Download 2-4 Rational Numbers

2-4 Rational Numbers
Rationals
Whole
Fractions
Terminating
/ repeating
decimals
Natural
Integers
A rational number is a number that can be expressed in a form of
b are integers and b  0.
Rational Numbers
Form of
3
4
3
4
7
7
1
.4
4
2
or
10
5
0
0
1
.333
1
3
Rational numbers can be graphed on the number line.
a
b
a
, where a and
b
-2 -1.5
-1
0
1
2
1 1.25
2
3
Comparing numbers on the number line
Using <, >, =
we can compare numbers.
(* for any two numbers, only one of those is true.)
-3 -2 -1 0
Negative
Direction
1 2 3
4
Positive
Direction
We can also use  ,  ,  to compare numbers.
Comparison Property of Rational Numbers
a
c
For any rational number
and
b
d
a
c
<
then ad < bc
b
d
a
c
If ad < bc then
<
b
d
If
and
Try these
7
4
?
13 15
7
8
?
8
9
7(15) ? 13(4)
7(9) ? 8(8)
Answer:
7
4
>
13 15
7
8
<
8
9
7(15) ? 13(4)
105> 52
7(9) ? 8(8)
63< 64
When b, d > 0
Another way to order rational numbers is by representing them as terminating or
repeating decimals.
3 4
1
Order: , , and
8 5
6
3
= 3 ÷ 8 = 0.375
8
4
= 4 ÷ 5 = 0.8
5
1
= 1 ÷ 6 = 0.1666666666
6
Order for the decimals is 0.16666666666, 0.375, 0.8
1 3 4
So
, ,
6 8 5
Comparing Unit Costs
Unit cost = total cost ÷ # of unit
Unit cost for 20 ounce bottle
Unit cost for 32 ounce bottle
1.25 ÷ 20 = .0625
1.75 ÷ 32 = .0546875
The 32 ounce bottle is the better buy for your $.
Density property
Between any two rational numbers is another rational number, infinite number of
rational numbers.
You can find a number between two numbers by finding the average of the two
numbers.
Between 1 and 2
(1 + 2) ÷ 2 = 1.5
Between 1.5 and 2
(1.5 + 2) ÷ 2 = 1.75
Between 1.75 and 2
( 1.75 + 2) ÷ 2 = 1.875
If fractions freak you out convert to decimals when possible.