The Distributive Property
In class work-pg 31 #'s 43,49,50,51,53
The Distributive Property is handy to help you get rid of parentheses.
a(b + c) = ab + ac
To multiply in algebra, you'll use the distributive law:
3x(x+4)
= 3x(x) + 3x(4)
=3x^2+12x
Commutative Property - In Class Work pg 35 #'s 35,37, 43,45,47
Commutative property is one of the basic properties of numbers. The word “commute” means “exchange” or “swap over”.
Commutative property states that numbers can be added or multiplied in any order.
That is:
- Commutative Property of Addition states that changing the order of addends does not change the sum. That is, a + b = b + a.
- Commutative Property of Multiplication states that changing the order of factors does not change the product. That is, a × b = b × a.
Examples of Commutative Property
- 2 + 3 = 3 + 2. Whether you add 3 to 2 or 2 to 3, you get 5 both ways.
- 4 × 7 = 7 × 4. Whether you multiply 4 by 7 or 7 by 4, the product is the same, i.e. 28.
NOTE:
Commutative property holds good for both addition and multiplication, but not for subtraction and division.
Associative Property
The associative property of addition says that when we add more than two numbers the grouping of the addends does not change the sum.
- The associative property of addition can be written as:
(a + b) + c = a + (b + c)
- Example:(3 + 6) + 8 = 3 + (6 + 8)
(3 + 6) + 8 = 3 + (6 + 8)
9 + 8 = 3 + 14
17 = 17
The associative property of multiplication says that when we multiply more than two numbers the grouping of the factors does not change the product.
- The associative property of multiplication can be written as:
(a × b) × c = a × (b × c)
- Example: (2 × 4) × 3 = 2 × (4 × 3)
(2 × 4) × 3 = 2 × (4 × 3)
8 × 3 = 2 × 12
24 = 24
NOTE:
Associative property holds good for both addition and multiplication, but not for subtraction and division.
