1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Evaluate each expression for the given values of the variables. 1. 2 x – 3 y for x = 17 and y = 6 2. 5( x + 3) + 4 y for x = 3 and y = 2 3. 6.9( x – 2.7) + 7.1 for x = 5.1 4. 5 x – 4 y for x = 0.3 and y = 0.2 16 38 23.66 0.7

3. 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. Also covered: NS1.1 California Standards

4. Vocabulary integer opposite absolute value

5. 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.

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

7. Use <, >, or = to compare the scores. Additional Example 1A: Sports Application Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. – 1 < 4 – 1 is to the left of 4. Felicity's score is less than Aaron's score. – 5 –4 –3 –2 –1 0 1 2 3 4 5

8. Use <, >, or = to compare the scores. 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. Place the scores on the number line and read them from left to right. In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5. – 5 –4 –3 –2 –1 0 1 2 3 4 5

9. Use <, >, or = to compare the scores. Check It Out! Example 1A Francie’s score is –2, and Joaquin's score is –3 . Place the scores on the number line. – 3 < –2 – 3 is to the left of –2. Joaquin's score is less than Francie's score. – 5 –4 –3 –2 –1 0 1 2 3 4 5

10. 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. Place the scores on the number line and read them from left to right. In order from the lowest score to the highest score, the scores are –3, –2, 0, and 1. – 5 –4 –3 –2 –1 0 1 2 3 4 5

11. Write the integers 8, –5, and 4 in order from least to greatest. Additional Example 2: Ordering Integers Graph the integers on a number line. Then read them from left to right. The integers in order from least to greatest are –5, 4, and 8. – 5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

12. Write the integers –4, –5, and 4 in order from least to greatest. Check It Out! Example 2 Graph the integers on a number line. Then read them from left to right. The integers in order from least to greatest are –5, –4, and 4. – 5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

13. 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| = 4 |4| = 4 – 5 –4 –3 –2 –1 0 1 2 3 4 5 4 units 4 units

14. Simplify each expression. Additional Example 3: Simplifying Absolute-Value Expressions A. |–3| B. |17 – 6| Subtract first: 17 – 6 = 11. – 3 is 3 units from 0, so |–3| = 3. |17 – 6| = |11| = 11 Then find the absolute value: 11 is 11 units from 0. – 5 –4 –3 –2 –1 0 1 2 3 4 5 3 units

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

16. Simplify each expression. Check It Out! Example 3 A. |–5| B. |12 – 4| Subtract first: 12 – 4 = 8. – 5 is 5 units from 0, so |–5| = 5. |12 – 4| = |8| = 8 Then find the absolute value: 8 is 8 units from 0. – 5 –4 –3 –2 –1 0 1 2 3 4 5 5 units

17. 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. = 11 D. |3 + 1| + |9 – 2| 3 + 1 = 4, 9 – 2 = 7. = 4 + 7 |–2| + |–9| = 2 + 9 |3 + 1| + |9 – 2| = |4| + |7| 4 is 4 units from 0, 7 is 7 units from 0. Add. = 11 Check It Out! Example 3

18. 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