1. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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.

2. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value Numbers on a number line increase in value as you move from left to right. Remember!

3. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value Use, or = to compare the scores. Example 1A: Sports Application Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. –1 < 4 –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 is to the left of 4. Felicity's score is less than Aaron's score.

4. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value Use, or = to compare the scores. 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

5. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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 –5 –4 –3 –2 –1 0 1 2 3 4 5 –3 is to the left of –2. Joaquin's score is less than Francie's score.

6. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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

7. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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

8. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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

9. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value –5 –4 –3 –2 –1 0 1 2 3 4 5 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 |–4| = 4 |4| = 4

10. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value Simplify each expression. 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. –5 –4 –3 –2 –1 0 1 2 3 4 5 3 units |17 – 6| = |11| = 11 Then find the absolute value: 11 is 11 units from 0.

11. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value Simplify each expression. 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

12. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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. –5 –4 –3 –2 –1 0 1 2 3 4 5 5 units |12 – 4| = |8| = 8 Then find the absolute value: 8 is 8 units from 0.

13. Evaluating Algebraic Expressions 1-3 Integers and Absolute Value 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