Multiplication and Division of Whole Numbers

1
Section 2.4

• Multiplication and Division of Whole Numbers

2
Properties of Multiplication of Whole Numbers
(page 100)

• Closure property of multiplication of whole
  numbers
• Commutative property of multiplication of whole
  numbers
• Associative property of multiplication of whole
  numbers
• Identity property of multiplication whole numbers
• Zero multiplication property of whole numbers.

3
Closure Property of multiplication of whole
numbers

• For any whole numbers a and b, ab is a unique
  whole number.
• This means the answer will never be
• Negative
• Fractional
• Zero
• Irrational
• Imaginary

4
Commutative property of multiplication of whole
numbers

• For any whole numbers a and b,
• ab ba
• 34 43

5
Associative property of multiplication of whole
numbers

• For any whole numbers a, b, and c
• (ab)c a(bc)
• (34)5 3(45)
• (12)5 3(20)
• 60 60

6
Identity property of multiplication whole numbers

• There is a unique number 1 such that for any
  number a,
• a1 a
• 41 4

7
Zero multiplication property of whole numbers.

• For any whole number a,
• a0 0a 0
• 40 0

8
Distributive property of multiplication over
addition for whole numbers

• a(b c) ab ac
• 3(x 5) 3x 15

9
Order of Operations

• 3 4 2 ?

10
Division Algorithm

• Given any whole numbers a and b with b ? 0, there
  exists unique whole numbers q and r such that
• a bq r
• Quotient q
• Remainder r
• 20 5 4
• 20 5(4) 0