Download Intro to 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.
OR a RATIONAL NUMBER is any number that
can be written as a fraction.
RATIONAL NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE
-6
-4
-2
0
2
4
NATURAL NUMBERS
(or counting numbers)
6
RATIONAL NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE
-6
-4
-2
0
2
4
WHOLE NUMBERS
6
RATIONAL NUMBERS
GRAPHING THE NUMBER SETS ON THE NUMBER LINE
-6
-4
-2
0
2
INTEGERS
4
6
RATIONAL NUMBERS
EXAMPLES OF RATIONAL NUMBERS
5
5 
1
7
-7 
1
0
0 
1
already a
fraction
3
0.3 
10
1
0. 3 
3
2
5
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
-6
-4
-2
0
0.5
2
4
6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
-6
-4
-2
0
8/
3
2
4
6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
-6
-4
-2
0
–32/5
2
4
6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
-6
-4
-2
0
2
{-3, -2, 0, 5}
4
6
RATIONAL NUMBERS
GRAPHING THE NUMBERS ON THE NUMBER LINE
-6
-4
-2
0
2
4
{0, 2, 4, 6,…}
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
-6
-4
-2
0
2
4
6
RATIONAL NUMBERS
The ABSOLUTE VALUE of any number is its
distance from zero on the number line.
|-3| = 3, because
3 units
-6
-4
-2
0
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
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
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
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
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
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
REVIEW
TRUE OR FALSE
5 is a rational number
YES
REVIEW
TRUE OR FALSE
0 is the smallest
natural number.
NO, 1 is the smallest
REVIEW
TRUE OR FALSE
-1 is the largest
negative integer.
YES
REVIEW
TRUE OR FALSE
Name a rational number
that is not an integer.
Any fraction
½, 0.6, 2.3, etc
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
FLASH CARDS
9 - (-1)
10
FLASH CARDS
-20 - (+10)
-30
FLASH CARDS
-5 - (-8)
3
FLASH CARDS
11 - (+8)
3
FLASH CARDS
25 - (-10)
35
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 + 5x
if x = -2
-7
FLASH CARDS
x + |-x| - |-x+2|
if x = -2
-4