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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.

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RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE NATURAL NUMBERS (or counting numbers) 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE WHOLE NUMBERS 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE INTEGERS 0 246-2 -4 -6

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RATIONAL NUMBERS EXAMPLES OF RATIONAL NUMBERS 5 - 7 0 0.3

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RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 0.5 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 8/38/3 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE –3 2 / 5 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {-3, -2, 0, 5} 0 246-2 -4 -6

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RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE {0, 2, 4, 6,…} 0 246-2 -4 -6

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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| 0 246-2 -4 -6 |3| = 3, because 3 units

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RATIONAL NUMBERS The ABSOLUTE VALUE of any number is its distance from zero on the number line. 0 246-2 -4 -6 |-3| = 3, because 3 units

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

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

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

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ADDING & SUBTRACTING RATIONAL NUMBERS SUBTRACTING 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

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

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ADDING & SUBTRACTING RATIONAL NUMBERS SUBTRACTING 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

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REVIEW 5 is a rational number YES TRUE OR FALSE

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

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

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

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

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

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ADDING & SUBTRACTING RATIONAL NUMBERS

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FLASH CARDS 8 + (+3) 11

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FLASH CARDS 5 + (-3) 2

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FLASH CARDS -7 + (-2) -9

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FLASH CARDS -5 + (+2) -3

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FLASH CARDS -7 + (+8) 1

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

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

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

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

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

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

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

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

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

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

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

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ABSOLUTE VALUES

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FLASH CARDS |-1| 1

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FLASH CARDS |0||0| 0

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|5| + |-2| 7

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

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

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

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FLASH CARDS |10 - 3| - |-1 - 3| 3

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

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FLASH CARDS x + |-x| - |-x+2| if x = -2 -4

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