RATIONAL NUMBERS NATURAL NUMBERS {1, 2, 3,…}+ {0} = WHOLE NUMBERS {0, 1, 2, 3,…}+ NEG. WHOLE...
Transcript of RATIONAL NUMBERS NATURAL NUMBERS {1, 2, 3,…}+ {0} = WHOLE NUMBERS {0, 1, 2, 3,…}+ NEG. WHOLE...
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)
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE
WHOLE NUMBERS
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE
INTEGERS
0 2 4 6-2-4-6
RATIONAL NUMBERS
EXAMPLES OF RATIONAL NUMBERS
51
5
- 71
7
01
0
5
2fraction
aalready
0.310
3
3.03
1
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
0.5
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
8/3
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
–32/5
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
{-3, -2, 0, 5}
0 2 4 6-2-4-6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
{0, 2, 4, 6,…}
0 2 4 6-2-4-6
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|
0 2 4 6-2-4-6
|3| = 3, because
3 units
RATIONAL NUMBERS
The ABSOLUTE VALUE of any number is its distance from zero on the number line.
0 2 4 6-2-4-6
|-3| = 3, because
3 units
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
ADDING & SUBTRACTING RATIONAL NUMBERS
ADDINGADDING
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
ADDINGADDING
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
SUBTRACTINGSUBTRACTING
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
SUBTRACTINGSUBTRACTING
The ADDITIVE INVERSE of a number is its opposite.
ADDITIVE INVERSE PROPERTYFor every number a, a + (-a) = 0
4 + (-4) = 0
10 + (-10) = 0
ADDING & SUBTRACTING RATIONAL NUMBERS
SUBTRACTINGSUBTRACTING
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
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)
6A.T
.O.
FLASH CARDS
9 - (-1)
10A.T
.O.
FLASH CARDS
-20 - (+10)
-30A.T
.O.
FLASH CARDS
-5 - (-8)
3A.T
.O.
FLASH CARDS
11 - (+8)
3 A.T.O
.??
FLASH CARDS
25 - (-10)
35A.T
.O.
ABSOLUTE VALUES
FLASH CARDS
|-1|
1
FLASH CARDS
|0|
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 + 5xif x = -2
-7
FLASH CARDS
x + |-x| - |-x+2|if x = -2
-4