1 3 Integers and Absolute Value California Evaluating

1 -3 Integers and Absolute Value California Evaluating Algebraic Expressions Standards 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. NS 2. 5

1 -3 Integers and Absolute Value Vocabulary Evaluating Algebraic Expressions integer opposite absolute value

1 -3 Integers and Absolute Value Evaluating Algebraic Expressions 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.

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

Integers and Absolute Value 1 -3 Additional Example 1 A: Sports Application Evaluating Algebraic Expressions 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 – 1 < 4 – 2 – 1 0 1 2 3 4 5 – 1 is to the left of 4. Felicity's score is less than Aaron's score.

Integers and Absolute Value 1 -3 Additional Example 1 B: Sports Application List the golf scores in order from the Evaluating Algebraic Expressions 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 – 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 -3 Integers and Absolute Value Check It Out! Example 1 A Evaluating Expressions Francie’s score is Algebraic – 2, and Joaquin's score is – 3. Use <, >, or = to compare the scores. Place the scores on the number line. – 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.

Integers and Absolute Value 1 -3 Check It Out! Example 1 B Evaluating Algebraic Expressions 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 – 1 0 1 2 3 4 5 In order from the lowest score to the highest score, the scores are – 3, – 2, 0, and 1.

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

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

Integers and Absolute Value 1 -3 A number’s absolute value is its distance from 0 on a number line. Absolute value is Evaluating Algebraic always positive because distance. Expressions is always positive. “The absolute value of – 4” is written as |– 4|. Opposites have the same absolute value. 4 units – 5 – 4 |– 4| = 4 – 3 – 2 4 units – 1 0 1 2 3 4 5 |4| = 4

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

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

1 -3 Integers and Absolute Value Check It Out! Example 3 Simplify each expression. Evaluating Algebraic Expressions A. |– 5| 5 units – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 5 is 5 units from 0, so |– 5| = 5. B. |12 – 4| = |8| =8 Subtract first: 12 – 4 = 8. Then find the absolute value: 8 is 8 units from 0.

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

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