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Integers on a Number Line: Absolute Value, Comparison, and Evaluation

Learn how to graph integers, find absolute value, compare numbers, and evaluate expressions involving integers. Practice real-life scenarios and improve your math skills.

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Integers on a Number Line: Absolute Value, Comparison, and Evaluation

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  1. Transparency 3 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 3-1a Objective Graph integers on a number line and Find the absolute value

  4. Example 3-1a Vocabulary Negative number A number less than zero

  5. Example 3-1a Vocabulary Integer Negative and positive whole numbers and zero Note: zero is neither positive or negative

  6. Example 3-1a Vocabulary Coordinate The point named by the integer on a number line

  7. Example 3-1a Vocabulary Inequality A sentence that compares 2 different numbers or quantities -5 < 4 -5 is less than 4 4 > -5 4 is greater than -5

  8. Example 3-1a Vocabulary Absolute Value The distance the number is from zero |4| = 4 |-4| = 4

  9. Example 3-1a Words that represent negative Words that represent positive Tax Discount Below Under Loss Under par (golf) Profit Above On top Gain Above par (golf)

  10. Lesson 3 Contents Example 1Write Integers for Real-Life Situations Example 2Write Integers for Real-Life Situations Example 3Compare Two Integers Example 4Compare Two Integers Example 5Order Integers Example 6Expressions with Absolute Value Example 7Expressions with Absolute Value Example 8Expressions with Absolute Value

  11. Write an integer to represent a discount. Example 3-1a Write problem 35 ¢ discount Look at the descriptive word to determine whether the integer is positive or negative - 35 Discount refers to a decrease which is a negative integer Write integer with negative sign Answer: –35 1/8

  12. Write an integer to represent a tax. Example 3-1b Answer: –25 1/8

  13. Example 3-2a Write an integer for the expression afever of 4 degrees above normal. Write problem 4 degrees above normal Look at the descriptive word to determine whether the integer is positive or negative + 4 Above refers to an increase which would be a positive integer Write integer with positive sign Answer: + 4 2/8

  14. Example 3-2b Write an integer for the expression a loss of 10 yards in football. Answer: - 10 2/8

  15. Example 3-3a Replace  with <, >, or = to make –3  3 a true sentence. Write problem < - 3 3 Remember: Negative numbers are always smaller than positive numbers So -3 is less than 3 The “alligator” eats the big number! : ) Answer: –3 < 3 3/8

  16. Replace  with <, >, or to make –2  2 a true sentence. Example 3-3b Answer: –2 < 2 3/8

  17. Replace  with <, >, or to make –2  –1 a true sentence. Example 3-4a Write problem < - 2 - 1 Remember: negative numbers get smaller as the number looks larger So -2 is less than -1 The “alligator” eats the big number! : ) Answer: –2 < –1 4/8

  18. Replace  with <, >, or to make –4  –6 a true sentence. Example 3-4b Answer: –4 > –6 4/8

  19. Example 3-5a FOOTBALLThe table below shows the number of yards rushing for several players on a football team during one game. Order these statistics from least to greatest. Graph each integer on a number line. 5/8

  20. Example 3-5a Draw number line Plot the - 6 Plot the 7 Plot the 4 Plot the 3 Plot the - 9 Plot the 5 Write the numbers as they appear from left to right. Answer: –9, –6, 3, 4, 5, 7 –9, –6, –9, –6, 3, –9, –6, 3, 4, –9, –6, 3, 4, 5, –9, 5/8

  21. Example 3-5b WEATHERThe table below shows the temperatures for several cities on January 31, 2000. Order these statistics from least to greatest. Answer: -54, -30, 81, 83 5/8

  22. Evaluate Example 3-6a Write problem  5 The absolute value signs are considered enclosures 5 Ask: How far is 5 away from 0 on the number line? Answer: 5 6/8

  23. Evaluate Example 3-6b Answer: 3 6/8

  24. Evaluate Example 3-7a Write problem Follow Order of Operations Rules P E MD AS  6 -  -5  The absolute value signs are considered enclosures 6 - 5 6 - 6 Ask: How far is 6 from 0 on the number line? 1 Bring down - Ask: How far is -5 from 0 on the number line? Subtract 6 - 5 Answer: 1 7/8

  25. Evaluate . Example 3-7b Answer: 3 7/8

  26. Example 3-8a Write problem Evaluate Replace x with -4 Follow Order of Operations Rules  x + 13 P E MD AS  -4 + 13 The absolute value signs are considered enclosures 4 + 13 4 Ask: How far is -4 from 0 on the number line? 17 Bring down + 13 Add 4 + 13 Answer: 17 8/8

  27. Example 3-8b * Evaluate Answer: 9 8/8

  28. End of Lesson 3 Assignment

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