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1-3 Integers and Absolute Value Preview Evaluating Algebraic Expressions Warm Up California Standards Lesson Presentation 1-3 Integers and Absolute Value Evaluating Algebraic Expressions Warm Up Evaluate each expression for the given values of the variables. 1. 2. 3. 4. 2x – 3y for x = 17 and y = 6 16 5(x + 3) + 4y for x = 3 and y = 2 38 6.9(x – 2.7) + 7.1 for x = 5.1 23.66 5x – 4y for x = 0.3 and y = 0.2 0.7 1-3 Integers and Absolute Value Evaluating Algebraic Expressions 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. Also covered: NS1.1 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 1A: 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 1B: 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 1A 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 –3 < –2 –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 1B 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 distanceExpressions 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| |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| = 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| |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| |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| = 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| |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 –4, 0, 5 Simplify each expression. 4. |–4| + |–2| 6 5. |6 + 13| – |7 – 5| 17