Commutative,Commutative,Associative, Identity & Associative, Identity &

Zero PropertiesZero Properties

Commutative and Associative Properties

• Properties refer to rules that indicate a standard procedure or method to be followed.

Commutative and Associative Properties

• Commutative Property means changing the order in which you add or subtract numbers does not change the sum or product.

• Associative Property means changing the grouping of numbers when adding or multiplying does not change their sum or product.

• Grouping symbols are typically parentheses (),but can include brackets [] or Braces {}.

Commutative Property of addition - (Order)

Commutative Property of addition - (Order)

Commutative Property of multiplication - (order)

Commutative Property of multiplication - (order)

For any numbers a and b , a + b = b + a.For any numbers a and b , a + b = b + a.

For any numbers a and b , a b = b a. For any numbers a and b , a b = b a.

45 + 5 = 5 + 4545 + 5 = 5 + 45

6 8 = 8 66 8 = 8 6

50 = 50 50 = 50

48 = 4848 = 48

Commutative PropertiesCommutative Properties

Associative Property of addition - (grouping symbols)

Associative Property of addition - (grouping symbols)

Associative Property of multiplication - (grouping symbols)

Associative Property of multiplication - (grouping symbols)

For any numbers a, b, and c,

(a + b) + c = a + (b + c).

For any numbers a, b, and c,

(a + b) + c = a + (b + c).

For any numbers a, b, and c,

(ab) c = a (bc).

For any numbers a, b, and c,

(ab) c = a (bc).

(2 + 4) + 5 = 2 + (4 + 5) (2 + 4) + 5 = 2 + (4 + 5)

(2 3) 5 = 2 (3 5) (2 3) 5 = 2 (3 5)

(6) + 5 = 2 + (9)(6) + 5 = 2 + (9)

11 = 11 11 = 11

(6) 5 = 2 (15)(6) 5 = 2 (15)

30 = 30 30 = 30

Associative PropertiesAssociative Properties

Evaluate: 18 + 13 + 16 + 27 + 22 + 24 Evaluate: 18 + 13 + 16 + 27 + 22 + 24

Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property)

Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property)

(18 + 22) + (16 + 24) + (13 + 27) (18 + 22) + (16 + 24) + (13 + 27)

(40) + (40) + (40) = 120(40) + (40) + (40) = 120

Commutative and Associative PropertiesCommutative and Associative Properties

• Commutative and Associative properties are very helpful to solve problems using mental math strategies.

Evaluate: 4 7 25 Evaluate: 4 7 25

Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property)

Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property)

4 25 7 4 25 7

(4 25) 7(4 25) 7

(100) 7 = 700(100) 7 = 700

Commutative and Associative PropertiesCommutative and Associative Properties

• Commutative and Associative properties are very helpful to solve problems using mental math strategies.

Identity Property The product of any number and 1

is that number.

For any number a and a x 1 = aFor any number a and a x 1 = a

72 x 1 = 7272 x 1 = 72

Zero Property The Product of any number and 0

is 0

For any number a and a x 0 = 0For any number a and a x 0 = 0

72 x 0 = 072 x 0 = 0

Practice Writing Expressions

1. A number multiplied by 52. 7 more than a number3. The product of 5 and a number4. 125 decreased by a number5. 96 added to a number

Evaluate (solve) Tell which property you used

1. 27 x 0 x 3 = 2. 1 x 17 x 2 =3. (49 x 500) x 2 =4. 36 x 0 x 8 =5. 5 x 27 x 2 =