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1-3 Integers and Absolute Value Key Terms Integer Opposite Additive inverse Absolute value Objective Learn to compare and order integers and to evaluate expressions containing absolute value. Integers are the set of whole numbers and their opposites. – Examples: …,-4, -3, -2, -1, 0, 1, 2, 3, 4,… Think and Discuss Explain how integers are used in real life to manage a bank account. On a number line, opposites, or additive inverses, are numbers that are the same distance from 0, but on opposite sides of 0 on the number line. Remember: numbers on a number line increase in value as you move from left to right! Example 1: Finding Additive Inverses Find the additive inverse of each integer. a) -7 7 is the same distance from 0 as -7 is on the number line. b) 23 -23 is the same distance from 0 as 23 is on the number line. c) 1.5 -1.5 is the same distance from 0 as 23 is on the number line. Think and Discuss Are -1, -4, and 5 are additive inverses? Why or why not? Example 2: Use <, >, or = to compare the scores. Kim’s score is 4, and Trevor’s score is –1. Place the scores on the number line. • –5 –4 –3 –1 < 4 –2 –1 • 0 1 2 3 –1 is to the left of 4. Trevor’s score is less than Kim’s. 4 5 Example 3: Use <, >, or = to compare the scores. 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. Example 4: Ordering Integers Write the integers 8, –5, and 4 in order from t least to greatest. 8 > –5, 8 > 4, Compare each pair of integers. and –5 < 4 –5, 4, and 8. –5 is less than both 4 and 8. Absolute Value A number’s absolute value is its distance from 0 on a number line. “The absolute value of –4” is written as 4 . Additive inverses have the same absolute value. 4 units 4 units –5 –4 –3 –2 –4 = 4 = 4. –1 0 1 2 3 4 Both 4 and –4 are 4 units from 0. 5 Think and Discuss Can there exist a negative measure of distance? Can absolute value be negative? Why or why not? Example 5: Evaluating AbsoluteValue Expressions Evaluate 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. In-class Problem 1 The boiling point of nitrogen is -196 degrees Celsius. The boiling point of oxygen is -183 degrees Celsius. Which element has the greater boiling point? Explain your answer. Oxygen! Oxygen has a greater boiling point than nitrogen because -183 > -196. In-class Problem 2 Can any number replace n to make the following equation true? Explain your reasoning. n 1 No! There is no value for n that could make the expression true, because the absolute value of a number represents a distance. A distance cannot be negative. Resources Copyright © by Holt, Rinehart and Winston.