Rational Numbers

1
Rational Numbers

• A number that can be written as
• a_
• b
• Where a and b are integers and b ? 0

2
Examples of Rational Numbers
6_ 1

• 6
• _ 3_
• 5
• 0.75
• -2 ¾

• 3_
• 5

3_ -5
3_ 4
75_ 100
_ 11_ 4
3
Ordering Rational Numbers

• -1, -1.6, 2/5, -1 ¾, -3/8

-2 -1
0 1 2
Show that each number is rational by writing it
in a form, then order from
b
least to greatest

4
Show that each number is rational by writing it
in a_ form, b then order from
least to greatest

• 2.5, -1, -5/8, -0.8

2½ 5_2
-8_ 10
0
1
2
3
-1
-2
-3
4
-4
4 1/5, -3.6, -3 8/9, 0
5
Are These Numbers Rational?

• 0
• -5.8
• 0.3333.
• 0.1
• 4 ?
• -15
• 1.675

6
Commutative Property of Addition

• You can add numbers in any order and still get
  the same sum
• a b b a

5 -8 -8 5
3.5 -3 6.5
7
Commutative Property of Multiplication

• You can multiply numbers in any order and still
  get the same product
• ab ba
• 4(-7) -7(4)

5(-9)(-4)
0.5(7)(8)
8
Associative Property of Addition

• Changing the grouping of terms will not change
  the sum
• (a b) c a (b c)
• (9 8) 6 9 (8 6)

0.9 (9.1 -2)
-13.4 (-3 -6.6)
9
Associative Property of Multiplication

• Changing the grouping of the terms does not
  change the product
• (ab)c a(bc)

(2 3) 4 2 (3 4)
10
Inverse Property of Addition

• The sum of a number and its additive
  inverse, or opposite, is 0
• a -a 0
• 5 -5 0

-3/4 5/6 3/4
94 87 -94
-53 -25 53
11
Inverse Property of Multiplication

• When you multiply a number and its multiplicative
  inverse, or reciprocal is 1

a . b 1 b a
3 . 4 12 1 4 3 12
1 . 5 . 3 3 6
12
Identity Property of Addition

• The sum of a number and the additive identity, 0,
  is the number
• a 0 a

-7 0 -7
13
Identity Property of Multiplication

• The product of a number and the multiplicative
  identity, 1, is the number.
• a(1) a
• 9(1) 9

14
The Zero Property of Multiplication

• The product of a number and 0 is 0
• a(0) 0
• -2(0) 0