1. California
Standards
NS2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

2. Vocabulary
integer
opposite
absolute value

3. Integers are the set of whole numbers and their opposites
Integers are the set of whole numbers and their opposites. Opposites are numbers that are the same distance from 0 on a number line, but on opposite sides of 0.

4. Numbers on a number line increase in value as you move from left to right.
Remember!

5. Additional Example 1A: Sports Application
Aaron’s score is 4, and Felicity’s score is –1.
Use <, >, or = to compare the scores.
Place the scores on the number line.
–5 –4 –3 –2 –
–1 < 4
–1 is to the left of 4.
Felicity's score is less than Aaron's score.

6. Additional Example 1B: Sports Application
List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3.
Use <, >, or = to compare the scores.
Place the scores on the number line and read them from left to right.
–5 –4 –3 –2 –
In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.

7. Francie’s score is –2, and Joaquin's score is –3.
Check It Out! Example 1A
Francie’s score is –2, and Joaquin's score is –3.
Use <, >, or = to compare the scores.
Place the scores on the number line.
–5 –4 –3 –2 –
–3 < –2
–3 is to the left of –2.
Joaquin's score is less than Francie's score.

8. Use <, >, or = to compare the scores.
Check It Out! Example 1B
List the golfer’s scores in order from the lowest to the highest. The scores are –3, 1, 0, and –2.
Use <, >, or = to compare the scores.
Place the scores on the number line and read them from left to right.
–5 –4 –3 –2 –
In order from the lowest score to the highest score, the scores are –3, –2, 0, and 1.

9. Additional Example 2: Ordering Integers
Write the integers 8, –5, and 4 in order from least to greatest.
Graph the integers on a number line. Then read them from left to right.
–5 –4 –3 –2 –
The integers in order from least to greatest are –5, 4, and 8.

10. Write the integers –4, –5, and 4 in order from least to greatest.
Check It Out! Example 2
Write the integers –4, –5, and 4 in order from least to greatest.
Graph the integers on a number line. Then read them from left to right.
–5 –4 –3 –2 –
The integers in order from least to greatest are –5, –4, and 4.

11. A number’s absolute value is its distance from 0 on a number line
A number’s absolute value is its distance from 0 on a number line. Absolute value is always positive because distance is always positive. “The absolute value of –4” is written as |–4|. Opposites have the same absolute value.
4 units 4 units
–5 –4 –3 –2 –
|–4| = 4
|4| = 4

12. Additional Example 3: Simplifying Absolute-Value Expressions
Simplify each expression.
A. |–3|
3 units
–5 –4 –3 –2 –
–3 is 3 units from 0, so |–3| = 3.
B. |17 – 6|
|17 – 6| = |11|
Subtract first: 17 – 6 = 11.
Then find the absolute value: 11 is 11 units from 0.
= 11

13. Additional Example 3: Simplifying Absolute-Value Expressions
Simplify each expression.
C. |–8| + |–5|
Find the absolute values first: –8 is 8 units from 0. –5 is 5 units from 0. Then add.
|–8| + |–5| = 8 + 5
= 13
D. |5 + 1| + |8 – 6|
|5 + 1| + |8 – 6| = |6| + |2|
5 + 1 = 6, 8 – 6 = 2.
= 6 + 2
6 is 6 units from 0, 2 is 2 units from 0. Add.
= 8

14. Simplify each expression.
Check It Out! Example 3
Simplify each expression.
A. |–5|
5 units
–5 –4 –3 –2 –
–5 is 5 units from 0, so |–5| = 5.
B. |12 – 4|
|12 – 4| = |8|
Subtract first: 12 – 4 = 8.
Then find the absolute value: 8 is 8 units from 0.
= 8

15. Check It Out! Example 3
Simplify each expression.
C. |–2| + |–9|
Find the absolute values first: –2 is 2 units from 0. –9 is 9 units from 0. Then add.
|–2| + |–9| = 2 + 9
= 11
D. |3 + 1| + |9 – 2|
|3 + 1| + |9 – 2| = |4| + |7|
3 + 1 = 4, 9 – 2 = 7.
= 4 + 7
4 is 4 units from 0, 7 is 7 units from 0. Add.
= 11

16. Lesson Quiz
1. At the end of the course, your golf score was –2. Your friend’s score was 7. Use <, >, or = to compare your scores.
Write the integers in order from least to greatest.
2. –17, –26, 23
3. 0, 5, –4
Simplify each expression.
4. |–4| + |–2|
5. |6 + 13| – |7 – 5|
–2 < 7
–26, – 17, 23
–4, 0, 5 6 17