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RATIONAL NUMBERS

RATIONAL NUMBERS. NATURAL NUMBERS {1, 2, 3,…}. + {0}. = WHOLE NUMBERS {0, 1, 2, 3,…}. + NEG. WHOLE NOS. = INTEGERS {…-2, -1, 0, 1, 2,…}. + PURE FRACTIONS. = RATIONAL NUMBERS. A RATIONAL NUMBER is any number that can be written in the form a / b , where a & b are integers and b ≠ 0.

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RATIONAL NUMBERS

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  1. RATIONAL NUMBERS NATURAL NUMBERS {1, 2, 3,…} + {0} = WHOLE NUMBERS {0, 1, 2, 3,…} + NEG. WHOLE NOS. = INTEGERS {…-2, -1, 0, 1, 2,…} + PURE FRACTIONS = RATIONAL NUMBERS A RATIONAL NUMBER is any number that can be written in the form a/b, where a & b are integers and b ≠ 0. OR a RATIONAL NUMBER is any number that can be written as a fraction.

  2. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE NATURAL NUMBERS (or counting numbers)

  3. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE WHOLE NUMBERS

  4. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE INTEGERS

  5. RATIONAL NUMBERS EXAMPLES OF RATIONAL NUMBERS 5 0.3 - 7 0

  6. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 0.5

  7. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 8/3

  8. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE –32/5

  9. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {-3, -2, 0, 5}

  10. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {0, 2, 4, 6,…}

  11. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS The ABSOLUTE VALUE of any number is its distance from zero on the number line. The absolute value of 3 is written |3| |3| = 3, because 3 units

  12. -6 -2 2 4 6 -4 0 RATIONAL NUMBERS The ABSOLUTE VALUE of any number is its distance from zero on the number line. |-3| = 3, because 3 units

  13. RATIONAL NUMBERS Evaluate: |-2 + 7| = |5| = 5 Evaluate: 3 + |-4| + |4| = 3 + 4 + 4 = 11 Evaluate: x + |x + 4| + 3, if x = -7 = -7 + |-3| + 3 = -7 + 3 + 3 = -1

  14. ADDING ADDING ADDING & SUBTRACTING RATIONAL NUMBERS Same Signs: Add their absolute values and use their common sign. 9 6 + (+3) = -9 -6 + (-3) = 12 4 + (+8) = -65 -20 + (-45) =

  15. ADDING ADDING ADDING & SUBTRACTING RATIONAL NUMBERS Different Signs: Subtract their absolute values and use the sign of the larger. 3 6 + (-3) = -3 -6 + (+3) = -4 3 + (-7) = 25 -20 + (+45) =

  16. SUBTRACTING SUBTRACTING ADDING & SUBTRACTING RATIONAL NUMBERS The ADDITIVE INVERSE of a number is its opposite. The additive inverse of 6 is -6 The additive inverse of -3 is 3 The additive inverse of 1/2 is -1/2 The additive inverse of -6.25 is 6.25

  17. SUBTRACTING SUBTRACTING ADDING & SUBTRACTING RATIONAL NUMBERS The ADDITIVE INVERSE of a number is its opposite. ADDITIVE INVERSE PROPERTY For every number a, a + (-a) = 0 0 4 + (-4) = 0 10 + (-10) =

  18. SUBTRACTING SUBTRACTING ADDING & SUBTRACTING RATIONAL NUMBERS To subtract signed numbers, add the opposite. (A.T.O.) and use the rules of addition. 6 + (-3) = 6 – (+3) = 3 6 + (+3) = 6 – (-3) = 9 -8 + (-2) = -8 – (+2) = -10 -30 + (+50) = -30 – (-50) = 20

  19. REVIEW TRUE OR FALSE 5 is a rational number YES

  20. REVIEW TRUE OR FALSE 0 is the smallest natural number. NO, 1 is the smallest

  21. REVIEW TRUE OR FALSE -1 is the largest negative integer. YES

  22. REVIEW TRUE OR FALSE Name a rational number that is not an integer. Any fraction ½, 0.6, 2.3, etc

  23. REVIEW Name a whole number that is not a natural number. 0

  24. REVIEW Name a whole number that is not an integer. NOT POSSIBLE

  25. ADDING & SUBTRACTING RATIONAL NUMBERS

  26. FLASH CARDS 8 + (+3) 11

  27. FLASH CARDS 5 + (-3) 2

  28. FLASH CARDS -7 + (-2) -9

  29. FLASH CARDS -5 + (+2) -3

  30. FLASH CARDS -7 + (+8) 1

  31. FLASH CARDS -3 + (-5) + (+2) -6

  32. FLASH CARDS 7 + (-3) + (-6) -2

  33. FLASH CARDS 20 + (+30) + (-50) 0

  34. FLASH CARDS -5 + (-3) + (-2) -10

  35. FLASH CARDS 2 + (-1) + (8) 9

  36. FLASH CARDS 7 - (+1) A.T.O. 6

  37. FLASH CARDS 9 - (-1) A.T.O. 10

  38. FLASH CARDS -20 - (+10) A.T.O. -30

  39. FLASH CARDS -5 - (-8) A.T.O. 3

  40. FLASH CARDS 11 - (+8) A.T.O.?? 3

  41. FLASH CARDS 25 - (-10) A.T.O. 35

  42. ABSOLUTE VALUES

  43. FLASH CARDS |-1| 1

  44. FLASH CARDS |0| 0

  45. FLASH CARDS |5| + |-2| 7

  46. FLASH CARDS |-2+(-3)| 5

  47. FLASH CARDS |2| + |-1| + |8| 11

  48. FLASH CARDS |2 - 1| + |-1 + 3| 3

  49. FLASH CARDS |10 - 3| - |-1 - 3| 3

  50. FLASH CARDS 3 + 5x if x = -2 -7

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