# 6.19 - Properties

6.19    The student will investigate and recognize

a)  the identity properties for addition and multiplication;

b)  the multiplicative property of zero; and

c)  the inverse property for multiplication.

Bloom's Level:  Analyze, Remember

### BIG IDEAS

• I can accurately solve problems by following the rules of number behaviors.
• I will be able to write symbolic representations of the way numbers behave.

### UNDERSTANDING THE STANDARD

• Identity elements are numbers that combine with other numbers without changing the other numbers. The additive identity is zero (0). The multiplicative identity is one (1). There are no identity elements for subtraction and division.
• The additive identity property states that the sum of any real number and zero is equal to the given real number (e.g., 5 + 0 = 5).
• The multiplicative identity property states that the product of any real number and one is equal to the given real number (e.g., 8 • 1 = 8).
• Inverses are numbers that combine with other numbers and result in identity elements.
• The multiplicative inverse property states that the product of a number and its multiplicative inverse (or reciprocal) always equals one (e.g., 4 • 1/4 = 1).
• Zero has no multiplicative inverse.
• The multiplicative property of zero states that the product of any real number and zero is zero.
• Division by zero is not a possible arithmetic operation. Division by zero is undefined.

### ESSENTIALS

• How are the identity properties for multiplication and addition the same? Different? For each operation the identity elements are numbers that combine with other numbers without changing the value of the other numbers. The additive identity is zero (0). The multiplicative identity is one (1).
• What is the result of multiplying any real number by zero?
The product is always zero.
• Do all real numbers have a multiplicative inverse?  No.  Zero has no multiplicative inverse because there is no real number that can be multiplied by zero resulting in a product of one.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

6.191  Identify a real number equation that represents each property of operations with real numbers, when given several real number equations.

6.192  Test the validity of properties by using examples of the properties of operations on real  numbers.

6.193  Identify the property of operations with real numbers that is illustrated by a real number equation.

NOTE: The commutative, associative and distributive properties are taught in previous grades.

### KEY VOCABULARY

identity property of addition, identity property of multiplication, multiplicative property of zero, inverse property for multiplication, multiplicative identity, additive identity, reciprocal, undefined, commutative property, associative property, distributive property, real numbers

Updated: Jun 06, 2017