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Introduction to Integers and Absolute Value

Learn about integers, their opposites, and how to compare and order them. Also, evaluate expressions with absolute value.

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Introduction to Integers and Absolute Value

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  1. 1-3 Integers and Absolute Value Warm Up Problem of the Day Lesson Presentation Course 3

  2. 1-3 Integers and Absolute Value Course 3 Warm Up Evaluate each expression for the given values of the variables. 1. 2x – 3y for x = 17 and y = 6 2. 5(x + 3) + 4y for x = 3 and y = 2 3. 6.9(x – 2.7) + 7.1 for x = 5.1 4. 5x – 4y for x = 0.3 and y = 0.2 16 38 23.66 0.7

  3. 1-3 Integers and Absolute Value Course 3 Problem of the Day Janie’s score is 3 times the sum of 1 and Maria’s score on the final exam. Maria scored 12 points. Whose score is highest? Janie

  4. 1-3 Integers and Absolute Value Course 3 Learn to compare and order integers and to evaluate expressions containing absolute value.

  5. 1-3 Integers and Absolute Value Course 3 Vocabulary integer opposite additive inverse Absolute value

  6. 1-3 Integers and Absolute Value Course 3 Integers are the set of whole numbers and their opposites. 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. Course 3

  7. 1-3 Integers and Absolute Value Remember! Numbers on a number line increase in value as you move from left to right. Course 3

  8. 1-3 Integers and Absolute Value –5 –4 –3 –2 –1 0 1 2 3 4 5 Course 3 Additional Example 1A: Sports Application Use <, >, or = to compare the scores. Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. • • –1 < 4 –1 is to the left of 4.

  9. 1-3 Integers and Absolute Value –5 –4 –3 –2 –1 0 1 2 3 4 5 Course 3 Additional Example 1B: Sports Application 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. • • • • In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.

  10. 1-3 Integers and Absolute Value –5 –4 –3 –2 –1 0 1 2 3 4 5 Course 3 Check It Out: Additional Example 1A Use <, >, or = to compare the scores. France’s score is –2, and Juaqin’s score is –3. Place the scores on the number line. • • –3 < –2 –3 is to the left of –2.

  11. 1-3 Integers and Absolute Value –5 –4 –3 –2 –1 0 1 2 3 4 5 Course 3 Check It Out: Additional Example 1B Use <, >, or = to compare the scores. 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, they are –3, –2, 0, and 1.

  12. 1-3 Integers and Absolute Value Course 3 Additional Example 2: Ordering Integers Write the integers 8, –5, and 4 in order from t least to greatest. Compare each pair of integers. 8 > –5, 8 > 4, and –5 < 4 –5 is less than both 4 and 8. –5, 4, and 8.

  13. 1-3 Integers and Absolute Value Course 3 Check It Out: Additional Example 2 Write the integers 7, –12, and 13 in order from least to greatest. Compare each pair of integers. 13 > –12, 13 > 7, and –12 < 7 –12 is less than both 7 and 13. –12, 7, and 13.

  14. 1-3 Integers and Absolute Value 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 . Additive inverses have the same absolute value. 4 units 4 units –5 –4 –3 –2 –1 0 1 2 3 4 5 –4 = 4 = 4. Course 3 Both 4 and –4 are 4 units from 0.

  15. 1-3 Integers and Absolute Value Course 3 Additional 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. –6 B. –14 14 14 is the same distance from 0 as –14 is on the number line. C. 0.5 –0.5 –0.5 is the same distance from 0 as 0.5 is on the number line.

  16. 1-3 Integers and Absolute Value Course 3 Check It Out: Additional 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. –12 B. –1.9 1.9 1.9 is the same distance from 0 as –1.9 is on the number line. C. 1 –1 –1 is the same distance from 0 as 1 is on the number line.

  17. 1-3 Integers and Absolute Value –8 = 8 –5 = 5 –1 = 1 Course 3 Additional Example 4: Evaluating Absolute-Value Expressions Evaluate each expression. A. –8 + –5 –8 is 8 units from 0. –5 is 5 units from 0. 8 + 5 = 13 B. 5 – 6 –1 is 1 units from 0.

  18. 1-3 Integers and Absolute Value 0 = 0 –2 = 2 –9 = 9 Course 3 Check It Out: Additional Example 4 Evaluate each expression. A. –2 + -9 –2 is 2 units from 0. –9 is 9 units from 0. 2 + 9 = 11 B. 1 – 1 0 is 0 units from 0.

  19. 1-3 Integers and Absolute Value Course 3 Lesson Quiz Write the integers in order from least to greatest. 1. –17, –26, 23 2. 0, 5, –4 Evaluate each expression. 3. The sum of 3 and the additive inverse of –8 4. – –4 + –2 5. At the end of the course, your golf score was –2. Your friend’s score was 7. What is the difference between your scores? –26, –17, 23 –4, 0, 5 11 -2 9

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