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Exploring Integers and Sets: Math Concepts Simplified

Discover the basics of integers, number lines, sets, subsets, inequalities, and arithmetic operations. Learn how to add, subtract, multiply, and divide integers with easy examples and clear explanations.

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Exploring Integers and Sets: Math Concepts Simplified

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  1. Integers

  2. Integers • Consist of positive and negative whole numbers

  3. The Number Line…… • A number line consists of positive numbers (right of 0) and negative numbers (left of 0). • A real life example of a number line is a temperature thermometer.

  4. For example….. • -5 would represent 5 degrees belowzero. • +4 would represent 4 degrees above zero.

  5. 7 degrees below 0 is (warmer/colder) than 4 degrees above 0. 7 degrees below 0 is a (lower/higher) temperature than 4 degrees above 0. Make the Comparison……

  6. Coordinates on a Graph…. • Find the best estimate of the point. a. -2 b. 2 c. -1.75 d. -1.5

  7. Sets and Subsets…… • A set is a group of numbers. Example: Set A = {1,2,3,4,5} • A subset is a group of numbers in which every member is in another set. Example: Set B = {1,2,3} • So, B is a subset of A.

  8. States Sales Tax Rate Amount of Gas in a Car Number of Students in Class A Dinner Receipt Which of the following would represent a subset of integers?

  9. Costs of a TV # of miles on the odometer of a car A person’s weight Number of residents in South Carolina You Try…Which of the following would represent a subset of integers?

  10. Inequalities….. • We use inequalities to compare numbers. • The following are inequalities:

  11. Examples……. • “4 is less than 7” - • “9 is greater than or equal to 5” -

  12. -5 -2 -7 2 4 -12 You Try……Insert the appropriate inequality sign.

  13. We have the Yellow Team and the Red Team…. Assign the left side of the room to the red team and right side to the yellow team.

  14. Who is favored & by how much if we have…

  15. So…how can I represent: -7 + 3 Start with: Which Leaves: Add 3:

  16. Use the counters….

  17. Use the counters….

  18. Use the counters….

  19. Use the counters….

  20. Use the counters….

  21. No Counters!

  22. No Counters

  23. So…How do I add signed numbers?

  24. How close were you? • Same Signs • Add the numbers • Take their sign • Different Signs • Subtract the numbers • Take the sign of the number with largest absolute value

  25. Opposites: • The opposite of 5 is -5. • What is –(-2)?

  26. Use the counters….

  27. Use the counters….

  28. Do the following: • 9 – 8 = • -6 – (-9)= • -14 + 3 = • 10 – 19 =

  29. Do the following: • 29 - 32 = • -82 – 12 = • -45 + 78 = • 16- (-27) =

  30. What’s 4 x -3? =

  31. Let’s Multiply:

  32. Let’s Multiply:

  33. So…How do I explain -3 x -4? • I like to think of this as – (3 x -4) and think of it as the opposite of (3 x -4). • Can you develop a rule for Multiplication?

  34. Let’s Multiply:

  35. So…what’s the rule for multiplying integers?

  36. Division:

  37. Divide:

  38. So..what’s the rule for Dividing integers

  39. Multiplying & Dividing: • Like signs – positive • Unlike signs - Negative

  40. Homework • Worksheet

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