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.

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 A/image131.jpg Google Image Result for A/image131.jpg

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

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 *

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

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.  operations/arithmetic_properties/v/identity-property-of-0 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!

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

Applying properties of operation to simplify expression.  /File/Middle%20School/Curriculum%20Document%202014%2015/Grade%20 7%20Curriculum%20Guide% pdf?sessionid=bb77cf26d854b5cbeef6ae555 a4ef87e /File/Middle%20School/Curriculum%20Document%202014%2015/Grade%20 7%20Curriculum%20Guide% pdf?sessionid=bb77cf26d854b5cbeef6ae555 a4ef87e

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