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.

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Adding and Subtracting Integers

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Presentation transcript:

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.

RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE NATURAL NUMBERS (or counting numbers)

RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE WHOLE NUMBERS

RATIONAL NUMBERS GRAPHING THE NUMBER SETS ON THE NUMBER LINE INTEGERS

RATIONAL NUMBERS EXAMPLES OF RATIONAL NUMBERS

RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE

RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE 8/38/

RATIONAL NUMBERS GRAPHING THE NUMBERS ON THE NUMBER LINE –3 2 /

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

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

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

RATIONAL NUMBERS The ABSOLUTE VALUE of any number is its distance from zero on the number line |-3| = 3, because 3 units

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

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

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

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 is 6.25

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

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) = – (-50) = (+50) = 20

REVIEW 5 is a rational number YES TRUE OR FALSE

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

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

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

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

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

ADDING & SUBTRACTING RATIONAL NUMBERS

FLASH CARDS 8 + (+3) 11

FLASH CARDS 5 + (-3) 2

FLASH CARDS -7 + (-2) -9

FLASH CARDS -5 + (+2) -3

FLASH CARDS -7 + (+8) 1

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

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

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

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

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

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

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

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

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

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

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

ABSOLUTE VALUES

FLASH CARDS |-1| 1

FLASH CARDS |0||0| 0

|5| + |-2| 7

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

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

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

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

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

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