 16, –13
B. –24, –13, 16
C. –13, 16, –24
D. 16, –13, –24
1-4 Integers and Absolute Value
Answer
1. Which of the following represents the given
integers in order from least to greatest?
–24, 16, –13
A. –24, 16, –13
B. –24, –13, 16
C. –13, 16, –24
D. 16, –13, –24
1-4 Integers and Absolute Value
Try this problem.
3. Evaluate the sum of 5 and the additive
inverse of –14.
A. –19
B. –9
C. 9
D. 19
1-4 Integers and Absolute Value
Answer
3. Evaluate the sum of 5 and the additive
inverse of –14.
A. –19
B. –9
C. 9
D. 19
1-4 Integers and Absolute Value
Try this problem.
4. Evaluate |–6| + |–12|.
A. –6
B. 6
C. 12
D. 18
1-4 Integers and Absolute Value
Answer
4. Evaluate |–6| + |–12|.
A. –6
B. 6
C. 12
D. 18