OR a RATIONAL NUMBER is any number that can be written as a fraction. 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 NATURAL NUMBERS (or counting numbers) GRAPHING THE NUMBER SETS ON THE NUMBER LINE 2 4 6 -2 -4 -6 NATURAL NUMBERS (or counting numbers)

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

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

EXAMPLES OF RATIONAL NUMBERS 5 - 7 0.3

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

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

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

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

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

The absolute value of 3 is written |3| 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 2 4 6 -2 -4 -6

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

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

Same Signs: Add their absolute values and use their common sign. 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

ADDING & SUBTRACTING RATIONAL NUMBERS 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

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

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

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

REVIEW TRUE OR FALSE 5 is a rational number YES

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

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

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

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

Name a whole number that is not an integer. 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)

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

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

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

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

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

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

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

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

ABSOLUTE VALUES

FLASH CARDS |-1| 1

FLASH CARDS |0|

FLASH CARDS |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