#### Math - 2017-18

# 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

*Adopted: 2009*

### 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**

6.19_{1} **Identify **a real number equation that
represents each property of operations with real numbers, when given several
real number equations.

6.19_{2} **Test **the validity of properties by using examples
of the properties of operations on real numbers.

6.19_{3} **Identify** the property of operations with real
numbers that is illustrated by a real number equation.

### 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*