Properties of real numbers - 7th grade math

1. 2e Identify the following properties using variables and apply them in solving problems. (DOK 1) • Zero property of multiplication • Inverse operations of addition/subtraction and multiplication/division • Commutative and associative properties of addition and multiplication • Identity properties of addition and multiplication • Distributive properties of multiplication over addition and subtraction By: Deia Sanders

2. Commutative Property Change Order Examples: a + b = b + a or a • b = b • a or ab = ba

3. Associative Property Who you “associate “ with is your GROUP of friends Examples: a + (b + c) = (a + b) + c or a • (b • c) = (a • b) • c or a(bc) = (ab)c

4. Identity Property The number keeps it’s identity Examples: a + 0 = a or a • 1 = a

5. Distributive Property The number outside the parenthesis gets distributed to everything inside the parenthesis Examples: a(b + c) = ab + ac or ab+ ac = a(b + c) Most important Property!!!

6. Zero Property of Multiplication Any number multiplied by zero equals ZERO Examples: 0(3x + 2y) = 0 or (3 • 0)(2 + 4) = 0 • 6 = 0

7. Inverse of Addition Adding opposites equals zero Examples: 2 – 2 = 0 or -3x + 3x = 0

8. Inverse of Multiplication Multiplying by an inverse (reciprocal) equals 1 Examples: or

9. Identify the Property 3x(y + 2) = 3xy + 6x Distributive 3x – 3x + 2y = 0 + 2y Inverse of Addition 0 + 2y = 2y Identity of Addition 2(3 + y) + 8 = 6 + 2y + 8 Distributive 6 + 8 + 2y = 8 + 6 + 2y This simplifies to 14 + 2y Commutative

10. Identify the Property 1(2x + 3y) = 2x + 3y Identity of Multiplication (3x)(5x – 2z)(0) = 0 Zero Property of Multiplication (2x – 4y) + 0 = 2x-4y Identity Property of Addition Inverse Property of Addition 3x – 2y + 2y = 3x

11. Complete Handout #1 page 73