Properties of Operations Objective: Identify properties of numbers

The Commutative Property You can add and multiply real numbers in any order. Numerically: 2 + 7 = 7 + 2 3 ● 9 = 9 ● 3 Algebraically: a + b = b + a ab = ba

The Commutative Property Commute: to move to and from Think of commuting to and from school. Just like you are moving from one place to the other, numbers can too!

The Associative Property Parenthesis move, numbers do not move. Numerically: (6 + 8) + 2 = 6 + (8 + 2) (7 ● 4) ● 5 = 7 ● (4 ● 5) Algebraically: (a + b) + c = a + (b + c) (ab)c = a(bc)

The Associative Property Associate: to keep company, as a friend Think of associating with your friends: you hang out with them and stick together. Numbers in parentheses are grouped, or friends!

Commutative vs. Associative Identify each property shown below. 1) 7 + 4 = 4 + 7 Comm. Prop. Of Add. 2) Assoc. Prop. Of Mult. 3) Comm. Prop. Of Mult. 4) (4 + 2) + 3 = (2 + 4) + 3 Comm. Prop. Of Add.

Additive Identity Property Multiplicative Identity Property The sum of a number and 0 is equal to the same number. The number’s identity does not change. Numerically: Algebraically: - 5 + 0 = -5 0 + y = y Multiplicative Identity Property The product of a number and 1 is equal to the same number. The number’s identity does not change. Numerically: Algebraically: 8 x 1 = 8 (y)(1) = y

Zero Property Any number multiplied by zero equals zero. Be careful not to mistake this for Identity Property! 5 x 0 = 0 a x 0 = 0

2x ● 4y + 0 = 2x ● 4y - 9 + 0 = - 9 7 x 1 = 7 1(3x + 4) = 3x + 4 Additive Identity Multiplicative Identity

Identify the property being illustrated. 3 + 4 = 4 + 3 b. 5b ● 2c ● 0 = 0 c. -12 + 0 = -12 d. (x + 3) + 5 = x + (3 + 5) Commutative Prop. of Add Mult. Property of Zero. Additive Identity Associative Prop. of Add

Identify the property being illustrated. h. 3d ● 4● 1 = 3d● 4 Additive Identity Commutative Prop. of Mult. Associative Prop. of Mult. Multiplicative Identity Prop.

Identify the property being illustrated. 9b - 2c + 0 = 9b – 2c 2. 5 (-3b + 1) = -15b +5 3. -13 + (12 + 5) = (-13 + 12) + 5 4. 0 + 2pq = 2pq Additive Identity Distributive Prop. Associative Prop. of Mult.

Identify the property being illustrated. 5. 9(mn) = (mn)9 6. 2(4x + 3) = 8x + 6 7. 4(ab) = (4a)b 8. 7xy ● 1 = 7xy Commutative Prop. Of Mult. Distributive Property Associative Prop. of Mult. Multiplicative Identity