1. Virginia SOL 7.16 The student will apply the following properties of operation with real numbers: Commutative and associative properties of addition and multiplication, the distributive property, the additive identity and multiplicative identity property, The additive inverse property, and the multiplicative property of zero.

2. Real Numbers  Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers.  Google Image Result for http://scimathmn.org/stemtc/sites/default/files/images/frameworks/math/ 8.1.1A/image131.jpg Google Image Result for http://scimathmn.org/stemtc/sites/default/files/images/frameworks/math/ 8.1.1A/image131.jpg

3. The Commutative and Associative Properties of addition and multiplication  Commutative property of addition- states that changing the order of the addends does not change the sum. EX. (5+4=4+5) (2x3)+6= 6+(2x3)  Commutative property of multiplication-states that changing the order of the factor does not change the product. EX. (5X4=4X5) (2+3)6=6(2+3)  Learn commutative property for addition | Arithmetic properties | Khan Academy Learn commutative property for addition | Arithmetic properties | Khan Academy  Commutative law of multiplication | Arithmetic properties | Khan Academy Commutative law of multiplication | Arithmetic properties | Khan Academy

4. The Commutative and Associative Properties of addition and multiplication  Associative property of addition-states that regrouping the addends does not change the sum. EX. 5+(4+3)=(5+4)+3  Associative property of multiplication-states that regroup the factors does not change the product. EX. 5(4X3)=(5X4)3  Learn associative law of addition | Arithmetic properties | Khan Learn associative law of addition | Arithmetic properties | Khan  AcademyAssociative law of multiplication | Arithmetic properties | Khan Academy AcademyAssociative law of multiplication | Arithmetic properties | Khan Academy  ****Subtraction and Division are neither commutative nor associative *

5. The Distributive Property  Distributive Property- states that the product of a number and the sum (or difference) of two numbers equal the sum (or difference) of the number and each other number. 5(3+7)=(5x3)+(5X7), or 5(3-7)=(5X3)-(5X7)  Learn the distributive law of multiplication over addition | The distributive property | Khan Academy Learn the distributive law of multiplication over addition | The distributive property | Khan Academy

6. The Additive and Multiplicative Identity Property  Additive Identity-states that sum of any real number and zero is equal to the given real number. EX. ( 5+0=5) The Identity Element is Zero.  Multiplicative identity- states that the product of any real number and one is equal to the given real number. EX (8X1=8) The multiplicative identity is One.  https://www.khanacademy.org/math/pre-algebra/order-of- operations/arithmetic_properties/v/identity-property-of-0 https://www.khanacademy.org/math/pre-algebra/order-of- operations/arithmetic_properties/v/identity-property-of-0  Identity property of 1 | Arithmetic properties | Khan Academy Identity property of 1 | Arithmetic properties | Khan Academy  There are no Identity Elements for Subtraction and Division!

7. Additive Inverse and Multiplicative Inverse  Additive Inverse-states that the sum of a number and its additive inverse always equal zero. EX. (5+(-5) =0)  Multiplicative Inverse-states that the product of a number and its multiplicative inverse (reciprocal) always equals one. EX. 4 x 1/4 =1  Inverse property of addition | Arithmetic properties | Khan Academy Inverse property of addition | Arithmetic properties | Khan Academy  Learn inverse property of multiplication | Arithmetic properties | Khan Academy Learn inverse property of multiplication | Arithmetic properties | Khan Academy  Zero has no multiplicative Inverse

8. Applying properties of operation to simplify expression.  http://math.departments.pwcs.edu/modules/groups/homepagefiles/cms/98 0800/File/Middle%20School/Curriculum%20Document%202014%2015/Grade%20 7%20Curriculum%20Guide%202014.pdf?sessionid=bb77cf26d854b5cbeef6ae555 a4ef87e http://math.departments.pwcs.edu/modules/groups/homepagefiles/cms/98 0800/File/Middle%20School/Curriculum%20Document%202014%2015/Grade%20 7%20Curriculum%20Guide%202014.pdf?sessionid=bb77cf26d854b5cbeef6ae555 a4ef87e

9. The Multiplicative Property of Zero  Multiplicative property of zero-states that the product of any real number and zero is zero.