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2e properties

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Properties of real numbers - 7th grade math

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2e properties

1. 1. 2e Identify the following properties using variables and apply them in solving problems. (DOK 1)<br />• Zero property of multiplication<br />• Inverse operations of addition/subtraction and multiplication/division<br />• Commutative and associative properties of addition and multiplication<br />• Identity properties of addition and multiplication<br />• Distributive properties of multiplication over addition and subtraction<br />By: Deia Sanders<br />
2. 2. Commutative Property<br />Change Order<br />Examples:<br />a + b = b + a<br />or<br /> a • b = b • a or ab = ba<br />
3. 3. Associative Property<br />Who you “associate “ with is <br />your GROUP of friends <br />Examples:<br />a + (b + c) = (a + b) + c<br /> or<br />a • (b • c) = (a • b) • c <br />or<br />a(bc) = (ab)c<br />
4. 4. Identity Property<br />The number keeps it’s identity<br />Examples: <br />a + 0 = a <br />or <br />a • 1 = a<br />
5. 5. Distributive Property<br />The number outside the parenthesis <br />gets distributed to everything inside <br />the parenthesis<br />Examples: <br />a(b + c) = ab + ac <br />or <br />ab+ ac = a(b + c)<br />Most important<br />Property!!!<br />
6. 6. Zero Property of Multiplication<br />Any number multiplied by <br />zero equals ZERO<br />Examples: <br />0(3x + 2y) = 0 <br />or<br />(3 • 0)(2 + 4) = 0 • 6 = 0<br />
7. 7. Inverse of Addition<br />Adding opposites equals zero<br />Examples: <br />2 – 2 = 0 <br />or<br />-3x + 3x = 0<br />
8. 8. Inverse of Multiplication<br />Multiplying by an inverse (reciprocal) equals 1<br />Examples: <br />or<br />
9. 9. Identify the Property<br />3x(y + 2) = 3xy + 6x<br />Distributive<br />3x – 3x + 2y = 0 + 2y<br />Inverse of Addition<br />0 + 2y = 2y<br />Identity of Addition<br />2(3 + y) + 8 = 6 + 2y + 8<br />Distributive<br />6 + 8 + 2y = 8 + 6 + 2y<br />This simplifies to 14 + 2y<br />Commutative<br />
10. 10. Identify the Property<br />1(2x + 3y) = 2x + 3y<br />Identity of Multiplication<br />(3x)(5x – 2z)(0) = 0<br />Zero Property of Multiplication<br />(2x – 4y) + 0 = 2x-4y<br />Identity Property of Addition<br />Inverse Property of Addition<br />3x – 2y + 2y = 3x<br />
11. 11. Complete Handout #1 page 73<br />