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Integer Operations and Absolute Value Lesson 2

Integer Operations and Absolute Value Lesson 2. -6. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. Number Line. Integers are positive & negative numbers. Is 0 positive or negative?. Neither!. -6. -5. -4. -3. -2. -1. 0. 1. 2. 3. 4. 5. 6. Ordering Integers. least.

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Integer Operations and Absolute Value Lesson 2

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  1. Integer Operations and Absolute Value Lesson 2

  2. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Number Line • Integers are positive & negative numbers. • Is 0 positive or negative? Neither!

  3. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Ordering Integers. least greatest Put the following numbers in order from least to greatest. Ex. 5, -2, -4, 3, 0, -1 -4…-2…-1…0…3…5

  4. On your own… Order from least to greatest • 10, 8, -5, 0, -2.5, -4, 9 • -6.2, -7, 5.4, 12, 1 Order from greatest to least. • 5, -3, 4, -4, 2, -2 • 10, 8, -5, 0, -2.5, -4, 9 -5, -4, -2.5, 0, 8, 9, 10 -7, -6.2, 1, 5.4, 12 5, 4, 2, -2, -3, -4 10, 9, 8, 0, -2.5, -4, -5

  5. What are inequalties? They look like equations but are separated with these symbols.

  6. ess than reater than reater than or equal to ess than or equal to

  7. Use <, >, = to complete the problem. > 5 4 Hold up 1 for > and 2 for <.

  8. Use <, >, = to complete the problem. > -2 -3 Hold up 1 for > and 2 for <.

  9. Use <, >, = to complete the problem. > 0 -1 Hold up 1 for > and 2 for <.

  10. Hold up 1 for true and 2 for false. -6 -4 -2 0 2 4 6 True or False?-6 < -2 True

  11. Hold up 1 for true and 2 for false. -6 -4 -2 0 2 4 6 True or False?-5 < 7 True

  12. Hold up 1 for true and 2 for false. -6 -4 -2 0 2 4 6 True or False?6 < 0 False

  13. Hold up 1 for true and 2 for false. -6 -4 -2 0 2 4 6 True or False?-6 > 5 False

  14. -6 -4 -2 0 2 4 6 Absolute Value: The number of units a number is from zero on the number line. (Always Positive) |-4| = 4

  15. Abso ute Va ue Is written using these brackets. Not to be confused with (parenthesis)

  16. Absolute Value |6| = 6 and |-6| = 6

  17. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Greater than or less than • Using the number line to determine which sign would make this true. |-4| |2| >

  18. -|5| |-2| < - 5 2

  19. Greater than or less than On your own… > • |-3| ___ |-2| • |-8| ___ |-4| • |-1| ___ |1| • -|-4| ___ |-8| • -|-3| ___ -|-2| • -|-4| ___ |0| > = < < <

  20. |5| + |-2| 5 + 2 7

  21. |5| - |-2| 5 - 2 3

  22. Integer Addition Adding Two Positive Integers Add the absolute values and keep the sign. The sum is positive. Adding Two Negative Integers Add the absolute values and keep the sign. The sum is negative. Adding a Positive Integer and a Negative Integer Add the absolute values and keep the sign from the greater absolute value. The sum is the same sign as the number with the greatest absolute value. Adding Integers Interactive Adding Integer Video

  23. Integer Subtraction Subtraction is like adding the opposite. Rewrite subtraction as addition, changing the subtraction sign and write the additive inverse of the subtrahend (second value in problem). 8–5 = 8+(-5) = 4–(-3) = 4+(___) = -6–2 = ___+(___) = -3–(-4) = ____+(____) = Subtracting Integer Video Subtracting Integer Interactive (counters) Subtracting Integer Interactive (number line)

  24. Addition/Subtraction 13 8 + 1) 13 + (-8) = 5 13 8 2) (-3) + (-12) = - 15 5 10 + 3) 17 – (-3) = 20 11 5 21 - 4) 5 + (-10) + (-11) = 16 3 4 - 5) -3 – 5 + (-7) – (-4) = 5 11 7 4 15

  25. Mr. Multidivision - - + Multiplying and Dividing Integers Video Multiplying and Dividing Integers Game

  26. Rules: What rules can we create based on the last 6 problems?

  27. Integer Multiplication Multiplying Two Positive Integers The product is positive. Multiplying Two Negative Integers The product is positive. Multiplying a Positive Integer and a Negative Integer The product is negative.

  28. - - - - - - + + + Examples: X = -15 Ex. 1) (-5)(3) X = 36 Ex. 2) (-12)(-3) = -81 Ex. 3) (9)(-9)

  29. - - - - - - + + + On Your Own: = -21 Ex. 1) (-7)(3) = 72 Ex. 2) (-9)(-8) = -30 Ex. 3) (5)(-6)

  30. Multiplying Three or More Integers Count the number of negative signs. If there is an odd number, the product is negative. If it is an even number of negative signs, your answer is positive.

  31. Multiplying Three or More Integers Example 5: Find the product • 2( -3)(4) • 3(-2)(-5) • (-3)(-4)(-2)(-1) • (-1)(-1)(-1)(-1)(-1) o

  32. Integer Division Dividing Two Positive Integers The quotient is positive. Dividing Two Negative Integers The quotient is positive. Dividing a Positive Integer and a Negative Integer The quotient is negative.

  33. - - - - - - + + + Examples: X X

  34. Practice: = -32 = -24 = 6 = -9

  35. Multiply/Divide - 1) 4(-5) = 20 + 24 2) (-3)(-8) = + 3) (-5)(-3)(2) = 30 - 4) –(-2)(-4)(6) = 48 5) (-3)(-2)(3) 18 + = = 2 9 9

  36. You Try

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