Algebraic Properties

1
Algebraic Properties

• Properties for Addition
• and Multiplication only

2
Commutative Property of Addition

• The order changes, but not the sum
• ex 4 7 7 4
• For any number a and b
• a b b a

3
Commutative Property of Multiplication

• The order changes, but not the product
• ex 6 9 9 6
• For any number a and b
• a b b a

4
Will the Commutative Property work for
Subtraction?

• How about Division?

Give an example why.
5
Associative Property of Addition

• The way numbers are grouped does not change the
  sum.
• ex ( 12 7 ) 3 12 ( 7 3)
• For any numbers a, b, and c
• ( a b ) c a ( b c )

6
Associative Property of Multiplication

• The way numbers are grouped does not change the
  product.
• ex ( 6 2 ) 5 6 ( 2 5)
• For any numbers a, b, and c
• ( a b ) c a ( b c )

7
Will the Associative Property work for
Subtraction?

• How about Division?

Give an example why.
8
Identity Property of Addition

• The sum of zero and any given number will equal
  that given number.
• ex 9 0 9
• For any number a
• a 0 a

9
Identity Property of Multiplication

• The product of any given number and one will
  equal that given number.
• ex 9 1 9
• For any number a
• a 1 a

10
Will the Identity Property work for Subtraction?

• How about Division?

Give an example why.
11
Distributive Property of Multiplication

• Distributing multiplication over addition or
  subtraction
• ex 3( 10 7 ) 3(10) 3(7)
• (multiply the number outside the parentheses to
  each number inside the parentheses)
• For any numbers a, b, and c
• a( b c ) a(b) a(c)

12
Multiplicative Property of Zero

• The product of zero and any number is
• ZERO
• ex 3 0 0
• For any number a
• a 0 0

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