Real Numbers and their Properties

The Real Number System

100

Name all the sets to which the number belongs.

-6

R, Q, Z

200

Name all the sets to which the number belongs.

5/6

R, Q

300

Name all the sets to which the number belongs.

27

R, Q, Z, W, N

400

Name all the sets to which the number belongs.

square root of 27

R, I

500

Name all the sets to which the number belongs.

Negative square root of 81

R, Q, Z

Give an Example of that Number Type

100

Give an example of an Integer that is not a Natural Number

Any number 0 or smaller.

200

True or False

-9 is a Whole Number

False

300

Name 3 Rational numbers that are not integers

Any fraction, terminating or repeating decimal.

400

give an example of a whole number that is not an integer.

There is none

500

Name 3 Irrational Numbers

Pie and any non-perfect Squares

Identify that Property

100

Name the Property shown:

If y=-5, then -5=y

Symmetric Property

200

Name the Property shown:

7(2x-5)=14x-35

Distributive Property

300

Name the Property shown:

3x+(7y+8)=(3x+7y)+8

Associative Property

400

Name the Property shown:

-7=-7

Identity Property

500

Give 3 examples of the Distributive Property

Answers will Vary

Identify that Property 2

100

Name the Property shown:

8x+7=7+8x

Commutative Property

200

Name the Property shown:

(2y+7z)*0=0

Property of Zero

300

Name the Property shown:

If x=5 and 5=y, then x=y

Transitive Property

400

Name the Property shown:

y(1/y)=1

Inverse Property

500

Give 1 example of each:

Commutative Property

Associative Property

Symmetric Property

Answers will vary

Closure

100

Which set of numbers is NOT closed under addition? Give an Example.

Natural Numbers

Whole Numbers

Integers

Odd Numbers

Odd Numbers

200

Which of the following expressions proves that the set of whole numbers is NOT closed under the operation of subtraction?

• A) 8 - 5 = 3
• B) 4 - 4 = 0
• C) 3 - 10 = -7
• D) 0 - 0 = 0

C

300

Marcus claims that the subset of odd integers is closed under addition. Which statement correctly evaluates his claim?

• A) Marcus is correct because adding any two odd numbers always results in another odd number.
• B) Marcus is incorrect because adding two odd numbers (e.g., 3 + 5 = 8) results in an even number.
• C) Marcus is correct because integers are closed under addition.
• D) Marcus is incorrect because adding odd numbers results in fractions.

B

400

The set of integers is closed under three of the four basic arithmetic operations. Under which operation is the set of integers NOT closed?

Division

500

Which set(s) of numbers is closed under subtraction

Rational and Integers