1 4 Integers and Absolute Value Warm Up

1 -4 Integers and Absolute Value Warm Up Evaluate each expression for the given values of the variables. 1. 2. 3. 4. 2 x – 3 y for x = 17 and y = 6 16 5(x + 3) + 4 y for x = 3 and y = 2 38 6. 9(x – 2. 7) + 7. 1 for x = 5. 1 23. 66 0. 7 5 x – 4 y for x = 0. 3 and y = 0. 2

1 -4 Integers and Absolute Value Integers: the set of whole numbers and their opposites. Opposites (additive inverses): numbers that are the same distance from 0, but on opposite sides of 0 on the number line.

1 -4 Integers and Absolute Value Example 1: Sports Application Use <, >, or = to compare the scores. A. 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 4 – 1 is to the left of 4. 5

1 -4 Integers and Absolute Value Additional Example 1: Sports Application Use <, >, or = to compare the scores. B. 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: Example 1 Use <, >, or = to compare the scores. A. 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: Example 1 Use <, >, or = to compare the scores. B. 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. – 5 – 4 • • – 3 – 2 – 1 • • 0 1 2 3 4 5 In order from the lowest score to the highest score, they are – 3, – 2, 0, and 1.

1 -4 Integers and Absolute Value Example 2: Ordering Integers Write the integers 8, – 5, and 4 in order from t least to greatest. 8 > – 5, 8 > 4, and – 5 < 4 Compare each pair of integers. – 5, 4, and 8. – 5 is less than both 4 and 8.

1 -4 Integers and Absolute Value Check It Out: 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 Example 3: Finding Additive Inverses Find the additive inverse of each integer. A. 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 is the same distance from 0 as 0. 5 is on the number line.

1 -4 Integers and Absolute Value Check It Out: Example 3 Find the additive inverse of each integer. A. 12 – 12 is the same distance from 0 as 12 is on the number line. B. – 1. 9 is the same distance from 0 as – 1. 9 is on the number line. C. 1 – 1 is the same distance from 0 as 1 is on the number line.

1 -4 Integers and Absolute Value absolute value: the distance from 0 on a number line. • always positive or 0 • “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 units – 1 0 1 2 3 4 5 Both 4 and – 4 are 4 units from 0.

1 -4 Integers and Absolute Value 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: 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 Lesson Quiz Write the integers in order from least to greatest. 1. – 17, – 26, 23 – 26, – 17, 23 2. 0, 5, – 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